Heat Transfer:
Overview of Heat Transfer Analysis
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Section 6 – Thermal Analysis
Objectives
Module 1: Overview of Heat Transfer
Page 2

Understand the basics of heat transfer analysis.

Study Conduction, Convection and Radiation modes of heat transfer.

Identify the considerations required for solving heat transfer
problems.
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Overview of Heat Transfer Analysis
Section 6 – Thermal Analysis
Module 1: Overview of Heat Transfer
Page 3
Heat – energy produced as a result of combustion, chemical reaction,
electrical resistance, friction, fission, fusion, incident solar radiation,
microwaves, etc .
Heat transfer – the exchange of heat from one body to another, the
study of which is applicable across a broad range of applications.
Common heat transfer problems include the calculation
of heat loss/gain :





Through windows
In electronic chips
Through pipes carrying steam
Through fins on a radiator
And many more…
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The Sun is by far the largest natural
source of heat for our planet.
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Modes of Heat Transfer
Section 6 – Thermal Analysis
Module 1: Overview of Heat Transfer
Page 4
Transfer of heat takes place from a body at a higher temperature to a
body at a lower temperature via one or more of the following
mechanisms:



Conduction
Convection
Radiation

Heat transfer can occur through a body via all three modes
simultaneously.

Cases with occurrence of more than one mode are termed as
conjugate heat transfer problems.
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Section 6 – Thermal Analysis
Conduction
Module 1: Overview of Heat Transfer
Page 5

Fourier Equation:
T
Q   kA
x



A
Q
Q = heat transferred
K = thermal conductivity
A = area
T
= Gradient of temperature
x

The negative sign in the Fourier equation serves to counter the
negative gradient of temperature.
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Section 6 – Thermal Analysis
Convection
Module 1: Overview of Heat Transfer
Page 6
Q  UhA(Tb  Ta )
Ta
Where:
U = Velocity of moving fluid
Tb
h = Convection coefficient
A = area of the plate
Tb = Temperature of the solid body
Ta = Ambient fluid temperature
Heat loss to air moving across fins on a radiator is a common engineering
problem that involves convection.
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Section 6 – Thermal Analysis
Conduction and Convection
Module 1: Overview of Heat Transfer
Page 7


Diffusion
Advection
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Diffusion
Conduction
Advection
Convection
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Section 6 – Thermal Analysis
Conduction and Convection
Module 1: Overview of Heat Transfer
Page 8
Ra 
gTL
3

Where:
  Volumetric Thermal Expansivity
  Thermal Diffusivity
 
Kinematic Viscosity
If the objective is to stop heat transfer, then convection can be curbed by
placing obstacles in the direction of flow.
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Section 6 – Thermal Analysis
Conduction and Convection
Module 1: Overview of Heat Transfer
Page 9

Both conduction and convection can be solved by the energy
equation.

The energy equation in simplified form:
q y
qx
qz



 divq
x
y
z

Energy in
Change in
Energy
Within the
system
Energy Out
The energy equation in full form:
1

D  (u 2  v 2  w2 )
 xy  yy  zy
 xx  yx  zx
 xz  yz  zz
2



 u.gradp u (


) (


)  w(


)  u.S M
Dt
x
y
z
x
y
z
x
y
z
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Section 6 – Thermal Analysis
Radiation
Radiative exchange between two
bodies is expressed by the equation:
4
4
b
a
Q  A(T  T )
Module 1: Overview of Heat Transfer
Page 10
Ta
Where:
  Surface Emissivity
  Stephan Boltzman Constant
A  Area of surface
Tb  Temperature in K of radiant body
Ta  Temperature in K of ambient sink
Radiative loss to the ambient at absolute zero:
4
Q  A(T )
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Tb
Unlike convection and conduction,
no medium is required.
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Section 6 – Thermal Analysis
Solving Heat Transfer Problems
Module 1: Overview of Heat Transfer
Page 11

Heat transfer problems, just like fluid flow problems, are now solved
predominantly using computational techniques.

Previously, heat transfer calculations involved calculating heat gain
and loss via different modes using the formulae mentioned in the
above slides.

For convection, the majority of calculations are done using
regressions evaluated by experimental techniques.

Finite difference methods (FDM) are often taught at the graduate
level for solving 2D conductive heat transfer.
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Section 6 – Thermal Analysis
Summary
Module 1: Overview of Heat Transfer
Page 12

Heat transfer affects us in profound ways.

Our very existence depends upon the transfer of heat.

The subject of heat transfer in engineering sciences is fundamental
and its application is almost inescapable.

Conduction, convection and radiation are the three modes of heat
transfer.

Conduction requires a stationary medium, while convection requires
a moving medium.

Heat transfer problems can be solved though numerical analysis.
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Section 6 – Thermal Analysis
Summary
Module 1: Overview of Heat Transfer
Page 13

The fundamental equation for conduction is the Fourier equation.

For convection cases, dimensionless parameters measured through
experiments are used.

In the case of radiation, the Stephen Boltzmann law applies and
surface properties influence this mode of heat transfer.

Today, heat transfer problems are solved with the help of 3D
computer software.

This has greatly reduced the need for experiments, thus cutting costs
and product turnaround times.
© 2011 Autodesk
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