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9

Thermal Analysis

9.1 Introduction
Many engineering problems are thermal problems in nature. Devices such as appliances,
advanced electronics, engines, and heating, ventilation, and air conditioning systems need
to be evaluated for their thermal performance during the design process. In this chap-
ter, we will discuss thermal analysis using the FEA. The objective of thermal analysis is
to understand response and behavior of a structure with thermal loading. The resulting
temperature distribution, heat flux distribution, and structural response under different
thermal loading conditions constitute important knowledge in assuring design success
of thermal engineering products. Both steady-state and transient thermal problems are
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introduced and a heat sink model is analyzed using ANSYS Workbench. Thermal stress
analysis, which is to find the structural response due to change of temperatures, is also
included and discussed.

9.2 Review of Basic Equations
To study heat transfer within an object or between objects, one may conduct thermal anal-
ysis, from which thermal quantities such as the temperature, thermal gradient, and heat
flux distributions can be determined. There are two types of thermal analyses: steady-state
thermal and transient thermal. Steady-state thermal analysis aims to find the temperature or
heat flux distribution in structures when a thermal equilibrium is reached, and transient
thermal analysis sets out to determine the time history of how the temperature profile and
other thermal quantities change with time. In addition, thermal expansion or contraction
of engineering materials often leads to thermal stress in structures, which can be exam-
ined by conducting thermal stress analysis. The basic equations for thermal and thermal
stress analyses are given as follows.

9.2.1 Thermal Analysis

For temperature field in a 1-D space, such as a bar (Figure 9.1), we have the following
Fourier heat conduction equation:

∂ T
f x =− k (9.1)
∂ x

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