Fundamentals of Heat and Mass Transfer

Chapter 3

General Differential Equations for Heat Conduction

3.1 Introduction

In heat transfer analysis, one of our objectives is to determine the temperature distribution within the body at any given instant, i.e. the temperature at every point in the body, taken as a continuum. Then, we can calculate the heat transfer rate at any point in a given direction by applying the Fourier’s law. Knowledge of temperature distribution is also required in other fields of engineering analysis; e.g. in calculation of thermally induced stresses, thermal expansion , optimum thickness of insulation, etc.

General technique to obtain the temperature distribution over the entire body is to consider a differential control volume within the body and apply the ...