ABSTRACT

This chapter focuses on the solution of both steady- and unsteady-state heat conduction problems by the finite-difference method. The essence of the finite-difference method consists of replacing the pertinent differential equation and boundary conditions by a set of algebraic equations. The chapter presents the fundamentals of the method and discusses the solution of finite-difference equations by numerical and graphical means. The finite-element method is another numerical method of solution. This relatively new method is not as straightforward, conceptually, as the finite-difference method, but it has several advantages over the finite-difference method in solving conduction problems, particularly for problems with complex geometries. The finite-difference representation of the heat conduction equation together with the boundary conditions of a steady-state problem results in a system of algebraic equations. The chapter considers the finite-difference formulation of problems in cylindrical coordinates. Finite-difference equations are algebraic equations that are solved numerically, and the numerical calculations are carried out only to a finite number of decimal places.