Engr. FRANCIS M. MULIMBAYAN

BSAE / MSMSE

INSTRUCTOR 4

ENSC 14a

Engineering Thermodynamics and Heat Transfer

Department of Engineering Science University of the Philippines –Los Banos

College, Los Banos, Philippines

Basics of

Heat Transfer

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Introduction

Thermodynamics Deals with the amount of heat

transfer as a system undergoes a process from one equilibrium state to another

First Law requires that the rate of energy transfer into a system should be equal to the rate of increase of energy of the system

Second Law requires that heat is transferred in the direction of decreasing temperature.

Makes no reference to how long the process will take

Chapter 9 Basics of Heat Transfer

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Introduction

Heat Transfer

Deals with the determination of the rates of energy transfer in the form of heat

Deals with systems that lack thermal equilibrium

Engineering Heat Transfer

Rating Problems – deal with the determination of heat transfer for an existing system at a specified temperature difference

Sizing Problems – deal with the determination of the size of a system in order to transfer heat at a specified rate for a specified temperature difference.

Chapter 9 Basics of Heat Transfer

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Introduction

Heat

Form of energy that can be transferred from one system to another as a result of temperature difference.

Sensible Heat

Heat absorbed or given off by a substance that is not in the process of changing its phase.

Latent Heat

Heat absorbed or given off by a substance while it is changing its phase.

Specific Heat (𝐶𝑝, 𝐶𝑣)

Represents energy required to raise the temperature of a unit mass of a substance by one degree in a specified way.

Chapter 9 Basics of Heat Transfer

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Introduction

Total Energy

Sum of thermal, mechanical, kinetic, potential, electrical, magnetic, chemical, and nuclear energy.

Microscopic Energy

Forms of energy related to the molecular structure of a system and the degree of the molecular activity

Internal Energy (U)

Sum of all microscopic forms of energy of solids and stationary fluids

Enthalpy (H)

Represents the microscopic energy of flowing fluids.

Chapter 9 Basics of Heat Transfer

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Introduction

Units of Energy

SI unit: kilojoules (kJ)

English: British Thermal Unit (BTU)

1 BTU = 1.055056 kJ

1 cal = 4.1868 J

British Thermal Unit

Energy needed to raise the temperature of 1 lbm of water at 60°F by 1°F.

Calories

Energy needed to raise the temperature of 1 gram of water at 14.5°F by 1°C.

Chapter 9 Basics of Heat Transfer

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Introduction

Energy Balance for a Closed System

𝑄 = 𝑚 ∆𝑢 = 𝑚 𝐶𝑣𝛥𝑇

Energy Balance for a Steady-Flow Systems

𝑄 = 𝑚 ∆ℎ = 𝑚 𝐶𝑝𝛥𝑇

Chapter 9 Basics of Heat Transfer

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Introduction

Amount of Heat Transfer (kJ or Btu) 𝐐 = 𝐦𝐂𝚫𝐓

Heat Transfer Rate (kW or Btu/hr)

𝐐 =𝐐

∆𝐭

Heat Transfer per unit length (kW/m or Btu/hr-ft)

𝐐 ′ =𝐐

𝐋

Heat Flux (kW/m² or Btu/hr-ft²)

𝐪 = 𝐐 ′′ =𝐐

𝐀𝐬

Heat Generation (kW/m³ or Btu/hr-ft³)

𝐠 = 𝐐 ′′′ =𝐐

𝐕

Chapter 9 Basics of Heat Transfer

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Application Areas of Heat Transfer

Chapter 9 Basics of Heat Transfer

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Modes of Heat Transfer

Chapter 9 Basics of Heat Transfer

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Modes of Heat Transfer

Chapter 9 Basics of Heat Transfer

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Conduction

Conduction

Transfer of energy from the more energetic particles of a substance to the adjacent less energetic ones as a result of interactions between the particles.

Transfer of thermal energy in solids or fluids at rest

In fluids, conduction is due to collisions and diffusion of the molecules during their random motion.

In solids, it is due to combination of vibrations of the molecules in a lattice and energy transport by free electrons.

Depends on the geometry, thickness and material composition of the medium and on the temperature difference across the medium.

Chapter 9 Basics of Heat Transfer

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Conduction

Physical Mechanism of Conduction

The thickness and area of a given large plane wall is ∆𝑥 = 𝐿 and 𝐴, respectively.

The temperature difference across the wall is,

ΔT = T2 − T1

Experiments revealed that,

Q ∝ AΔT

L

Incorporating the proportionality constant and letting Δx → 0, results to

𝐐 𝐜𝐨𝐧𝐝 = −𝐤𝐀𝐝𝐓

𝐝𝐱

→ 𝐅𝐨𝐮𝐫𝐢𝐞𝐫′𝐬 𝐋𝐚𝐰 𝐨𝐟 𝐇𝐞𝐚𝐭 𝐂𝐨𝐧𝐝𝐮𝐜𝐭𝐢𝐨𝐧

Chapter 9 Basics of Heat Transfer

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Conduction

Fourier’s Law of Heat Conduction

The temperature gradient is the slope of the temperature curve on the T-x diagram

Thermal conductivity of a material is the measure of the ability of the material to conduct heat.

The negative sign indicates that the heat transfer in the positive x direction is a positive quantity.

𝐐 𝐜𝐨𝐧𝐝 = −𝐤𝐀𝐝𝐓

𝐝𝐱

Chapter 9 Basics of Heat Transfer

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Conduction

Sample Problem 9.1 Calculate the rate of heat transfer through a pane of window glass (𝑘 = 0.81 W/m-K) 1 m high, 0.5 m wide, and 0.5 cm thick, if the outer surface temperature is 24°C and the inner-surface temperature is 24.5°C.

Chapter 9 Basics of Heat Transfer

𝑄 𝑐𝑜𝑛𝑑 = −𝑘𝐴𝑑𝑇

𝑑𝑥= 𝑘𝐴

𝑇1 − 𝑇2𝐿

=0.81

𝑊𝑚 − 𝐾

1 𝑚 𝑥 0.5 𝑚 24.5 − 24 𝐾

0.005 𝑚= 𝟒𝟎. 𝟓 𝑾

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Convection

Convection

Thermal energy is transferred to or from a fluid near a solid surface

Conduction with added complexity of thermal energy transfer by moving fluid molecules

Physical Mechanism

Energy is first transferred to the air layer adjacent to the block by conduction.

The energy is then carried away from the surface by convection

Chapter 9 Basics of Heat Transfer

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Convection

Types of Convection

Forced Convection

Also known as assisted convection

Occurs when fluid motion is induced by an external mean such as pump or fan

Natural Convection

Also known as free convection

Brought by buoyancy forces due to density differences caused by temperature variations in the fluid

Chapter 9 Basics of Heat Transfer

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Convection

Newton’s Law of Cooling

𝐐 𝐜𝐨𝒏𝒗 = 𝒉𝑨(𝑻𝒔 − 𝑻∞)

Convective Heat Transfer Coefficient (𝒉)

Depends on all the variables influencing convection such as surface geometry and orientation, flow regime, properties of fluids, bulk velocity, etc.

Chapter 9 Basics of Heat Transfer

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Conduction

Sample Problem 9.2 Calculate the rate of heat transfer by natural convection between a shed roof of area 20 m x 20 m and ambient air, if the roof surface temperature is 27°C, the air temperature is -3°C, and the average convection heat transfer coefficient is 10 W/m2-K.

Chapter 9 Basics of Heat Transfer

𝑄 𝑐𝑜𝑛𝑑 = ℎ𝐴𝑠 𝑇𝑠 − 𝑇∞

= 10𝑊

𝑚2 − 𝐾20 𝑚 𝑥 20 𝑚 (27

− (−3))𝐾

= 120,000 𝑊

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Radiation

Radiation Heat Transfer

Thermal energy is transferred by electromagnetic waves

Does not require medium

Electromagnetic radiation

Emitted by all bodies with temperature greater than absolute zero

e.g. x-rays, gamma rays, microwave, television waves

Chapter 9 Basics of Heat Transfer

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Radiation

Chapter 9 Basics of Heat Transfer

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Radiation

Thermal Radiation

Radiation emitted by bodies because of their temperature

Stefan-Boltzmann Law

Gives the blackbody emissive power or the maximum rate of radiation per unit surface area that can be emitted by a body at an absolute temperature 𝑇𝑠

𝐐 𝐞𝐦𝐢𝐭,𝐦𝐚𝐱 = 𝛔𝐀𝐬𝐓𝐬𝟒

σ = 5.67 × 108W

m2 ∙ K4= 0.1714 × 108

Btu

hr ∙ ft2 ∙ R4

As = Surface area in 𝑚2 𝑜𝑟 𝑓𝑡2

Blackbody

Idealized surface that emits radiation at its maximum rate

Chapter 9 Basics of Heat Transfer

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Radiation

Emissivity, 𝛆

Ratio of the radiation emitted by the surface at a given temperature to the radiation emitted by a blackbody at the same temperature.

Real Surfaces

Radiation emitted is always less than the radiation emitted by blackbody at the same temperature.

𝐐 𝐞𝐦𝐢𝐭 = 𝛆𝛔𝐀𝐬𝐓𝐬𝟒

Irradiation, G

Radiation flux incident on a surface from all directions

Radiosity, J

Radiation flux leaving a surface from all directions

Chapter 9 Basics of Heat Transfer

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Radiation

Absorptivity (𝜶)

The fraction of irradiation absorbed by the surface

Reflectivity 𝝆

The fraction of irradiation reflected by the surface

Transmissivity 𝝉

The fraction of irradiation transmitted by the surface

𝜶 + 𝝆 + 𝝉 = 𝟏

Chapter 9 Basics of Heat Transfer

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Radiation

Opaque material

It has 𝝉 = 𝟎

It allows thermal radiation to be emitted or absorbed within the first few microns of the surface, and thus radiation for this material are said to be a surface phenomenon.

Semi-transparent material

Allows certain type of radiation to penetrate while inhibits other type of radiation.

Chapter 9 Basics of Heat Transfer

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Radiation

Net Radiation Heat Transfer

Difference between the rates of radiation emitted by the surface and the radiation absorbed

The emitted radiation is given by the Stefan-Boltzmann Law

The absorbed radiation is α𝐺

Simplifying Assumptions

Radiation exchange occurs between surfaces in which 𝜶 = 𝟏 and that 𝝆 = 𝟎

All surfaces involved are opaque, that is, 𝝉 = 𝟎

Each surface is isothermal and diffuse

𝑸 𝟏−𝟐 = 𝝈𝑨𝟏[𝜺𝟏𝑻𝟏𝟒 − 𝜺𝟐𝑻𝟐

𝟒]

Chapter 9 Basics of Heat Transfer

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Conduction

Sample Problem 9.3 A long, cylindrical electrically heated rod, 2 cm in diameter, is in a vacuum furnace. The surface of the heating rod has an emissivity of 0.9 and is maintained at 1000 K, while the interior walls of the furnace are black and are at 800 K. Calculate the net rate at which heat is lost from the rod per unit length.

Chapter 9 Basics of Heat Transfer

𝑸 𝟏−𝟐 = 𝝈𝑨𝟏[𝜺𝟏𝑻𝟏𝟒 − 𝜺𝟐𝑻𝟐

𝟒] = (𝟓. 𝟔𝟕

× 𝟏𝟎−𝟖) 𝝅 𝟎. 𝟎𝟐 𝟏 𝟎. 𝟗 𝟏𝟎𝟎𝟎 𝟒

− 𝟏 𝟖𝟎𝟎 𝟒

= 𝟏𝟕𝟒𝟕. 𝟏 𝐖

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