ABSTRACT
This chapter examines finite difference representation and solution of one-dimensional, steady-state problems in Cartesian, cylindrical, and spherical coordinates. It considers the diffusive and convective systems, and discusses the effects of flow on the numerical stability of the resulting finite difference equations. The correct choice of the interpolation functions is one of the most critical steps when solving the conservation equations. One of the first attempts to approximate the derivatives at the boundaries of the control volumes was by using the finite difference central differencing scheme. The chapter briefly introduces the finite volume method for solving diffusive–convective problems. The problems of steady-state heat flow through fins or extended surfaces are typical examples of one-dimensional heat conduction where a partial lumping formulation is used; that is, gradients are approximated by the boundary conditions in the fin cross section. Applications of fins include, heat transfer in internal combustion engines, automobile radiators, boiler tubes, electrical transformers, electronic equipment cooling, and heat transfer enhancement.
