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This book was published in 2015 by MET220 students at Purdue College of Technology in Columbus, Indiana.

It is a humorous simplification of the following title:

Cengel, Y. (2008). Introduction to Thermodynamics and Heat Transfer (2nd ed.). New York, NY: McGraw-Hill.

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About the Authors

Brent Byers is a junior at Purdue University majoring in Mechanical Engineering and

Technology. As soon as Brent graduates, he is moving far away from Columbus, IN.

Jacob A DeBusk is a senior student at the Purdue College of Technology. He is studying

Mechanical Engineering Technology while also working at Cummins Engine Company.

Casey Jones is a senior at Purdue University College of Technology in Columbus, IN as a

Mechanical Engineering Technology Major.

Kristina Linville is currently a student at Purdue College of Technology in Columbus,

IN. She is currently in her second year of schooling and is studying to get her BS degree in

Mechanical Engineering Technology. Before attending Purdue she graduated from Columbus

Signature Academy - New Tech in the year of 2013.

Jordan Ezell, was born on May 5, 1994 in Franklin, IN and grew up outside of Shelbyville,

IN where he graduated from high school at Southwestern Jr. / Sr. High School. In 2012 he stared

college at IUPUC, and is currently finishing up his BSMET degree at Purdue College of

Technology in Columbus, IN.

Riley Ellison is a sophomore at Purdue University studying for a Mechanical Engineering

Technology degree. Ellison is working toward a future goal of LEGO engineering.

Doug Weber is a senior studying for his Bachelor’s Degree in Mechanical Engineering

Technology. He is employed as a Quality Manager at a steel forging plant in Columbus, Indiana.

He enjoys playing and watching ice hockey in his spare time.

Eric Catlow studies at the Purdue College of Technology. He enjoys pumping NWA on the

stereo in his car whenever the Fuzz hang around.

Jalen Ulrey is currently a junior Mechanical Engineering Technology student at the Purdue

University College of Technology in Columbus, IN. He is currently employed at Faurecia

Emission Control Technologies and plans to continue with the company after graduation.

Dr. Tatiana Goris, Clinical Assistant Professor, School of Engineering Technology,

Purdue University

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Table of Contents

Chapter 1: Introduction and Overview………………………………………....5

Chapter 2: Introduction and Basic Concepts………………………………….11

Chapter 3: Energy, Energy Transfer, and General Energy Analysis………...20

Chapter 4: Properties of Pure Substances…………………………………….26

Chapter 5: Energy Analysis of Closed Systems…………………………….....32

Chapter 6: Mass and Energy Analysis of Control Volumes………………….37

Chapter 7: The Second Law of Thermodynamics……………………………46

Chapter 8: Mechanisms of Heat Transfer…………………………………….51

Chapter 9: External Forced Convection……………………………………....59

References ……………………………………………………………….……..64

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CHAPTER 1: INTRODUCTION AND OVERVIEW

Thermal Sciences

The first concept to understand is the world of thermal sciences. Thermal science is exactly what

it sounds like, the study of heat and how it acts in the world we live in. Heat is actually a form of

energy, and because energy can be converted from one form to another, thermal sciences must

consider the other forms of energy as well.

The world of thermal sciences is significant in the life of the average person. It is what allows for

blankets to keep you warm, occurs when a hair dryer is being used and is the reasoning for why

rubbing your hands together creates heat. Without it cars would not run, television would never

exist and humans would doubtfully have ever made it to the moon. Almost anywhere at any instant,

thermal sciences are taking place in our lives, and have been since the beginning of time.

Thermodynamics

Thermodynamics is the scientific study of energy, which in itself, has no official definition.

Thermal science is technically categorized underneath thermodynamics because of heat being a

form of energy, and that energy then is transferred to some sort of power through thermodynamics.

There are two laws that accompany this concept. The first law states that energy itself cannot be

created nor destroyed, which is the definition of something called the conservation of energy

principle. The second law says that the energy that is being transferred actually has a definable

amount, and a specific quality to it. This law also states that the body with more energy transfers

it to another body or area with less energy.

For example, if you make yourself a tub of ice cream and leave it on the kitchen table, overtime it

will either be eaten or the surrounding warm air will begin to transfer to the cold ice cream. This

will continue until the temperatures are the same in both mediums. In chemistry, it is known that

substances are made up of things called molecules. These molecules make up particles which are

observed in one type of thermodynamics called statistical thermodynamics. This type deals with

particles in groups and is concerned with the behavior of groups. Classical thermodynamics is the

second type and it only worries about what can be seen or studied without a microscope. Many of

the real world problems people deal with can be achieved using the classical method for analysis.

A major concept that is essential in solving thermodynamics problems is the Conservation of

energy principle. To understand this term, it is imperative to know that energy itself cannot be

produced from nothing. Energy also can never be destroyed, the principle states that it can only be

transferred through different forms. Although the forms of the energy may change, the quantitative

value will remain the same. Say you had a basket of 10 apples you just stole from your local

farmers market and want to place them in plastic bag. By using something like a machete, the form

of the apples can be changed and transferred to another medium (the plastic bag). Even though the

pieces are different and located somewhere else, the amount of apple is still the same as when the

experiment began.

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The Transfer of Heat

Heat transfer is something that is interested in the rate of which is heat being moved from one

medium to another in a process. Heat itself is considered to be a type of energy that can only be

transferred between two bodies, or areas, if their individual temperatures are different. It is

important to note that the principle of heat transfer falls within the laws of thermodynamics.

However, thermodynamics’ main focus is on something called equilibrium states and how they

change to another. This means the goal of thermodynamics is essentially to know the amount of

energy (or heat) transferred during a process.

To find the rate of heat transferred with respect to time, the principle of heat transfer is needed.

For heat transfer to take place, it may be obvious to state that a temperature difference between

two systems must exist. One body must be cooler or warmer than the other, or else they are

considered to be in thermal equilibrium and cannot be approached using heat transfer aspects.

Dimensions and Units

The terms associated with dimensions and units are heard in everyday life. When a weather man

reports the temperature, or when you see a speed limit sign, certain values, are attached to those

numbers to define what unit scale is being used. This means that normally in the science and

academic fields, any letters or words that follow a numeric value are considered to be units.

Dimensions are assumed to be anything that has some sort of physical quantity to it. So when you

hear the weather man say, “It’s going to be 125°F today,” the 125 is the dimension and the “°F,”

for Fahrenheit, is the unit. Other things like length, mass (the weight of something without gravity

acting upon it) and time are also dimensions and are considered to be called primary, basic, or

fundamental dimensions. Factors like volume, velocity and energy are called secondary

dimensions.

There are two unit systems that are accepted as the major systems to use in the world. However,

one is much simpler than the other. The first is known to most people as the metric system, but the

industry and academic fields recognize it as the SI. SI is an abbreviation for some fancy French

words meaning International System. This is what most of the world is using because of it is easy

conversions and obvious scale basses (0°C is when water freezes and 100°C is when water boils).

The other system, English, was created and solely used by the United States of America. The units

within the system are not scaled in a logical manner and there is no definite base. Many of the

conversions to transfer from one scale to another involve ambiguous calculations and conversion

factors. Even though the English system was created in America, many companies produce

products utilizing metric units. The SI is also mainly used by Americans in industrial fields for

ease of use and international consistency. Table 1 provides an example of the length scale for both

systems.

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Table 1: US Customary vs. SI

English

12in = 1ft

3ft = 1yd

1760yd = 1mi

SI

10mm = 1cm

100cm = 1m

1000m = 1km

SI and English Units

Each system has their own units for each dimension. In SI, length is measured in meters (m), mass

is a kilogram (kg) and time is in seconds (s). The mass in English is considered to be a pound-mass

(lbm), length is a foot (ft) and time is the same. There are other types of primary dimensions that

require calculations to be resolved. Force (F) is an example of one. As seen in the formula below,

both mass and acceleration values are required. Mass (m) is equal to a kilogram or pound-mass,

and acceleration is equal to meter per second per second or foot per second per second.

𝑭 = (𝒎)(𝒂) (1-1)

Force is also expressed differently for each system. In English, a force is considered to be a pound-

force (lbf). Force in SI is called a Newton (N). The 𝒂 in the equation represents the acceleration.

In many cases, acceleration is considered to be equal to gravity. Although gravity is essentially a

force, it can be observed as the rate at which the gravitational force of the Earth pulls objects close

to its surface. The individual accelerations for gravity are given in table 2.

Table 2: US customary and SI Units

System Force Mass Acceleration from

Gravity

English lbf lbm 32.174𝑓𝑡/𝑠2

SI N kg 9.81𝑚/𝑠2

Force is also many times used to express weight. Since weight is actually the mass of something

with gravity acting on it, the formula for force is applicable. However, it is normally good practice

to rewrite the force formula when solving for weight as follows:

𝑾 = 𝒎𝒈 (1-2)

Weight is considered to be either pounds or Newtons. From observing the formula, it is clear to

see that gravity has an obvious effect on the weight of an object. This is why astronauts are able

to bounce across the moon’s surface with ease. Mass, however, is something that will remain

constant regardless of its location. Sometimes it is necessary to know what is called the specific

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weight (γ) of a substance. This can be thought of as the weight per unit volume given in 𝑘𝑁

𝑚3 and

𝑙𝑏𝑓

𝑓𝑡3.

For this equation, density (𝒑) is needed along with gravity. Density is considered to be in 𝑘𝑔

𝑚3.

𝜸 = 𝒑𝒈 (1-3)

The term Work is often thought of as referring to an occupation held by an individual. It is also a

type of energy and is expressed in terms of something called joules (J). A joule is actually equal

to one Newton-meter (N·m). Expressing work in these units allows us to see that work is actually

a force, or energy, applied over some distance. A literal example would be to imagine yourself

carrying laundry from the dryer to the bedroom. The act of physically lifting a load and walking

to the dresser is expending energy during motion.

The British Thermal Unit and Calorie Counting

For some reason, people decided they wanted to know how much energy it would take to make

some water (1lbm) get a little warm (68°F-69°F). The unit was named the Btu (British thermal

unit) and is apparently used in the English system. The SI uses something called a calorie, different

from the kind people lie to you about. This calorie is scaled using similar methods, however it is

acquired using 1g of water heated from 14.5°C to 15.5°C. SI also insists on using the kilojoule

(kJ). They are almost interchangeable depending on the tolerance solution needed. This because

the Btu and kJ have similar values.

1𝐵𝑡𝑢 = 1.0551 𝑘𝐽

Similar Dimensions

There are many different unit scales in thermodynamics and science fields. For many of the

equations to work properly, all of the units associated with their numbers must match up somehow.

This means every number in the equation must ultimately have the same dimension. The term for

this requirement is called dimensionally homogeneous. If you try to solve an equation without it

being dimensionally sound, then the result will most likely be wrong. Changes to units or

dimensions means changes to the numeric value in most cases. Unity conversion ratios exist to

help in cases where the units themselves are equal to 1.

𝑁

𝑘𝑔 ∙𝑚

𝑠2

= 1 𝑙𝑏𝑓

32.174𝑙𝑏𝑚∙𝑓𝑡

𝑠2

= 1

These ratios have no actual units, but can be used in cases to replace values within equations.

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Thermodynamics Math Methods

Most of the math the average person is required to due on daily basis does not entail much more

than simple addition and subtraction. This is not the case for most critically based science

problems. Much of thermodynamics is consisted of tedious calculations and methods. These

procedures are meant to help determine the solution as accurately and quickly as possible.

Step 1: Problem Statement

It would be wise to insure you completely understand the question being asked to you before you

even look at a pencil. A recommendation is to read the problem several times out loud. Even during

a test, it is always good to just make sure everyone knows you’re three problems ahead of them.

Once you have a solid understanding, write down a summarized sentence of what is being asked.

Step 2: Doodle Time

Time to bust out that 64 pack of Crayolas and draw some systems. Everything that is moving, or

is some sort of fixed plane or has mass needs to be drawn and annotated. This means units and

arrows showing directions of action. Any calculations or other information should also be listed

somewhere in the vicinity. This is also a section to list any specific details as well (the type of steel

being used).

Step 3: Educated Guessing

Normally a problem will state if something about the environment is a little wacky. Factors such

as gravitational force or pressure in certain areas may vary and need to be considered when

approaching a problem analytically. Some values may be obviously assumed (the surface on which

the problem is taking place could be the zero point relating to heights). It is not very often that

there is a trick value not easily established. Information such as being on the moon is typically

given.

Step 4: Physics

Asses the entire situation and observe any physical principles that need to be applied. For instance,

if the problem includes a car on an inclined plane, it is obvious to think that gravity would cause

the car to roll down the hill. It is also good to keep in mind the medium in which the problem is

taking place. Look for any areas where significant friction may occur and analyze forces.

Step 5: Properties of Substances/Materials

All materials, gasses, fluids and vapors act differently in the world. Values like yield strength or

specific heat may be needed find solutions. Many material properties are listed in tables in

scholarly sources and other online references. Normally, information such as pressure and

temperature are required to find such property values.

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Step 6: Math

By this step, all other missing quantities should be fulfilled other than the final solutions. It is

good practice to write out equations using their alphabetic symbol, then substitute in the numeric

values. Always make sure the units for every value match up or will cancel out somehow.

Step 7: Talking Time

Do not assume the answer is correct. Perform a logic check to insure everything makes sense. If

you are working in group, discuss the results with your colleagues for a more accurate analysis. Is

the power output of the Honda really 500kW, or is your thumb too big for the division key? If

possible, try to utilize different equations known to achieve the same values. Use this time to insure

that everything pending grading is legible. This aids not only the instructor, but also yourself from

creating algebraic mistakes.

SigFigs

Significant digits are something that is usually taught in grade school. In the engineering fields,

normally three digits are used. The point of this method is to attempt to prevent false dimensions

from being calculated. In a situation where the final answer comes out to something like 7.47897

lbs, the final answer should be rounded to 7.48 lbs. This prevents any errors in calculations or

unwanted dimensions.

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CHAPTER 2: BASIC CONCEPTS

In this chapter we will introduce the following terminology as well as many more concepts.

Boundary- The real or imaginary surface that separates the system from its surroundings.

Closed system- Consists of a fixed amount of mass, and no mass can cross its boundary.

Continuum imaginary – disregard atomic nature of substance and view it as a homogenous

matter. Assume that properties of system vary with no jump discontinuities despite the large gaps

between molecules, a substance can be treated as continuum because of the very large number of

molecules even in an extremely small volume.

Density- Mass per unit volume ρ(density) = m(mass) / V(volume)

Equilibrium- State of a balance; there are no driving forces within the system, and no changes in

time. A system is not in thermodynamic equilibrium unless the conditions of all relevant types of

equilibrium are satisfied.

Extensive properties- Those that depend on the size of the system.

In general, density depends on temperature and pressure.

Intensive properties- Those that are independent of the mass.

Isolated system- Energy is not allowed to cross the boundary.

Open system- Properly selected region in space.

Property- Any characteristic of a system (volume, temperature, mass, etc.)

Property- characteristics of the system

Specific Gravity (relative density)- Is a ratio of a substance to the density of some standard

substance (usually water at 4 ◦C)

Specific volume- Volume per unit mass which is the reciprocal to density. v = V/m = 1/ρ

Specific weight = density*gravity

Surroundings- The mass or region outside the system.

System- A quantity of matter or a chosen region in space.

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In the current moment in the United States, we use four major temperature scales that can be

transferable from one to another using the following calculations:

Kelvin to the Celsius

T(K) = T (C) + 273.15

Rankine to Fahrenheit

T(R) = T (F) + 459.67

Rankine to Kelvin

T(R) = 1.8 T(K)

Fahrenheit to Celsius

T (F) = 1.8 T (C) + 32

Different types of pressures are used throughout thermodynamics. These will help you remember

which means what, and how it is calculated.

Absolute pressure- The actual pressure at a given position and measured relatively to absolute

vacuum.

Gage pressure- Is the difference between the absolute pressure and the local atmospheric pressure.

Pgage =Pabs – Patm

Vacuum Pressure- Is the difference between atmospheric pressure and the absolute pressure.

Pvac = Patm – Pabs

Pascal's law- Pressure exerted anywhere in a confined incompressible fluid is transmitted equally

in all directions throughout the fluid such that the pressure variations (initial differences) remain

the same.

Pressure (atm) = density*gravity*height

Closed system

Piston- Cylinder Device: What happens to the gas when it heated? The gas expands. Below is a

closed system which means no mass is crossing the boundary; only energy can cross the boundary.

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Figure 2.1

In a closed system, no mass may be transferred in or out of the system boundaries. Figure 2.1

shows the system always contains the same amount of matter, but heat and work can be exchanged

across the boundary of the system. Whether a system can exchange heat, work, or both is

dependent on the property of its boundary.

Adiabatic boundary – not allowing any heat exchange: A thermally isolated system

Rigid boundary – not allowing exchange of work: A mechanically isolated system

Open System (controlled volume)

This is a specifically selected space or region usually enclosed by a device that involves mass flow

(compressor or turbine) like in Figure 2.2.

In an open system, mass and energy can both cross the boundaries. In general, any random region

in space can be selected as a controlled volume open system.

Control surfaces have boundaries of control volume, which can be real or imaginary.

Most control volumes have fixed boundaries.

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Figure 2.2

In an open system, matter may flow in and out of some segments of the system boundaries. There

may be other segments of the system boundaries that pass heat or work but not matter. Respective

account is kept of the transfers of energy across those and any other several boundary segments.

A hot water heater is an example of an open system. Hot water leaves the tank and replaced by

cold water; while the interior surfaces of the tank make up the control surface.

Using Figure 2.3, you can get a better understanding of what the following terms are actually

expressing.

Thermal equilibrium- The temperature is the same through the entire system.

Mechanical equilibrium- There is no change in pressure at any point in system.

Phase equilibrium- The mass of each phase reaches equilibrium level.

Chemical Equilibrium- Chemical composition does not change in time.

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Figure 2.3

Equilibrium thermodynamics is the systematic study of transformations of matter and energy in

systems as they approach equilibrium. The word equilibrium implies a state of balance.

Equilibrium thermodynamics, in origins, derives from analysis of the Carnot cycle.

Simple Compressible System- In the absence of electrical, magnetic, and gravitational motion

there is a need in 2 independent properties to fix the state. Two properties are independent if one

property can be varied while the other one is held constant. Temperature and specific volume are

always independent properties; together they can fix the state of simple compressible system.

Figure 2.4 shows temperature and specific volume.

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Figure 2.4

Process- Any change that system undergoes from one equilibrium state to another.

Path- A series of states through which a system passes during a process.

Figure 2.5 represents a path between states 1 and 2 and the process pass.

Quasi-Equilibrium process- A sufficiently slow process that allows the system to adjust itself

internally, so that properties in one part of the system do not change faster than those at other parts.

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Piston moved slowly (Figure 2.6, A) The molecules have sufficient time to re-distribute. Pressure

inside of the cylinder will rise at the same rate in all locations.

Gas is compressed suddenly (Figure 2.6, B) Molecules near the piston do not have enough time to

escape; creating of a high pressure region there.

Figure 2.6

Figure 2.7

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Cycle- A system returns to its initial state at the end of the process. Figure 2.7 shows this using a

graph overhead a cylinder.

Isothermal Process: T –constant

Isobaric process: P-constant

Steady process- Means no change in time.

Steady-flow process – Fluid flows through

a control volume steadily. Figure 2.8

During a steady-flow process, fluid properties

within the control volume may change with

position but not with time. Figure 2.9

Under steady flow conditions, the mass and

energy contents of a control volume remain

constant. Figure 2.10

The zeroth law of thermodynamics- If two bodies are in thermal equilibrium with a third body

(often it is just a thermometer), they are also in thermal equilibrium with each other.

Figure 2.11 shows that when a body is brought into contact with another body that is at different

temperature, heat is transferred from the body at higher temperature to the one at lower temperature

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until both bodies attain the same temperature. The diagram below states that if you place a piece

of iron that is 150 degrees on top of a piece of copper that is 20 degrees; then the iron will transfer

heat until both are at equilibrium.

Figure 2.11

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CHAPTER 3: ENERGY,

ENERGY TRANSFER,

AND GENERAL ENERGY ANALYSIS

This Chapter will highlight the general importance of energy in life, some of the instances of

transfer as well as what “work” is.

Introduction

Energy is conserved, this is a phrase we heard as a child, it’s something that makes sense; that is

until you apply the real world. Energy conserved, is an expression of the 1st law of

Thermodynamics. This law stands true.

A great example of this is putting a refrigerator in a sealed, insulated room. The room has no other

energy entering in expect for the electrical energy. This is to say the electrical energy is transferred

to thermal energy. Since no energy can escape the room, the energy would be put into the air,

causing the temperature to rise.

(Just don’t let this hot air get to your head)

Forms of Energy

Energy can take many forms; many people think that when things are inefficient, the energy not

directly involved in the intended action (motion in the engine) just goes away. The energy simply

goes into other forms.

An example of this can be illustrated with a gasoline engine. Think, some of the energy is lost in

friction of the internal parts; Noise is a form of energy. Energy is also converted into motion, as

intended. If someone was able to capture all the energy released in every form, it would equal the

energy input, the gasoline.

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Macroscopic energy relates to the energy acting on an object, such as kinetic energy of a moving

ball or the potential energy of an object on top of a tall building. These along with internal energy

of an object, make up the system analyzed.

Nuclear reactions show internal energy released, instead of chemical reactions (most often

illustrated as combustion). Nuclear energy works by releasing the internal energy of a molecule.

This reaction is related to𝐸 = 𝑀𝑐2. This equation shows the relationship of energy to mass. “E”

is energy, measured in joules. “M” is mass measured in kilograms and “C” is the speed of light in

𝑀/𝑆 (8000000

The amount of energy released in nuclear reactions is massive. 1kg of uranium can release enough

energy as 3000 tons of burned coal.

This is fantastic for humanity and energy usage, however nuclear energy has its own set of

problems. The reaction also produces several other elements that are harmful.

Flow rates of energy are energies with one dimension of time. Flow rates, can show not only the

motion of energy, but how it moves.

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Energy Transfer by Heat

Heat is a form of energy that is transferred between two systems and its surroundings by virtue of

temperature difference.

This is to say that energy can be transferred through heat. Something we all know implicitly, but

have difficulty applying as a stated law. Heat flow is like energy flow, specifically associated with

the movement of energy through heat. A process where there is no heat transfer is an adiabatic

process.

Heat Transfer by Work

Work, like heat is and energy interaction between a system and its surroundings. It is the other

form energy can take when crossing a boundary, which is not heat. Work is force multiplied by a

distance. Power is a rate of work, meaning that it is work with a unit of time.

Mechanical Forms of Work

Work is the integration of a function of work with regard to distance from point start to finish.

The fact that work is utilizing an integration, means that it is a path function. This is to say that the

function of force can change at any point within the start and finish points and we’re looking for

the area underneath the curve.

Shaft work is energy transmission that is very common in engineering. Torque equals force

multiplied than radius of the rotating shaft. 𝑇 = 𝐹𝑟

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Spring Work utilizes

𝐹 = 𝑘𝑥

(k= spring constant) (x is the distance of extension)

𝑊 =𝑘𝑥2

2 (this looks familiar to the kinetic energy equation)

This is to say that the force of a spring increases linearly as the distance of the spring is increased

or it is stretched, but the work done to achieve the stretched distance increases exponentially and

is the integration of the force equation with respect to distance.

Work needed to raise or to accelerate a body.

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Work is needed to raise a body, because by raising an object you are increasing the total

macroscopic energy in the system, by giving the object a potential energy. Power just applies a

dimension of time which can show the movement of energy.

A great example is in the book, here

Example 1

Notes on the Example: As we see here, 𝑊 =𝑚𝑣2

2 (w is work in joules, m is mass in kilograms, v

is velocity in m/s) This gives us the amount of work done, in a certain amount of time. This allows

for us to solve for power.

3-6 First Law of Thermodynamics.

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This part of the chapter refers to the transfer of energy into different forms. A good example of

this is to imagine a rock on top of a cliff. As the rock sits on top it has 10 units of potential energy,

however when the rock starts to fall the energy transfers from potential to kinetic. The total energy

however is still equal at all points in time.

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CHAPTER 4: PROPERTIES OF PURE SUBSTANCES

Pure Substances: A pure substance is a substance that is made out of the same material throughout

and has the same properties throughout. A pure substance cannot be separated into other

substances. The reason that it cannot be separated is simply because it is only made out of one

material. All matter can be separated into two categories. These categories are pure substances and

mixtures. Some examples of pure substances are water and oil. If these two pure substances were

mixed together, they would no longer be pure substances. They would now be considered a

mixture. A few more examples of substances with a fixed chemical composition are salt, nitrogen,

helium, and carbon dioxide. Sometimes a mixture can be considered a pure substance, but only if

it is a homogeneous mixture. A homogeneous mixture is a mixture where the components of the

mixture are evenly distributed throughout the mixture. For example, the reason that water and oil

cannot be a pure substance when they are mixed together is because they want to separate from

each other. Oil goes to the top and water goes to the bottom and they are not evenly mixed.

Mixtures of two things that can be a pure substance are salt and sand. If they were mixed together

very well, they would be evenly distributed and would not separate like oil and water. Salt and

sand mixed together is an example of a homogeneous mixture. Matter has three phases, gas, liquid,

and solid. A mixture of two of more phases of a pure substance can still be a pure substance as

long as the substances still have the same composition throughout. A mixture of ice and water is a

great example of this. The ice will still float to the top, but the ice has the same chemical

composition as the water, so it is still a pure substance.

Phases of a Pure Substance: There are three main phases of a pure substance, liquid, solid, and

gas. To better understand these I will use water as an example. When water is frozen into ice, this

is its solid state. When water is at room temperature, and we are able to drink it, this is its liquid

state. When water is boiled, it evaporates. This vapor that it is transformed to is its gaseous state.

An intermolecular force is the force of attraction or repulsion that acts between neighboring

particles in a substance. This is simply the force that holds them all together. The intermolecular

bonds are the weakest when the substance is in its gaseous state and the strongest when a substance

is in its solid state. This explains why solids have molecules that are closely packed together and

gases have particles that are pretty far apart. The molecules in a solid substance are arranged in a

three-dimensional pattern that is evenly repeated throughout it (As shown in figure 2-1). Since the

particles are so closely packed together, they are almost in fixed positions. The intermolecular

forces that were explained earlier are attraction forces until the particles get too close to each other,

then the force turns to a repulsion force to make sure that the molecules stay where needed and

don’t pile up on each other.

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Figure 4-1

The little area that each particle is moving around in is its equilibrium position. The temperature

of these particles controls how fast they are moving around in their equilibrium positions. When

the temperature gets too high and they start moving too fast, they can overcome the intermolecular

force holding them together. This will allow the particles to start breaking away, which is also

called the melting process.

The difference between a solid state and a liquid state is that, in a liquid state the particles aren’t

in fixed positions relative to one another anymore. The intermolecular forces are weaker in liquids,

causing the molecules to group together in small groups and move freely about one another.

In a gaseous state, the intermolecular forces are even smaller than those in a liquid, causing the

particles to move around at random. The only time the particles come in contact with each other

is when they randomly collide. Particles in a gas phase have a decently higher amount of energy

that those in a solid or liquid state. Therefore, when a gas is going to be converted back to a solid

or liquid, it will need to release a decent amount of energy before it does so.

Section 3- Phase-Change Process of Pure Substances: The phase change processes of pure

substances are very important to understand in this chapter. We will go over a few terms to get

started. A compressed liquid, also called a subcooled liquid, is a liquid that is not about to vaporize.

The opposite of a compressed liquid is a saturated liquid. A saturated liquid is a liquid that is about

to vaporize. An example of this is water that is slowly being heated up. The temperature that it

starts out at is 20 degrees Celsius and 1 atm pressure. At this point, the water still fully exists in

the liquid phase and is not even trying to vaporize, so it is a compressed liquid. When the water is

heated up to 100 degrees Celsius, it is not yet vaporizing but is extremely close to vaporizing. In

this case the water is a saturated liquid. If we now pretend that this water that is about to vaporize

is in an expandable container, and is being heated up even more. When it is heated up and it

vaporizes, all the vapor will raise to the top and the water will stay at the bottom until it all

vaporizes too. Now, the heat will be taken away from the container and the vapor will start to cool.

As the temperature gets lower, the vapor will get closer to condensing. This means that it will be

changing from a vapor back to a liquid soon. Right before it does this, it is a saturated vapor. When

this water starts condensing, but not all of it is condensed, it is considered a saturated liquid-vapor

mixture. This means the water is part liquid and part vapor. If the heat were not taken off of this

water after it vaporized, and the vapor continued to heat up, it would be considered a superheated

vapor. A superheated vapor is a vapor that is not about to condense, meaning the temperature is

extremely high and would have to drop a decent amount for the vapor to get even close to

condensing.

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When the last example was completed, the pressure stayed at 1 atm the whole time. Conditions are

not always ideal and stay at a constant pressure. When the pressure raises and lowers, the

temperature at which a liquid will boil changes too. At a given pressure, the temperature at which

a pure substance changes phase is called the saturation temperature. The opposite of the saturation

temperature is the saturation pressure. Saturation pressure is defined as the pressure at which a

pure substance changes phase when at a given temperature. When you put both of these terms

together on a graph, you get a liquid-vapor saturation curve. The curve will change for every pure

substance because they are all different. The example below is a liquid-vapor saturation curve for

water.

Figure 4.2

It is easy to see, as the saturation pressure increases, so does the saturation temperature.

The amount of energy it takes to melt a solid or vaporize a liquid is decently high. For example, to

turn water into vapor, the water has to be 100 degrees Celsius. To get water up to 100 degrees

Celsius, it is going to take quite a bit of energy. The amount of energy that is absorbed or released

by this water as it changes from one phase to another is called latent heat. When water, or any

other pure substance, is being changed from one phase to another, the amount of energy needed to

change it and change it back is going to be the same. For example, the amount of energy it takes

for water to melt is equal to the amount of energy it takes for water to freeze. A few terms that are

related to this are latent heat of fusion and latent heat of vaporization. Latent heat of fusion is

simply the amount of energy absorbed when a substance melts, and latent heat of vaporization is

the amount of energy absorbed when a substance vaporizes.

Property Diagrams for Phase-Change Processes: In this section we will discuss three different

diagrams for pure substances. These include the T-v diagram, the P-v diagram and the P-T

diagram. The T-v diagram shown below is for the heating process of water at a constant

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temperature. This diagram only has one line so that it is easier to understand at first. When more

pressures are added to the graph, more lines are created. The saturated mixture line is the horizontal

line in the center. When the pressure gets higher, the saturated mixture line gets shorter and shorter.

When the pressure gets high enough, this line eventually disappears. When it disappears, it

becomes a point. This point is called the critical point, and is defined as the point at which the

saturated liquid and saturated vapor states are identical.

Figure 4-3

The next diagram is the P-v diagram. The P-v diagram is extremely similar to the T-v diagram,

except the superheated vapor region is going down instead of up. This is because the pressure

inside the container that we talked about earlier is being decreased slowly, causing the volume of

the water to slightly increase. When this volume increases, the vapor region line is slowly sifted

to the right as the temperature drops. The critical point that we talked about earlier is on the P-v

diagram too. Nothing has changed with this point. It still represents the same thing.

Figure 4-4

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The third diagram that needs to be discussed is the P-T diagram. The P-T diagram is also called a

phase diagram, because it displays all three phases of a pure substance on one diagram. The phase

diagram below is a phase diagram of water. It still has the critical point which still means the same

thing it has in the last two graphs. Something that the phase diagram has that the T-v diagram and

the P-v diagram doesn’t, is a triple point. The horizontal lines on the P-v and the T-v diagrams are

often called the triple line. On the P-T diagrams, this is a point instead of a line; therefore it is

called the triple point. All phases that are on the triple line have the same pressure and temperature

but have different specific volumes. This is the same concept for the triple points. All three phases

are separated by lines to let one know at what pressure and temperature they will be changing from

one phase to another.

Figure 4-5

Property Tables: Throughout all the examples that have been discussed this chapter, water has

been used for every one of them. It has been used, because it is one of the easiest to understand.

Many thermodynamic properties are too much of a hassle to be presented by equations, so tables

were made to make things a bit easier. There are many of these tables in the back of

thermodynamics texts books to help work through problems faster and with ease. An example of

a saturated ammonia table is shown below. Most tables include the temperature, pressure, specific

volume, internal energy and the enthalpy of different substances.

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Equations: There are tons of equations that relate to this topic to help find different numbers about

pure substances. Not all of the equations are listed, but the ones that are listed are very important.

The first equation (Equation 1) is Pv=RT . This equation is known as the equation of state and is

fairly simple. If one has three of the four variables, the fourth one can easily be solved with basic

algebra. In this equation, P is the absolute pressure, T is the absolute temperature, v is the specific

volume and R is the gas constant (8.31447 kJ/kmol*K).

The second equation (Equation 2) is Pv=ZRT. This equation is the compressibility factor equation.

Just like the previous formula, this one needs all but one value to be able to solve the unknown

variable. In this compressibility factor equation, Z is the compressibility value of a given

substance, P is the absolute pressure, T is the absolute temperature, v is the specific volume and R

is the gas constant (8.31447 kJ/kmol*K).

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CHAPTER 5: ENERGY ANALYSIS OF CLOSED SYSTEMS

Moving Boundary Work

One common form of mechanical work is associated with the expansion and compression of gas

in a piston-cylinder device. This expansion and compression work is often called moving boundary

work (Figure 5-1). Boundary work is the primary form of work involved in the car engine. During

the expansion or power cycle in an automobile engine, ignited combustion gases force the piston

to move, which forces the engines crankshaft to rotate. In reality, when a piston is moving at high

speed, it is hard for the gas to remain stable because the boundary is moving rapidly. When a

system remains stable nearly at all times is when the piston moves at a low speed. This process of

a system remaining stable at all times is called a quasi-equilibrium or quasi-static process.

A gas does a different amount of work as it forces a piston to move (Figure 5-2). The work can be

calculated by multiplying the absolute pressure and the change in volume.

Figure 5-1

The work associated with a moving boundary is

called boundary work.

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The quasi-equilibrium expansion process is shown on a P-V diagram in Figure 5-3. On the P-V

diagram shown, the area under the curve represents the boundary work done per unit mass.

Figure 5-3

The area under the curve on a P-V diagram

represents the boundary work. As the volume

increases, the pressure decreases, and as the

volume decreases, the pressure increases.

Figure 5-2

A gas does a differential amount of work as it

forces the piston to move a certain distance.

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Example 5-1 shows how to calculate the boundary work using a pressure and specific volume

graph.

Gas can follow several different paths as it expands from state 1 to state 2. The boundary work is

related to the path followed. The net work done during a cycle is the difference between the work

done by a system and the work done on the system (Figure 5-4).

Figure 5-4

The net work done during a cycle is the

difference between the work done by the

system and the work done on the system.

Example 5-1

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Energy Balance for Closed Systems

Energy balance for any system is a difference between energy in and energy out. For a closed

system undergoing a cycle, the initial and final states are identical. Therefore, the heat to be

transferred to the system is equal to the work to be done by the system (Figure 5-5).

Various forms of the first-law and energy balance relationship can be found in Figure 5-6. These

relationships furthermore validate the first law of thermodynamics.

Figure 5-5

For a cycle, the change in energy = 0,

therefore Q = W.

Figure 5-6

Various forms of the first-law relation for

closed systems.

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Specific Heats

As discussed in earlier chapters, it takes different amounts of energy to raise the temperature of

identical masses of different substances by one degree. Specific heat is a property that allows the

comparison of the energy storage capabilities of various substances. Specific heat is defined as the

energy required to raise the temperature of a unit mass of a substance by one degree. There are

two certain types of specific heats we will deal with; specific heat at constant volume Cv ad specific

heat at constant pressure Cp. Cv is a measure of the variation of internal energy of a substance. Cp

is a measure of the variation of enthalpy of a substance.

Internal Energy, Specific Heats of Ideal Gases, and Incompressible Substances

An ideal gas is defined as a gas whose temperature, pressure, and specific volume are related by

Equation 5-4.

A substance whose specific volume (or density) does not change is called an incompressible

substance. The specific volumes of solids and liquids remain constant during a process (Figure 5-

7). Math shows that the constant-volume and constant-pressure specific heats are identical for

incompressible liquids. Both specific heats for an incompressible substance can be represented by

the symbol c (Equation 5-5).

Equation 5-4

Ideal Gas Law

P is pressure, v is specific volume, R is

ideal gas constant, and T is temperature.

Vl = constant

Vs = constant

Equation 5-5

Specific Heat for Incompressible

Liquid

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CHAPTER 6: MASS AND ENERGY ANAYLSIS OF CONTROL VOLUMES

Understanding Mass and Energy of an Area (Control Volume) in Space

Conservation of Mass Principle (Keep the Mass Safe!)

Mass (m): not the same as weight! This is a measure of how much “stuff” is in something. Figure

2 defines mass and shows a fun way to understand it.

Weight (w): is a force and can be calculated by multiplying the mass by the acceleration of gravity

(at standard sea level of the earth this equals 9.81 meters per second squared.)

Mass and energy are conserved properties. Their systems do not interact with the environment

and certain mechanical properties of the system cannot

change.

An object would have the same mass on the Moon as it does

on Earth, however, the same object would weigh six-times as

much on Earth as it would on the Moon.

Mass cannot be created or destroyed!

If mass is not added or taken away, the amount of mass in a

closed area must stay the same over time.

Figure 2: Mass, defined

Energy (E): The strength needed to continue an activity and

the ability to do work. This can come in many forms such as

heat, light, and electrical to name a few. Mass is a form of

energy and mass and energy are related according to physicist

Albert Einstein’s (1879-1955.) mass-energy equivalence

formula shown in Figure 1. To understand this, the formula

he suggested was E = mc2 (Formula 1) where E is energy, m is mass, and c is the speed of light in

a vacuum (an empty place where air has been removed.) The value c is always the same, it is a

constant, and since light moves at 186,282 miles per second or 2.9979 x 108 meters per second,

this is used as c in the equation. The “2” means that this value is multiplied by itself. This equation

as a whole simply means that when mass changes, energy also changes.

Mass flow rate (ṁ): the amount of mass traveling through something in a certain amount of time.

The dot above the m just means that time is involved. You can think of a pipe with water going

through it to better understand this. Figure 3 describes mass flow rate with a picture and also

shows the equation of continuity and volume flow rate formula. The formula describing mass flow

rate looks like this:

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δṁ = ρVndAc (Formula 2)

δ is usually used for amounts of heat, work, and mass transfer

δṁ is mass flow rate of fluid traveling over a small area

ρ is density which is the amount of mass something has divided by its volume

Volume: the amount of space that something occupies

Vn is the velocity (speed) of the flow

perpendicular to dAc

dAc is the small area

Since water slows down near the pipe

walls or boundaries, the velocity is

never the same at every location inside

a pipe. Figure 3: Understanding mass flow rate

The average velocity (Vavg) is the

average speed of Vn over the entire cross-

section of a pipe. Figure 4 shows what a

cross-section is.

Velocity is never uniform over a cross section of a pipe

because of the fluid sticking to the surface and therefore

having zero velocity at the wall.

Vavg = ṁ/ρAc (Formula 3)

Figure 4: Cross-section example

Volume flow rate (ὐ): the volume of fluid that is going through a cross section per unit of time.

Mass flow rate and volume flow rate are related when the specific volume is included. Specific

volume (v) is the ratio of the substance's volume to its mass. It is the reciprocal of density (1/ρ)

and is a basic property of matter. It can be defined as the number of cubic meters occupied by one

kilogram of a particular substance. ṁ = ρὐ = ὐ/v (Formula 4)

As described before, the conservation of mass principle for closed systems requires that the mass

of the system remain constant during a process. For control volumes, however, mass can cross the

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boundaries, so we need to keep track of the amount of mass entering and leaving the control

volume.

Figure 5: Conservation of Mass Principle

This can be done with the following formula which basically states that the total mass entering

minus the total mass leaving equals the net change, or what is left over during a time change.

Figure 5 explains the definition and what is happening in words. Figure 6 is the same formula

except it is represented with symbols. Figure 7 shows a graphic representation of this principle.

Figure 6: Conservation of Mass

∑ means the sum of all, therefore, the sum of all the mass entering (in) minus the sum of all mass

exiting. ∆ means the change in, therefore, the change in mass in the control volume.

Figure 7: Graphic describing a control volume and conservation of mass

Mass Balance for Steady-Flow Process

The steady flow process occurs when the total amount of mass inside a control volume (mcv) does

not change with time. The total amount of mass entering a control volume must equal the total

amount of mass leaving it. For a steady flow process we are interested in the amount of mass that

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flows per unit of time (mass flow rate.) The picture below in Figure 8 shows the conservation of

mass principle for a two-inlet/one-outlet steady flow system.

ṁ1 = ṁ2 (Formula 5) ρ1V1A1 = ρ2V2A2 (Formula 6)

Where: m is mass, ρ is density, V is volume, and A is area

Special Case: Incompressible Flow

The conservation of mass relationship can be simplified even more

when the fluid is incompressible (the density of the fluid does not

change.) For a steady flow of liquids, the density cancels from both

sides of the equation showing that the sum of volume flow rates in

equals the sum of volume flow rates out. ∑ὐin = ∑ὐout

(Formula 7)

Figure 8: Steady flow system

Since there is no “conservation of volume principle,” the volume

flow rates going in and out of a steady-flow device may be different even though the mass flow

rates are the same. An air compressor is a good example of this case. The

volume flow rate at the outlet of a compressor is much less than that at the

inlet even though the mass flow rate of air through the compressor stays

constant.

Figure 9: Air compressor example

Flow Work and the Energy of a Flowing Fluid (Work is required!)

Control volumes involve mass flow across boundaries and work is required

to push the mass in or out of the control volume. This type of work is called

flow work, or flow energy. This work is necessary for keeping the flow continuous through a

control volume. To understand look at Figures 10 and 11 below, which show imaginary pistons.

The fluid element has a certain volume (V) and the fluid to the right forces the fluid in the element

to enter the control volume (CV.) If the fluid pressure (P) and the cross-sectional area of the fluid

element is (A), the force applied on the fluid element by the imaginary piston is: F = PA (Formula

8)

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To push the entire fluid element into the control volume, the force must act along a distance (L.)

Wflow = FL = PAL = PV (Formula 9)

The flow work per unit of mass is:

Wflow = PV (Formula 10)

If there is no acceleration then the force applied on a fluid

by the piston is equal to the force applied on the piston by

the fluid. Figure 10: Imaginary piston

Figure 11: Force

on piston

Total Energy of a Flowing Fluid

The total energy of a simple compressible system

consists of three parts: internal, kinetic, and potential

energies. Figure 11 helps explain different types of

energy.

Figure 11: Energy explanation

This energy (e) can be expressed by:

(Formula 11)

In this equation, u is internal energy, ke is kinetic energy, and pe is potential energy. Kinetic

energy is expressed by the velocity squared divided by two and potential energy is expressed by

gravitational acceleration multiplied by the elevation of the system as compared to an external

reference point. If the fluid is flowing, the fourth part, flow energy (Pv) is added to the formula. θ

is a total energy per unit mass. It is defined as the total energy of a flowing fluid. Figure 12 shows

examples of these formulas.

Figure 12: Energy equation for flowing vs. nonflowing fluid

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Energy Analysis of Steady-Flow Systems (No change with time!)

Many engineering devices such as turbines, compressors, and nozzles operate for long periods of

time under the same conditions once the start-up period is complete. These devices are called

steady-flow devices. The process that is involved in these devices is called the steady-flow

process. This is a process during which a fluid flows through a control volume steadily (it means

there is no change with time.) The fluid properties can change from point to point within the

control volume, but at any point, they remain constant during the entire process. The volume (V),

mass (m), and total energy content (E) of the control volume remain constant. Since these

properties remain constant, the boundary work is zero for steady-flow system.

Boundary work is a form of mechanical

work that is usually found when gas

expands or compresses in a piston-

cylinder device. During this process, part

of the boundary (the inner face of the

piston) moves back and forth leading to

expansion and compression work. The

fluid properties at an inlet or exit also

remain constant during a steady-flow

process. The properties may be different

at different inlets and exits and may vary

over the cross section of an inlet or exit but

the properties, including velocity and

elevation, must remain constant with time

at a fixed point at an inlet or exit.

Figure 13: Energy analysis of steady-flow system

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The heat and work interactions between a steady-flow system and the surroundings also do not

change with time meaning the power delivered by a system and the rate of heat transfer remain

constant as well. Figure 13 explains that power plants operate under steady systems and shows

what happens in these conditions. Noting that energy can be transferred by heat, work, and mass

only, the energy balance for a general steady-flow system can be written: Ėin = Ėout (or)

Qin + Win + ∑ṁθ = Qout + Wout + ∑ṁθ (Formula 12)

● Q is the rate of heat transfer between the control

volume and its surroundings (when the control

volume is losing heat Q is negative. If the control

volume is well insulated then Q is zero.

Figure 14: Hot-water tank control volume

● W is power. For steady-flow devices, the control

volume is constant so there is no boundary work

involved. Since many steady-flow devices such as turbines, compressors, and pumps move power

through a shaft, W is the shaft power for the devices. W can also represent electrical work done

per unit of time. If neither are present then W is zero. Figure 14 shows a hot-water tank control

volume with cold water in and hot water out.

Some Steady-Flow Engineering Devices

Nozzle: a device that increases the velocity of a fluid at the expense of pressure

Diffuser: a device that increases the pressure of a fluid by slowing it down

Nozzles and diffusers are commonly used in jet engines, rockets, spacecraft, and garden hoses.

Nozzles and diffusers perform opposite tasks. The rate of heat transfer between the fluid flowing

through a nozzle or a diffuser and the surroundings is very small (Q = 0) since the fluid has such

high velocities and therefore does not spend enough time in the device for any significant heat

transfer to take place. Nozzles and diffusers usually do not involve work (W = 0) but do involve

very high velocities.

Turbine: in steam, gas, or hydroelectric power plants, this device drives the electric generator

The turbine produces work when fluid passes through it and the shaft rotates. Blades are attached

to the shaft and the work is done against the blades.

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Compressors: along with pumps and fans, these devices are used to increase the pressure of a

fluid

Work is supplied to these devices from an external source through a rotating shaft. These devices

function similarly but do different tasks. A fan increases the pressure of a gas slightly and is

mainly used to move a gas. A compressor is capable of compressing the gas to very high pressures.

Pumps work very much like compressors except that they handle liquids instead of gases.

Figure 15: Engineering Devices

Mixing chambers: the section where the mixing process of two streams of fluids takes place

These are usually well insulated and do not involve any kind of work.

Heat exchangers: devices where two moving fluid streams exchange heat without mixing

These are widely used in various industries and come in many designs. Heat exchangers also

involve no work interactions most of the time.

Let’s Review!

The conservation of mass principle states that the net mass transfer to or from a system during a

process is equal to the net change (increase or decrease) in the total mass of the system during that

process.

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The amount of mass flowing through a cross section per unit time is called the mass flow rate.

The volume of the fluid flowing through a cross section per unit time is called the volume flow

rate.

The work required to push a unit mass of fluid into or out of a control volume is called flow work

or flow energy.

Thermodynamic processes involving control volumes can be considered in two groups: steady-

flow processes and unsteady-flow processes. During a steady-flow process, the fluid flows

through the control volume steadily, experiencing no change with time at a fixed position. The

mass and energy remain constant also.

There are several types of steady-flow engineering devices.

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CHAPTER 7: THE SECOND LAW OF THERMODYNAMICS

In order for any process to occur, both the first and second laws of thermodynamics must be

satisfied. The first law tells us that energy cannot be created nor destroyed. Energy can, however,

change forms and can flow from one place to another. The first law does not control the order in

which a process takes place. Any naturally occurring process occurs in only one direction. Think

of an ice cube in a glass of water. The ice cube melts over time as the warmer water transfers its

heat to the ice cube. This causes the water to become colder until the liquid and the ice are the

same temperature. The ice cube does not transfer its cold to the rest of the liquid, instead it absorbs

the warmth in the liquid and melts. This process will continue until the liquid and ice are the same

temperature. This is where the second law comes into play. The second law of thermodynamics

tells us that processes occur in a specific direction. Processes always occur in the direction from

a higher temperature to a lower temperature. The second law also states that energy has quality

connected to it, not just quantity. The quality of energy is a big concern of engineers and the

second law gives the tools necessary to measure the quality and how much it drops during a

process.

Thermal energy reservoirs are used in helping to understand the second law. These reservoirs are

bodies with a large size to take in or provide a certain amount of heat with no change in its own

temperature. Many different bodies can be considered reservoirs, such as rivers, lakes, oceans, or

the air in the atmosphere. There are two kinds of thermal energy reservoirs and they both deal

with energy in the form of heat. A reservoir is a source if it provides energy in the form of heat.

On the other hand, a reservoir that absorbs energy is called a sink. It is easiest to remember which

type of reservoir does what by thinking about a kitchen faucet and sink. Think of the water the

flows from the faucet as heat. The faucet, in this case, can be thought of as the source. The sink

takes the rejected water and disposes of it. An important part of thermal energy reservoirs to

understand is that size does not necessarily mean something is a reservoir. The size relative to the

heat being supplied or absorbed is the key. Let us use the ice cube as an example again. While a

river or lake would be considered a thermal energy reservoir if an ice cube were added to it, a five

gallon bucket of water would be one as well. As the ice melts, it would not change the temperature

of the water in the bucket. The temperature of a glass of water, on the other hand, would change

from the same ice cube. When thermal energy reservoirs are used in industrial applications, heat

transfer is something to be concerned about. When these parts of the environment are used as

sinks, the heat being transferred must not be so great that it changes the temperature of the

reservoir. A rise in this temperature could result in marine life being disrupted. This is what is

known as thermal pollution and must be carefully considered.

Work can be changed to heat directly and completely, however changing heat to work requires

something called a heat engine. All heat engines operate in the same way and this process is a

relatively simple one. Work is pulled out of heat that flows from a hot object to a cooler object.

The components of heat engines are a pump, a condenser, a boiler and a turbine which produces

work. There are many different heat engines today, but they all have four basic characteristics:

1) A high temperature source provides them with heat.

2) Part of this heat is converted to work.

3) Remaining waste heat is sent to a low-temperature sink.

4) Operation occurs on a cycle.

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Two methods can be used to determine the amount of work output from a heat engine. Let’s start

by defining a few variables for these equations:

Qin = amount of heat supplied from a high-temperature source.

Qout = amount of heat rejected to a low-temperature sink.

Wout = amount of work delivered that operates the turbine.

Win = amount of work needed to compress water to boiler pressure.

Heat engines are open systems that can be studied as closed systems which means the amount of

useful work, or net work, they provide can be determined by looking at the work in and work out,

or by the amount of heat supplied and the amount of heat rejected.

𝑊𝑛𝑒𝑡,𝑜𝑢𝑡 = 𝑊𝑜𝑢𝑡 − 𝑊𝑖𝑛 Equation 1

𝑊𝑛𝑒𝑡,𝑜𝑢𝑡 = 𝑄𝑖𝑛 − 𝑄𝑜𝑢𝑡 Equation 2

The thermal efficiency of heat engines is something that is a concern of engineers. The Kelvin-

Planck Statement of the second law tells us that it is impossible for any device that operates on a

cycle to receive heat from a single reservoir and produce an amount of work. This statement can

be further understood to mean that no heat engine can turn all of the energy it gets into work. Some

of this energy is rejected. A heat engine must exchange heat with a low-temperature reservoir as

well as a high-temperature source in order for it to operate. There are many different ways energy

will be lost while a heat engine is running. Heat could leak into the surrounding area from the heat

source, or from the piping used to transfer heat not being properly protected. There will also be

some loss of energy through friction in the bearings that are in the turbine. Lastly, some of the

energy will be passed on to the cooling water, or low-temperature sink. With heat engines, only a

small amount of the heat they get is used as work. This is called their thermal efficiency. Thermal

efficiency is determined by the net work output divided by the total heat input, that is:

𝑇ℎ𝑒𝑟𝑚𝑎𝑙 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦, 𝜂𝑡ℎ =𝑁𝑒𝑡 𝑤𝑜𝑟𝑘 𝑜𝑢𝑡𝑝𝑢𝑡

𝑇𝑜𝑡𝑎𝑙 ℎ𝑒𝑎𝑡 𝑖𝑛𝑝𝑢𝑡=

𝑊𝑛𝑒𝑡,𝑜𝑢𝑡

𝑄𝑖𝑛 Equation 3

Another equation for thermal efficiency is:

𝜂𝑡ℎ = 1 −𝑄𝐿

𝑄𝐻 Equation 4

Where QL is the amount of heat transfer between the device and the low-temperature sink. On the

other hand, QH is the amount of heat transfer between the device and the high-temperature source.

The automobile gasoline engine is an example of a heat engine. The high-temperature source is

the burning fuel while the exhaust into the environment is the low-temperature sink. (Heat Engine

Cycle) The automobile gasoline engine, only operates at about 25 percent efficiency. That is, 25

percent of the burning fuel provided to it is converted to work that can be used to make the vehicle

move. One of the most efficient heat engines used today is the combined gas-steam power plant

which operates at an efficiency of about 60 percent. Therefore, about half of the energy received

is sent out into the environment with no work resulting from this lost energy. The efficiency of

heat engines is directly related to the temperature drop across them. The larger the temperature

difference between the heat coming in and the heat exiting, the more efficient the heat engine is.

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Since heat engines reject heat, the question then becomes, can the rejected heat be recycled and

used again in the same engine? Unfortunately, the answer to this question is no. Heat engines run

on cycles and have to complete one cycle before the next one can start. Without some kind of heat

exiting the engine, a cycle cannot be completed. This rejected heat will be at a lower temperature

than the reservoir. We know that heat is always transferred from the higher temperature to the

lower, so no energy will be gained by feeding rejected, lower temperature, heat back into the

engine. This waste heat can be used for other applications. Thomas Edison was one of the first to

use energy recycling. The world’s first commercial power plant, Pearl Street Station built in 1882,

was a combined heat and power plant. It produced both electricity and thermal energy and used

the waste heat from its process to warm neighboring buildings. Recycling of waste allowed this

plant to achieve approximately 50 percent efficiency. (Cogeneration)

Heat transfer occurs naturally from higher temperatures to lower temperatures and no device is

required to enable this process. For the opposite process to occur, a common household appliance

is required. Refrigerators transfer heat from a lower temperature to a higher one. There are five

basic items involved in a refrigeration cycle; refrigerant, a compressor, a condenser, an expansion

valve, and an evaporator. The compressor does just that, it compresses the gas refrigerant which

raises its temperature. As this occurs, the refrigerant is pushed into the condenser coils where the

hot gas transfers its heat to the cooler air temperature and becomes liquid. Now in liquid form, at

high pressure, the refrigerant cools down as it flows through the coils inside the refrigerator. At

this point, the refrigerant absorbs the heat inside the refrigerator which cools the air inside. Finally,

the refrigerant evaporates into gas in the evaporator and flows back into the compressor, where the

cycle starts again. (Sforza, n.d.) When a refrigerator is running, warm air can be felt behind it.

This is from energy in the form of heat being pulled from the refrigerated space, then exhausted

into the room. The energy source, in this case, is the refrigerated space and the sink is the room,

or kitchen where the refrigerator is located. If a refrigerator were to be left open for a long period

of time, it would begin to get very warm due to the refrigerator constantly operating and trying to

cool down the open refrigerated space.

Heat Pumps are another device that works opposite of the normal direction of heat flow. Heat

pumps absorb heat from a cold space and release it to a warmer one. These are commonly used in

heating homes during the cold winter months. There are two types of heat pumps, air-source and

ground-source (geothermal). Air-source heat pumps get heat from cold air outside. These kind of

heat pumps do not work well in colder climates. Their efficiency drops significantly when

temperatures are below freezing. For colder climates, ground-source pumps are used. This kind

of pump costs more to install because they require underground piping. They are about 45 percent

more efficient because they get their heat from the ground. The ground is warmer than the air,

therefore geothermal pumps get their heat from a warmer source.

The efficiency of both refrigerators and heat pumps can be found by the coefficient of performance

(COPR and COPHP). Both of these coefficients use the same calculation, but they use slightly

different variables. All of these variables have been presented previously.

𝐶𝑂𝑃𝑅 =𝐷𝑒𝑠𝑖𝑟𝑒𝑑 𝑜𝑢𝑡𝑝𝑢𝑡

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝐼𝑛𝑝𝑢𝑡=

𝑄𝐿

𝑄𝑛𝑒𝑡,𝑖𝑛 Equation 5

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𝐶𝑂𝑃𝐻𝑃 =𝐷𝑒𝑠𝑖𝑟𝑒𝑑 𝑜𝑢𝑡𝑝𝑢𝑡

𝑅𝑒𝑞𝑢𝑖𝑟𝑒𝑑 𝐼𝑛𝑝𝑢𝑡=

𝑄𝐻

𝑄𝑛𝑒𝑡,𝑖𝑛 Equation 6

An air conditioner works a lot like a refrigerator. It takes heat from a room and discharges it to

the outside. If this same air conditioner were turned around in cold weather, it would work like a

heat pump. It would pull the heat from the outside cold air and discharge it into the room as warm

air. From this comparison, it is easy to see that there is not much difference between refrigerators

and heat pumps. They basically function in opposite ways to one another. The Clausius Statement

says that it is impossible to build a device that operates in a cycle that produces no effect other

than to transfer heat from a low-temperature body to a higher-temperature body. What this

suggests is that a refrigerator can be built and work as it is intended, but only if it operates with

some help. We use electricity as the help to make it operate.

In thermodynamics, processes can be completed either reversibly or irreversibly. The goal of

reversible processes is to get most of their work from energy rather than from heat. Since heat

cannot be fully converted to work, it is lost, usually to the surroundings where the process is taking

place. (Reversible process (thermodynamics)) Reversible processes do not leave any trace on

their surroundings. For this to occur, the net heat and network between the system and its

surroundings must be zero. These types of processes do not occur naturally. They may be models

of actual devices, however a truly reversible process cannot exist. Reversible processes are used

to find the theoretical limits of irreversible processes.

Irreversible processes occur naturally. The system and its surroundings cannot be brought back to

their original states prior to the process occurring. Although the system itself might be able to be

brought back to its original state, the environment will have had some kind of effect from the

process that will not allow it return to its original state. There are many things which cause a

process to be irreversible. These things are called irreversibilities. A few examples are friction,

mixing of two fluids, and heat transfer across a certain temperature difference, and solids that are

deformed such that they will not return to their original state. (Cengel, 2008) Consider a car

stopped on a street. There are four tires all in a certain position to start. The car then begins to

move down the street. The car could very easily return to the original position, however some

changes will have occurred to both the tires and the environment due to friction. Depending on

how far and fast the vehicle travelled, the tires will have lost some amount of their tread. As well,

both the tires and the environment will have gained some heat. This would be considered an

irreversible process since neither the tires nor the environment will return to their original state.

Another example of an irreversible process could be a tube of toothpaste. When the tube is

squeezed, toothpaste comes out and the tube is deformed. The tube will not go back to how it was

before it was squeezed, nor will the toothpaste be replaced unless some amount of work is done to

add more toothpaste to the tube.

The quality of energy is very important due to the fact that higher quality energy results in more

work that can be made from it. As can be seen in efficiency equations which were shown earlier,

this results in a more efficient device. When considering the quality of energy, the higher its

temperature, the greater its quality. Whenever energy is used, the quality of it is reduced. Low

quality energy is expensive, difficult, and sometimes cannot be used. It cannot be used in nature.

Consider the sun constantly shining its light and providing its heat to Earth. Without this heat

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being provided, no plants would be able to survive and neither could humans or animals. Thinking

about the universe as a whole, energy is constantly being used. Stars are constantly using energy

in the form of hydrogen. As more and more time passes, the quality of energy in the universe

worsens. As we know from the first law of thermodynamics, energy cannot be created. Therefore,

the universe is always working towards a balance of energy. When this point is reached,

everything will be the same temperature. Atoms and molecules will still be moving and colliding,

but they will all have the same average level of energy. Heat transfer will no longer occur because

there will no longer be any difference in the concentrations of energy from one body to another.

(Watson, n.d.) This will take a very long time and will not occur in our lifetimes. However, based

on our understanding of thermodynamics and physics, this is the direction the universe is going.

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CHAPTER 8: MECHANISMS OF HEAT TRANSFER

Introduction

We will talk about the different types heat can be transferred to; conduction, convection, and

radiation. As seen in Figure 1 below, a pot of boiling water produces three types of heat transfer.

The heat from the fire produces radiation which is what heats up the bottom of the pot. When cold

water is added to the pot, the cold water “sinks” down and as the cold water is warmed up, the

warmer water rises to the surface and pushes more cold water down to the bottom. This process of

warm water rises and cold water sinking is called convection. Finally, the heat from the surface of

the water is transferred to the handle of the pot. This is known as conduction.

If you can recall, heat is the thermal energy transported from one system to another due to a

temperature difference. For example, say you have two identical systems with equal temperatures,

energy will not flow. On the flip side, if you have two systems with different temperatures, the

energy will start to flow. Heat can do anything: move from one area to another, get atoms excited,

and even increase energy. You might ask where energy comes into play,

well really heat is energy. So when you increase the heat in a system,

you’re really increasing the amount of energy in the system. Energy is

transferred on an atomic level, which is just fancy term for saying a really

small scale. The unit of measure for heat is typically given in a calorie.

You might be thinking, “Calories, like the calories that are in food?”

Yeah just about, except these calories are measured as the amount of

energy needed to raise the temperature of one gram of water by one

degree Celsius. This knowledge becomes handy when measuring the

specific heat capacity. The specific heat capacity is also the amount of

energy required to raise the temperature of one gram of a substance by

one degree Celsius. Because it is energy, scientists use the units of Joules

to measure it. Get this; one calorie equals 4.186 Joules which also equals

4.186 Watt-seconds (Ws). So wait a minute, does that mean you can measure the amount of energy

you make in your body in one second and express that in terms of an electric value? Yes! The rate

Figure 1: Three Mechanisms of Heat Transfer

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at which energy is created and used in your body can actually be expressed as electrical power.

Talk about mind boggling!

Conduction

Conduction is the transfer of heat within a system or between two systems that are touching. Say

you put a perfectly good Popsicle on the table to sit and you

came back to what’s seen in Figure 2. Well according to

conduction, your Popsicle started melting due to the change

of temperatures. If you were to put your finger into the liquid

of your melted Popsicle, you’ll feel the liquid at the same

temperature that is in the room. Conduction takes place in

solids, liquids, or gases. When trying to solve problems with

conduction, you are typically trying to calculate the rate of

heat conduction. The rate of heat conduction depends on the

geometry of what you’re looking at. In order to solve for

heat conduction, you will need the thermal conductivity which is either a given variable or can be

found online or in a thermodynamic textbook. Thermal conductivity is basically a materials ability

to conduct heat. You will also need to know the thickness of the material, the area, and the

temperature difference. When solving problems, the variable �̇�𝑐𝑜𝑛𝑑 stands for the rate of heat

conduction. As mentioned earlier, the variable k stands for thermal conductivity and the variable

A is used for area. The formula will look something like this: �̇�𝑐𝑜𝑛𝑑 =

𝑘𝐴∆𝑇 (𝐶ℎ𝑎𝑛𝑔𝑒 𝑖𝑛 𝑇𝑒𝑚𝑝𝑒𝑟𝑎𝑡𝑢𝑟𝑒)

𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠.

Thermal Conductivity

Thermal conductivity is the ability of materials to conduct heat. Specific heat capacity is

represented by the symbol 𝐶𝑝, which is a measure of material to store thermal energy. Again,

thermal conductivity is denoted by k. It is also the rate of heat transfer through a unit of thickness

of the material per unit area per unit temperature difference (See formula). 𝑘 = 𝐿 (𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠)

𝐴𝑟𝑒𝑎(𝑇1− 𝑇2)∗ �̇�.

Where k is the thermal conductivity of a material, L is the thickness of the material, A is the area

of the material, �̇� is the rate of heat, and T is the temperature of the material. In the case of thermal

Figure 2: Melting Popsicle Example

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conductivity, you will have two temperatures per geometry you are looking at. If you get a value

of k that is high, it indicates that the material is a good heat conductor and if the value is low, the

material is an insulator. The range of thermal conductivity varies based of the materials at room

temperature. The heat capacity of the material can also be given as 𝜌𝐶𝑝. This is useful when solving

for thermal diffusivity. Where α represents the thermal diffusivity, k is the heat that is conducted

in a material, and 𝜌𝐶𝑝 is the heat stored. α = 𝐻𝑒𝑎𝑡 𝐶𝑜𝑛𝑑𝑢𝑐𝑡𝑒𝑑

𝐻𝑒𝑎𝑡 𝑆𝑡𝑜𝑟𝑒𝑑=

𝑘

𝜌𝐶𝑝.

Convection

Convection is the way heat is transferred from one area to another when there is a “bulk movement

of matter.” It is the movement of huge amounts of material, taking the heat from one area and

placing it in another. An example of this is when warm air rises and cold air replaces it. The heat

has moved, this is known as the transfer of heat by motion of objects. The faster the fluid motion,

the greater the convection heat transfer. In the absence of any bulk fluid motion, heat transfer

between a solid surface and the adjacent fluid is by pure conduction. The presence of bulk motion

of the fluid enhances the heat transfer between solid surface and the fluid, but it also complicates

the determination of heat transfer rates. The rate of convection heat transfer is observed to be

proportional to the temperature difference, and is conveniently expressed by Newton’s law of

cooling. Newton's law of cooling is expressed as �̇�𝑐𝑜𝑛𝑣 = ℎ𝐴𝑠(𝑇𝑠 − 𝑇∞) where h is the convection

heat transfer coefficient, As is the surface area through which convection heat transfer takes place,

Ts is the surface temperature and T is the temperature of the fluid sufficiently far from the surface.

Convection can be split up into two types of convection, forced convection and natural (or free)

convection.

Forced Convection

Forced convection is when the fluid is forced to flow over the surface by external means such as

a fan, pump, or the wind. Forced convection should be considered one of the main methods of

useful heat transfer as significant amounts of heat energy can be transported very efficiently.

Figure 3 below shows a pan that is being heated up and the fan is blowing over the pan. This is an

example of forced convection, because the fan is forcing the fluid to flow over the pan.

Figure 3: Forced Convection Example

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Natural Convection

Natural convection is when the fluid motion is not generated by an external source and only by

density differences in the fluid occurring due to temperature rises. An example of this is in the

absence of a fan, heat transfer from the surface of the hot block is by natural convection since any

motion in the air in this case is due to the rise of the warmer air near the surface and the fall of the

cooler air to fill its place. Figure 4 shows that heat transfer happens without any external forces,

such as a fan, to force the fluid over unlike forced convection.

Radiation

Radiation is when the transfer of energy

happens when there is no conductive medium

such as space. That lack of medium means

there is no matter there for heat to pass

through. Radiation is the energy carried by

electromagnetic waves (light). Those waves

could be radio waves, infrared, visible light,

UV or Gamma rays. Heat radiation is usually found in the infrared sections of the electromagnetic

spectrum. Figure 5 shows how the radiation is going from the fire to the person’s hands. This

merely means that the heat from the fire is being transferred to the hands, so that the hands start to

warm up. Scientists have discovered that objects that are good at giving off thermal radiation are

also good at absorbing the same energy. Usually the amount of radiation given off by an object

depends on the energy of the objects and molecules surrounding you. Thermal radiation is

interesting in the studies of heat transfer, because the form of radiation is emitted by bodies because

of their temperature. It differs from other forms of electromagnetic radiation such as x-rays, gamma

Figure 5: Radiation Example

Figure 4: Natural Convection Example

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rays, microwaves, radio eaves, and television waves that are not related to temperature. Radiation

is expressed by Stefan-Boltzman law as:

�̇�𝑟𝑎𝑑 = 𝜀𝜎𝐴𝑠(𝑇𝑠4 − 𝑇𝑠𝑢𝑟𝑟

4 ) where 𝜀 is the emissivity of surface, As is the surface area, Ts is the

surface temperature, Tsurr is the average surrounding surface temperature and 𝜎 =5.67𝑥10−8𝑊

𝑚2∗°𝐾4 is

the Stefan-Boltzman constant.

Simultaneous Heat Transfer Mechanisms

As mentioned earlier in the chapter, there are three mechanisms of

heat transfer, but not all three can exist at the same time in a medium.

For example, heat transfer is only by conduction in opaque solids, but

by conduction and radiation in semitransparent solids. Thus, a solid

may involve conduction and radiation but not convection. However,

a solid may involve heat transfer by convection and/or radiation on

its surfaces that are exposed to a fluid or other surfaces. For example,

the outer surfaces of a cold piece of rock will warm up in a warmer

environment as a result of heat gained by convection from the air and

the radiation from the sun or the warmer surrounding surfaces, but the

inner parts of the rock will warm up as the heat is transferred to the

inner region of the rock by conduction. As a summary, heat can be

transferred by conduction and/or radiation in a still fluid (no bulk

fluid motion) and by convection and/or radiation in a flowing fluid.

When heat is transferred through a fluid you will either have

conduction or convection, but not both. Gases are practically

transparent to radiation, except for those gases that are known to

absorb radiation at certain wavelengths. Finally, heat transfer through

a vacuum is by radiation only since conduction or convection requires

the presence of a material medium.

Practice Problems

Problem 1: An aluminum pan whose thermal conductivity is 237 W/m* ºC has a flat bottom with

diameter 15 cm and thickness 0.4cm. Heat is transferred steadily to boiling water in the pan through

its bottom at a rate of 800 W. If the inner surface of the bottom of the pan is at 105ºC, determine

the temperature of the outer surface of the bottom pan.

Given:

𝑘 = 237𝑊

𝑚∗°𝐶 𝐷𝑖𝑎𝑚𝑒𝑡𝑒𝑟 = 15𝑐𝑚 = 0.15𝑚

�̇�𝑐𝑜𝑛𝑑 = 800𝑊 𝑇ℎ𝑖𝑐𝑘𝑛𝑒𝑠𝑠 = 0.4𝑐𝑚 = 0.004𝑚

𝑇2 = 105°𝐶

105C

800 W 0.4 cm

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Heat transfer area:

𝐴𝑟𝑒𝑎𝑐𝑖𝑟𝑐𝑙𝑒 = 𝛱𝑟2 = 𝜋(0.075𝑚)2 = 0.018𝑚2

Conduction heat transfer through bottom pan:

�̇�𝑐𝑜𝑛𝑑 = 𝑘𝐴∆𝑇

𝐿= 𝑘𝐴

𝑇2 − 𝑇1

𝐿

800 𝑊 = (237𝑊

𝑚 ∗ °𝐶)(0.0177 𝑚2)

𝑇2 − 105°𝐶

0.004𝑚

Answer: 𝑇1 = 105.76°𝐶

Problem 2: Hot air at 80°C is blown over a 2m x 4m flat surface at 30°C. If the average convection

heat transfer coefficient is 55𝑊

𝑚2∗°𝐶 , determine the rate of heat transfer from the air to the plate, in

kW.

Given:

ℎ =55𝑊

𝑚2∗°𝐶 𝐴𝑠 = 2𝑥4 = 8𝑚2

∆𝑇 = (80°𝐶 − 30°𝐶) = 50°𝐶

Convection heat transfer:

�̇�𝑐𝑜𝑛𝑣 = ℎ𝐴𝑠∆𝑇

�̇�𝑐𝑜𝑛𝑣 = (55𝑊

𝑚2 ∗ °𝐶)(8𝑚2)(50°𝐶)

Answer: �̇�𝑐𝑜𝑛𝑣 = 22,000𝑊 = 22𝑘𝑊

80C

Air

30C

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Problem 3: Consider a person standing in a room maintained at 20°C at all times. The inner

surfaces of the walls, floors, and ceiling of the house are observed to be at an average temperature

of 12°C in winter and 23°C in summer. Determine the rates of radiation heat transfer between this

person and the surrounding surfaces in both summer and winter if the exposed surface area,

emissivity, and the average outer surface temperature of the person are 1.6𝑚2, 0.95, and 32°C

respectively.

Given:

𝜀 = 0.95 𝐴𝑠 = 1.6𝑚2 𝑇𝑠 = 32°𝐶 + 273 = 305°𝐾

Summer: 𝑇𝑠𝑢𝑟𝑟 = 23°𝐶 + 273 = 296°𝐾

Winter: 𝑇𝑠𝑢𝑟𝑟 = 12°𝐶 + 273 = 285°𝐾

Stefan-Boltzman law: 𝜎 =5.67𝑥10−8𝑊

𝑚2∗°𝐾4

Radiation heat transfer:

Summer: �̇�𝑟𝑎𝑑 = 𝜀𝜎𝐴𝑠(𝑇𝑠4 − 𝑇𝑠𝑢𝑟𝑟

4 )

�̇�𝑟𝑎𝑑 = (0.95) (5.67𝑥10−8𝑊

𝑚2 ∗ °𝐾4) (1.6𝑚2)[(305°𝐾)4

− (296°𝐾)4]

Answer: �̇�𝑟𝑎𝑑 = 84.2 𝑊

Winter: �̇�𝑟𝑎𝑑 = 𝜀𝜎𝐴𝑠(𝑇𝑠4 − 𝑇𝑠𝑢𝑟𝑟

4 )

�̇�𝑟𝑎𝑑 = (0.95) (5.67𝑥10−8𝑊

𝑚2 ∗ °𝐾4) (1.6𝑚2)[(305°𝐾)4 − (285°𝐾)4]

Answer: �̇�𝑟𝑎𝑑 = 177.2 𝑊

Tsurr

Qrad

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Summary

In conclusion, there are three mechanisms of heat transfer. One of them is conduction which is the

heat that is transferred within a system or between two systems that are touching. Another one was

convection. Convection can be split into two subcategories; natural convection and forced

convection. Forced convection is where the fluid is being forced to flow over a surface externally

by something like a fan or pump. Natural convection is when the fluid motion is caused by

resistance forces that are induced by density differences due to the variation of temperature in the

fluid. The last mechanism of heat transfer is radiation. Radiation is when the transfer of energy

happens and there is no conductive medium such as space. That lack of medium means there is no

matter there for heat to pass through.

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CHAPTER 9: EXTERNAL FORCED CONVECTION

As you have probably surmised, or if you haven’t bothered to read the title yet, this chapter covers

the topic of convection, particularly forced convection. Unfortunately, we will also be discussing

some math and equations about convection. Just remember the equations are more scared of you

than you are of them.

Physical Mechanism of Convection

Earlier in this guide to learning thermodynamics, we discussed that there are three basic types of

heat transfer mechanisms: conduction, convection and radiation. Conduction and convection are

alike in the fact that they both need a physical object in order to transfer, but convection also

requires fluid motion. You have probably stopped reading to think of different forms of

convection. You have probably thought hard enough to go on a ten minute day dream, so let me

give a few examples to prevent this. Turning on an outdoor garden hose lying in the hot sun is one

form. As water flows through, the hose slowly cools down. This is a form of forced convection,

where an outside force causes some form of fluid transfer across the object in question. Forced

convection could even be as simple as blowing on your bowl of soup. By forcing air across the

soup’s surface, water molecules in the air are forced along with the air. Yes, even vapor forms of

fluid can count as fluids.

Convection can be difficult to wrap your head around, but the equations that come with it are fun

and simple (usually). For this section, we are only going to look at two equations. Below is the

first of which, Newton’s law of cooling (9-1). It is the rate of convection heat transfer (qconv)

proportional to, or equal to, the difference in temperature (Ts and T∾). When the section of the

fluid being observed is far from the surface being observed, its temperatures, velocities, etc. are

considered infinite, hence the infinity symbol subscribing the temperature. The (h) represents the

convection heat transfer coefficient. You will be seeing it often in this chapter.

𝑞𝑐𝑜𝑛𝑣 = ℎ(𝑇𝑠 − 𝑇∾) (9-1)

The second equation we are going to look at is something called the Nusselt number (9-2). This

number will come out dimensionless. Usually, like in this case, the equations will be

nondimensionalized to make things easier further down the road to solving the problem.

𝑁𝑢 =ℎ𝐿𝑐

𝑘 (9-2)

The (h) is the same value as in the previous equation. I told you it would come back. Next we have

the characteristic length (Lc) and the thermal conductivity (k). Be careful with (Lc) in equations of

fluid-related mechanics. Sometimes you will use it for length and other times you will use it for

width.

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Classification of Fluid Flow

Convection transfer goes hand in hand with fluid mechanics, the science dealing with static and

dynamic fluid behaviors. A multitude of problems can occur with fluid flow. These problems are

typically categorized by a common quality. Below are a few of these categories:

Viscosity: This is basically friction in fluid terms. A slow layer of fluid causes friction with

a fast layer of fluid. There is one key aspect to understanding viscosity; no fluid has zero

viscosity. All fluids have some form of internal resistance to flow. There are two major

types of frictional effects in flow: viscous flows and inviscid flow regions. Viscous flows

are flows with significant frictional effects while inviscid flow regions have considerably

small friction effects when compared to the other inertial forces or pressures. Inviscid flows

are often neglected to help simplify the analysis while staying fairly accurate.

Internal/External Flow: These two types of flows are exactly what they sound like. External

flows are unbound and travel across a surface. Internal flows are forced through confined

spaces and channels. Viscosity greatly affects internal flows while external flows are only

affected by the viscous effects of boundary layers (see below for boundary layers).

Compressibility: This is a dependent value of a fluid depends on the level of varying

density while the fluid flows. If the flow is incompressible, this means the density is

relatively the same throughout the system. This also means the volume is unchanged as it

flows throughout the system. In general, since density is relatively constant, fluid flow is

determined incompressible. This is why most fluids are called incompressible substances.

Laminar/Turbulent Flow: Fluid flow can be orderly or chaotic. These changes in flow are

described as being laminar or turbulent. Laminar flows are smooth and streamlined with

low velocities. Turbulent flows, on the other hand, move at fluctuating, high velocities. If

a flow changes from one flow type to another, it is considered to be transitional. Think of

the way smoke billows from a fire. The smoke’s movements begin smooth and gentle, but

they quickly turn violent and random. This is a perfect example of the changes of flow.

The smoke begins in laminar flow, slowly becomes transitional, and finally ends up as

turbulent flow.

Forced Flow: Depending on how a fluid’s motion began, it can be determined natural flow

or forced flow. Natural flow occurs when natural forces takes effect on fluids. For example,

the buoyancy effect causes warm fluid to rise and cool fluid to fall. Forced flow is the

opposite of natural flow; the fluid flows from an outside influence. An easy example is the

circulatory system of nearly every living creature on Earth. The heart pumps blood

throughout our bodies through veins. This is no different from any machine containing a

hydraulic system.

Steady Flow: Steady and uniform are terms often used in technical applications, even the

classification of devices and machines. A steady flow device can be almost any device that

runs at constant conditions for a long time. Some of these devices start up as with transient,

or unsteady, flow. This is simply the opposite of steady flow; unsteady flows change

throughout the operation. A perfect example of this is a rocket engine. As it starts up, the

engine builds pressure and the flow accelerates. Once the rocket gets high enough, the

engine slows down to a uniform flow.

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Boundary Layers

Boundary layers are the flow regions next to the wall where significant viscous flows are present.

Think of cholesterol in your arteries. As the outermost layer of cholesterol begins causing friction

with the interior wall of you arteries, it slowly begins to harden and build up. This is why fluid

powered machines malfunction; they have high cholesterol. In reality, all boundary layers are

simply the outside layer of fluid. Here, we are going to discuss two types of boundary layers:

velocity and thermal layers.

Velocity Boundary Layers

Inside a pipe, when the outermost layer is at an assumed velocity, it will slow down with friction.

This creates a domino effect as it slows down the adjacent layer, which slows down the next layer

and so on. If a flow area with this situation feels the effects of shearing viscous forces, the area is

called a velocity boundary layer. In Fig. 1, you can see a flow area that changes from laminar flow

to transitional flow and then to turbulent flow throughout the diagram. The entire pink/red region

is the velocity boundary layer. At the bottom, you can see individually labeled layers. These small

layers are those that create the domino effect throughout the entire layer.

The friction happening between the boundary and the outermost layer is called friction force. For

readers who don’t know much about forces, stress is equal to force (F) over area (A) (9-3). To

clarify, a force spread out over an area will create some form of force or pressure. That is why you

have to distribute your weight on ice.

Standing straight up in one small spot creates

a lot of pressure, but by spreading yourself out

you create a wider area with less force or

pressure. In this scenario, friction force (Ff)

over unit mass (A) produces a different type

of stress: shear stress (9-4). This shear stress

is given the variable (τ), the Greek latter Tau

(pronounced tauw).

Figure 1: Velocity Boundary Layer

Figure 2: Icy Accident

http://blog.cheaperthandirt.com/survive-falling-ice/

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𝜎 =𝐹

𝐴 𝜏 =

𝐹𝑓

𝐴 (9-3) and (9-4)

Thermal Boundary Layer

Similar to the assumed velocity for velocity layers, thermal boundary layers are almost the same

except for the use of an assumed temperature. In this type, flow area affected the domino effect of

temperatures where there is a significant variation of temperature is called a thermal boundary

layer. To be truthful, the biggest difference between these two types of boundary layers is the

names and labels of the effects at hand. Each has a domino effect system taking effect and an area

of flow in which there is significant change in something.

More Laminar/Turbulent Flows

As a recap, laminar flows are streamlined and ordered, turbulent flows have fluctuating velocities

and disordered motion and transitional flows gradually change from one to the other. Do you

remember the individual layers in Fig. 1 we talked about? This is where they make their debut.

Starting from the outermost layer next to the boundary we have the viscous sublayer. This layer

experiences linear velocities in its streamlined flow. This is the most laminar of the layers in the

movement. Next in line is the buffer layer. The buffer layer feels strong turbulent effects, but is

trumped by other viscous effects. This layer is followed by the overlap layer. It feels more powerful

turbulence than the buffer layer, but is still trumped by viscous effects. The last layer is the

turbulent layer, in which turbulent effects finally overcome the viscous effects that constrained the

lower layers.

Drag & Heat Transfer

The flow of fluid over a solid object can cause a wide variety of physical changes to the

environment as well as to the object in question. One of the more well-known types of these

changes is drag force. Drag force exists in most moving objects. It exists in the lift necessary for

air travel. It causes the upward force on water particles that collect into clouds and the dust that

travels along high winds. Strong, the Force is. Control it, you must. In a way, the Force in Star

Wars is a more malleable and bendable type of drag force that can be wielded by the strong of

mind and will. Apparently, only humans who live in a galaxy far, far away can use it.

The velocity of the fluid in question can be defined by its distance from the immersed object in

question. When the velocity of a fluid in question relative to immersed object in question is far

from the object, the velocity is considered free-velocity. This value is typically equal to the

upstream velocity (V), also known as the approach velocity. What we have just seen is one

particular velocity number with three different possible definitions. Out of the three names this

velocity has, upstream velocity will be the most used. You’re probably wondering what this has to

do with drag. This has absolutely nothing to do with drag. The only reason it’s here is so you don’t

freak out when you see the term upstream velocity in drag equations. This will be diverted,

however, now that you know what it means. You’re welcome.

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Drag

Ordinarily, when a fluid flows over or across a solid body, there will be a form of frictional

resistance. This resistance is called drag. When an object is immersed into a still fluid, the only

force on it is the normal force of the pressure in the fluid. If the object is immersed into a moving

fluid instead, it will have additional shear forces running tangentially along the objects surface

along with the normal force. In general, forces can be split into separate parts to make things easier.

For example, you have a grid of x and y axes with a line moving diagonally. This diagonal line

can be split up into two lines, one moving horizontally and one moving vertically. This method is

of splitting a force is very similar to using the Pythagorean Theorem in algebra. The combination

of each of the force components flowing in the direction of the fluid flow cause the object to move

with the fluid flow as well. This phenomenon is known as lift. Think of it as underwater aircraft

flight. The only difference is that aircrafts have less water around them and the main force acting

on it is from its thrusters.

Heat Transfer

The effects of drag described above also cause effects to the transfer of heat within the

fluid. The temperature as well as the properties of the fluid varies between the outer boundary and

the thermal boundary layer. This variation can be evaluated using something called the film

temperature (Tf). The formula for this value is shown below.

𝑇𝑓 =𝑇𝑠+𝑇∾

2 (9-4)

This is also the mathematical average of the temperatures of the surface temperature (Ts) and the

free-stream temperature (T∞).

Flow across Cylinder/Spheres

While you study fluids and the properties and behaviors of fluids, you will come across

problems that involve flow around circular objects like cylinders or spheres. Think of a golf ball

flying through the air. The dimpled surface of the ball was designed using fluid processes to create

the smoothest and longest possible flight.

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