Islamic Azad University Karaj Branch

Dr. M. Khosravy

Chapter 1 Introduction to Heat Transfer

1

Introduction Thermodynamics: •  Energy can be transferred between a system and its

surroundings. •  A system interacts with its surroundings by exchanging work

and heat •  Deals with equilibrium states •  Does not give information about:

–  Rates at which energy is transferred –  Mechanisms through with energy is transferred

In this chapter we will learn !  What is heat transfer !  How is heat transferred !  Relevance and importance Dr. M. Khosravy 2

Definitions •  Heat transfer is thermal energy transfer that is induced by a temperature

difference (or gradient)

Modes of heat transfer •  Conduction heat transfer: Occurs when a temperature

gradient exists through a solid or a stationary fluid (liquid or gas).

•  Convection heat transfer: Occurs within a moving fluid, or between a solid surface and a moving fluid, when they are at different temperatures

•  Thermal radiation: Heat transfer between two surfaces (that are not in contact), often in the absence of an intervening medium.

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Example: Design of a container

A closed container filled with hot coffee is in a room whose air and walls are at a fixed temperature. Identify all heat transfer processes that contribute to cooling of the coffee. Comment on features that would contribute to a superior container design.

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1. Conduction Transfer of energy from the more energetic to less energetic particles of a substance by collisions between atoms and/or molecules. ! Atomic and molecular activity – random molecular motion

(diffusion)

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T1>T2

T2

T1

x

xo

T2

qx”

1. Conduction

!  Under steady-state conditions the temperature varies linearly as a function of x.

!  The rate of conductive heat transfer in the x-direction depends on

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Consider a brick wall, of thickness L=0.3 m which in a cold winter day is exposed to a constant inside temperature, T1=20°C and a constant outside temperature, T2=-20°C.

T1=20°C

T2= -20°C

L=0.3 m x

T

qx”

LTT

qx21" !"

Wall Area, A

1. Conduction •  The proportionality constant is a transport property,

known as thermal conductivity k (units W/m.K)

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LT

kLTT

kqx!="= 21"

•  For the brick wall, k=0.72 W/m.K (assumed constant), therefore qx”= 96 W/m2

?  How would this value change if instead of the brick wall we had a piece of polyurethane insulating foam of the same dimensions? (k=0.026 W/m.K)

!  qx” is the heat flux (units W/m2 or (J/s)/m2), which is the heat transfer rate in the x-direction per unit area perpendicular to the direction of transfer.

!  The heat rate, qx (units W=J/s) through a plane wall of area A is the product of the flux and the area: qx= qx”. A

1. Conduction •  In the general case the rate of heat transfer in the

x-direction is expressed in terms of the Fourier law:

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dxdTkqx !=" T1(high)

T2 (low)

x

qx”

•  Minus sign because heat flows from high to low T !  For a linear profile

0)()(

12

12 <!!=xxTT

dxdT

x1 x2

2. Convection Energy transfer by random molecular motion (as in conduction) plus bulk (macroscopic) motion of the fluid. –  Convection: transport by random motion of molecules and by bulk

motion of fluid. –  Advection: transport due solely to bulk fluid motion.

!  Forced convection: Caused by external means !  Natural (free) convection: flow induced by buoyancy forces, arising

from density differences arising from temperature variations in the fluid

The above cases involve sensible heat (internal energy) of the fluid

!  Latent heat exchange is associated with phase changes – boiling and condensation.

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2. Convection Air at 20°C blows over a hot plate, which is maintained at a temperature Ts=300°C and has dimensions 20x40 cm.

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CT !20=!

q” CTS!300=

Air

The convective heat flux is proportional to

!"# TTq Sx"

2. Convection •  The proportionality constant is the convection heat

transfer coefficient, h (W/m2.K)

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)("!"= TThq Sx Newton’s law of Cooling

•  For air h=25 W/m2.K, therefore the heat flux is qx”= 7,000 W/m2

?  How would this value change if instead of blowing air we had still air (h=5 W/m2.K) or flowing water (h=50 W/m2.K)

•  The heat rate, is qx= qx”. A = qx”. (0.2 x 0.4) = 560 W. •  The heat transfer coefficient depends on surface geometry, nature of

the fluid motion, as well as fluid properties. For typical ranges of values, see Table 1.1 textbook.

•  In this solution we assumed that heat flux is positive when heat is transferred from the surface to the fluid

3. Radiation •  Thermal radiation is energy emitted by matter •  Energy is transported by electromagnetic waves (or photons). •  Can occur from solid surfaces, liquids and gases. •  Dos not require presence of a medium

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Surface at Ts

!  Emissive power E is the rate at which energy is released per unit area (W/m2) (radiation emitted from the surface)

!  Irradiation G is the rate of incident radiation per unit area (W/m2) of the surface (radiation absorbed by the surface), originating from its surroundings

Surroundings at Tsur

Eqemitted ="Gqincident =

"

3. Radiation •  For an ideal radiator, or blackbody:

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4sbemitted TEq !=="" Stefan-Boltzmann law

where Ts is the absolute temperature of the surface (K) and s is the Stefan-Boltzmann constant, (s = 5.67x10-8 W/m2.K4)

•  For a real (non-ideal) surface: 4"semitted TEq !"== e is the emissivity 10 !"!

•  The irradiation G, originating from the surroundings is:

4"surincident TGq !"== a  is the absorptivity

For a “grey” surface, a=e 10 !! a

3. Radiation •  Assuming a = e, the net radiation heat transfer from

the surface, per unit area is

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)( 44"sursrad TTq !"#=

•  The net radiation heat exchange can be also expressed in the form:

)( sursrrad TTAhq != ))(( 22surssursr TTTTh ++!"=where

Summary: Heat Transfer Processes

Identify the heat transfer processes that determine the temperature of an asphalt pavement on a summer day

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Summary: Heat Transfer Processes

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Identify the heat transfer processes that occur on your forearm, when you are wearing a short-sleeved shirt, while you are sitting in a room. Suppose you maintain the thermostat of your home at 15°C throughout the winter months. You are able to tolerate this if the outside air temperature exceedes –10°C, but feel cold if the temperature becomes lower. Are you imagining things?

Example 1 Satellites and spacecrafts are exposed to extremely high radiant energy from the sun. Propose a method to dissipate the heat, so that the surface temperature of a spacecraft in orbit can be maintained to 300 K.

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Given a=0.4, e=0.7, qsolar = 1000 W, Ts=300K, Tspace=0 K, s = 5.67x10-8 W/m2.K4

Example 2 (1.2 Textbook) An uninsulated steam pipe passes through a room in which the air and the walls are at 25°C. The outside diameter of the pipe is 70 mm, and its surface temperature and emissivity are 200°C and 0.8 respectively. What are the surface emissive power (E), and irradiation (G)? If the coefficient associated with free convection heat transfer from the surface to the air is h=15 W/m2.K, what is the rate of heat loss from the surface per unit length of pipe, q’?

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Reminder: The General Balance Equation

Accumulation = Creation – Destruction + Flow in – Flow out

Rate Equation

Rate of Rate of Rate of Rate of Rate of Accumulation = Creation – Destruction + Flow in – Flow out

Applicable to any extensive property: mass, energy, entropy, momentum, electric charge

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Reminder: System and Control Volume

•  A system is defined as an arbitrary volume of a substance across whose boundaries no mass is exchanged. The system may

experience change in its momentum or energy but there is no transfer of mass between the system and its surroundings. The system is

“closed”.

•  A control volume is an arbitrary volume across whose boundaries mass, momentum and energy are transferred. The control volume

may be stationary or in motion. Mass can be exchanged across its boundaries. Useful in fluid mechanics, heat and mass transfer

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Reminder: Approaches for Analysis of Flow

In analyzing fluid motion we may take two paths:

1.  Working with a finite region (=the control volume), making a

balance of flow in versus flow out and determining flow effects

such as forces, or total energy exchange. This is the control

volume method. This approach is also called “macroscopic” or

“integral method of analysis”.

2.  Analysing the detailed flow pattern at every point (x,y,z) in the

field. This is the differential analysis, sometimes also called

“microscopic”.

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Conservation of Energy

•  Energy conservation on a rate basis:

Control Volume (CV)

Surroundings, S

Boundary, B (Control Surface, CS)

-Accumulation (Storage) -Generation Addition

through inlet Loss through outlet

stst

outgin EdtdE

EEE !!!! ==!+

inE! outE!gE!

stE!

!  Inflow and outflow are surface phenomena !  Generation and accumulation are volumetric phenomena

Units W=J/s (1.1)

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The Energy Balance

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The Energy Balance !  Rate of Energy Flow into CV: ininint WqmzgVu !! ++!!"

#$$%

&++

in2

2

!  Rate of Energy Flow out of CV: outoutoutt WqmzgV

u !! ++!!"

#$$%

&++

out2

2

!  Rate of Energy Accumulation: CV

!"

#$%

&''(

)**+

,++ zgVum

dtd

t 2

2

ut :internal energy, V: velocity, z: potential energy, q: heat rate, W: work

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The Energy Balance

02

2

2

2

=!!"

#

$$%

&++''(

)**+

,++

-!!"

#

$$%

&++''(

)**+

,++

outoutout

out

t

ininint

WqmzgV

u

WqmzgV

u

!!

!!

in

!  Substituting in equation (1.1) and assuming steady-state conditions:

" Convention

inoutoutnet

outininnet

WWW

qqq!!! !=

!=

,

,q is positive when transferred from surroundings to system. W is positive when transferred from system to surroundings

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The Energy Balance •  For steady-state conditions the energy balance reduces to:

022

22

=!+""#

$%%&

'++!""#

$%%&

'++ outnetout

out

tint WqmzgV

umzgV

u ,in

!!!

(1.2)

The net work is:

inout, ]m ) [(]m ) [(P !!!! !! PWW shaftoutnet "+=

Injection Work

"  The work term is divided in two contributions: Flow work, associated to pressure forces (=pu, where u is the specific volume) and (shaft) work done by the system.

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Steady-Flow Energy Equation

!pui t +=

0

22

22

=!+

+""#

$%%&

'+++!""#

$%%&

'+++

shaft

out

Wq

zgV

pumzgV

pum

!

!! in

((

Recall:

!

!mVA

VAm

c

c

!!

!

=="

= Mass flow rate (kg/s)

Volumetric flow rate (m3/s)

Units of [J/s]

Enthalpy per unit mass:

and )()( outinpoutin TTcii !=!

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Simplified steady-flow energy equation

•  For steady state conditions, no changes in kinetic or potential energy, no thermal energy generation, neglible pressure drop:

)( inoutp TTCmq != !

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Example (Problem 1.36 textbook) In an orbiting space station, an electronic package is housed in a compartment having a surface area As=1 m2, which is exposed to space. Under normal operating conditions, the electronics dissipate 1kW, all of which must be transferred from the exposed surface to space. (a) If the surface emissivity is 1.0 and the surface is not exposed to the sun, what is its steady-state temperature? (b) If the surface is exposed to a solar flux of 750 W/m2 and its absorptivity to solar radiation is 0.25, what is its steady-state temperature?

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Surface Energy Balance For a control surface:

0

0

""" =!!

=!

radconvcond

outin

qqq

orEE !!

T

x

T1

T2

!T

qcond” qrad”

qconv”

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Example (Problem 1.55 textbook) The roof of a car in a parking lot absorbs a solar radiant flux of 800 W/m2, while the underside is perfectly insulated. The convection coefficient between the roof and the ambient air is 12 W/m2.K.

a)  Neglecting radiation exchange with the surroundings, calculate the temperature of the roof under steady-state conditions, if the ambient air temperature is 20°C.

b)  For the same ambient air temperature, calculate the temperature of the roof it its surface emissivity is 0.8

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Chapter 1: Summary Modes of Heat Transfer: Conduction Convection Radiation

dxdTkqx !=" )("

!"= TThq Sx )( 44"sursrad TTq !"#=

)( sursrrad TTAhq !=

qx”(W/m2) is the heat flux qx (W=J/s) is the heat rate

Energy Balances – written on a rate basis (J/s):

!  Conservation of Energy for a Control Volume !  Surface Energy Balance (does not consider volumetric phenomena)