Heat Transfer:
Steady State Heat Transfer
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Section 6 – Thermal Analysis
Objectives
Module 4: Steady State Heat Transfer
Page 2
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Understand steady state heat transfer.
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Explore linear steady state analysis.
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Explore nonlinear steady state analysis.
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Study an example:
 Thermal analysis of a heat sink assembly
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Section 6 – Thermal Analysis
Steady State Heat Transfer
Module 4: Steady State Heat Transfer
Page 3

Steady state heat transfer occurs when temperatures, thermophysical properties, surface properties and bulk motion of fluid are
constant over time.

Temperature has reached equilibrium.
Heat In
Element under
study
Heat Out
Any machinery running at constant speed is a
good example of steady state heat transfer.
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Section 6 – Thermal Analysis
Linear Steady State Heat Transfer
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Page 4
A linear steady state problem is approximated when the
thermophysical properties (e.g., conductivity, density, viscosity) are
not dependent on temperature. Moreover, radiation loss is
unaccounted for.
Thermal conductivity of a material in real life can vary significantly
depending upon the material temperature.
If the material properties are fixed, the problem is said to be linear
steady state.
T
q  kA

Module 4: Steady State Heat Transfer
L
If “k” in the above relationship is approximated as not dependent on
temperature, then the problem is linear steady state.
An example where a linear steady state heat transfer approximation
can be used is heat loss from domestic hot water pipes when the
temperature differential is low.
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Section 6 – Thermal Analysis
Nonlinear Steady State Heat Transfer
Module 4: Steady State Heat Transfer
Page 5
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Nonlinear steady state heat transfer occurs when thermophysical
properties are assumed to vary with temperature.
T
q  kA
L




If “k” in this equation is a function of temperature
f(T), than the problem becomes nonlinear.
This is closer to real life conditions; however more complex to solve.
To solve such problems, an iterative scheme is used by assuming
initial temperatures and evaluating through calculations later.
The material properties are adjusted for new temperatures and
calculated again until convergence is reached (for example, when
heat entering and heat exiting the system boundaries are equal).
Most examples of heat transfer are nonlinear, such as heat loss from
a car engine block (engine temperature varies significantly).
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Section 6 – Thermal Analysis
Simplifying Heat Transfer Analysis
Module 4: Steady State Heat Transfer
Page 6
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Problems can be simplified by avoiding the need to calculate for
conjugate heat transfer.
For instance at low temperatures (<70⁰ C), radiation may be ignored.
If the material properties do not vary significantly (for example, the
percentage change is < 20%), the problem can be assumed to be
linear steady state.
Likewise, if the effect of body forces such as gravitational force is
overwhelmed by forces responsible for bulk fluid flow, natural
convection can be ignored.
Geometrical symmetry, if present, should be used to avoid the need
to create a full model.
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Section 6 – Thermal Analysis
Example: Heat Sink Assembly
Module 4: Steady State Heat Transfer
Page 7
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A heat sink assembly is a
common design element in
electronics such as desktop
computers, laptops and audio
systems.
A two-part video presentation for
this module using this example is
available. The second part covers
steady state heat transfer
analysis.
© 2011 Autodesk
20°
B C
Fins
(Aluminium)
Heat Spreader
(Copper)
Microprocessor
(Silicon)
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40
Watts
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Section 6 – Thermal Analysis
Summary
Module 4: Steady State Heat Transfer
Page 8
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Steady state heat transfer conditions are said to occur when a
system is in equilibrium.

For instance, the engine on a car travelling at a constant speed on a
highway would more or less lose a fixed amount of heat every
second.

Steady state heat transfer can be linear or nonlinear.

Nearly all real life examples are nonlinear; however, systems can be
approximated as linear if temperature variation is insignificant.
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Section 6 – Thermal Analysis
Summary
Module 4: Steady State Heat Transfer
Page 9
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If the temperature variation is high, thermal properties of substances
involved in heat transfer can change.

For instance: thermal conductivity, fluid density and viscosity
changes due to temperature create a nonlinear system which is
much more complicated to solve than a linear system.

If thermophysical properties do not vary significantly, linear analysis
approximation should be used to reduce computational expense.
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