ABSTRACT
With the help of modern computers, the heat conduction problem can be easily solved by using the finite-difference energy balance method for complex boundary conditions (BCs). This chapter illustrates the typical numerical grid distribution for two-dimensional heat conduction with given surface temperatures as BCs. The accuracy of the numerical solutions depends on the number of finite-difference grids used for energy balance calculations. In general, the accuracy improves with the increase of grid points. The chapter obtains the discrete temperature distribution by using the finite-difference method. At a given interior point, heat conductions from the neighborhood points are based on the time-step temperatures in order to increase that point temperature during the incremental time-step change. In general, the finite-difference energy balance method (explicit or implicit method) can be used to solve one-dimensional, two-dimensional, and three-dimensional transient heat conduction problems for Cartesian, cylindrical, and spherical coordinates with various BCs.
