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6
Transient Heat Conduction
Analysis
6.1 Introduction
In the previous chapters, we have discussed steady state heat conduction in which the
temperature in a solid body was assumed to be invariant with respect to time. However,
many practical heat transfer applications are unsteady (transient) in nature and in such
problems the temperature varies with respect to time. For instance, in many components
of industrial plants such as boilers, refrigeration and air-conditioning equipment, the heat
transfer process is transient during the initial stages of operation. Other transient processes
include crystal growth, casting processes, drying, heat transfer associated with the earth’s
atmosphere, and many more. It is therefore obvious that the analysis of transient heat
conduction is very important.
Analytical techniques such as variable separation, which are employed to solve transient
heat conduction problems, are of limited use (Ozisik 1968), and a solution for practical heat
transfer problems by these methods is difficult. Thus, it is essential to develop numerical
solution procedures to solve transient heat conduction problems. In the following section,
a simplified analytical method for the solution of transient problems is presented before
discussing the finite element solution for such problems in Section 6.3.
6.2 Lumped Heat Capacity System
In this section, we consider the transient analysis of a body in which the temperature is
assumed to be constant at any point within and on the surface of the body at any given
instant of time. It is also assumed that the temperature of the whole body changes uniformly
with time. Such an analysis is called a lumped heat capacity method and is a simple and
approximate procedure in which no spatial variation in temperature is allowed. The change
Fundamentals of the Finite Element Method for Heat and Fluid Flow R. W. Lewis, P. Nithiarasu and K. N. Seetharamu
2004 John Wiley & Sons, Ltd ISBNs: 0-470-84788-3 (HB); 0-470-84789-1 (PB)
