Analytical Solutions of Heat Conduction Problems

Abstract

The following thesis deals with the analytical methods which are in vogue for solving problems to the area of heat conduction. There have been discussed two methods, an old method known as the HEAT BALANCE INTEGRAL METHOD, and a relatively newer method christened as the DIFFERENTIAL TRANSFORMATION METHOD. The latter is dealt with first, as it is easier of the two. Dealing involves the basic idea of the method used, followed by the general theorems adopted. Two problems follow, illustrating the ease of use of this method, along with a comparison with the solutions of the problem using the numerical methods.
The former method, on the other hand, is more of an assumptive method, where one has to guess a temperature profile for proceeding. This is, nonetheless, a very accurate method, albeit a long one. Similar comparisons have been made for this method, like the ones made for the DT method.
The reader may use either method with ease, as it was for the simplification of the problem that these methods were developed.