Fundamentals of Heat and Mass Transfer

Chapter 8

Numerical Methods in Heat Conduction

8.1 Introduction

In chapter 3, we derived the general differential equation for heat conduction in cartesian, cylindrical and spherical coordinates. Subsequently, considering one-dimensional conduction, we solved these differential equations, with appropriate boundary conditions, for cases of simple geometries such as a plane wall, cylinder and sphere and obtained temperature distribution in those geometries; then, by applying Fourier’s law, heat transfer rate was obtained. The analytical solutions obtained for temperature distribution are known as ‘exact solutions’ since temperature at any point in the solid is obtained by applying the equations derived. While getting an exact solution is always ...