Analysis of two-dimensional steady-state heat transfer in a rectangular region

The objective of this investigation is to apply a new version of the Rayleigh-Ritz method, called the Rayleigh-Schmidt method (RSM), to a two-dimensional heat conduction problem involving a rectangular region with convective boundary conditions on three sides and with or without internal heat generation. Numerical results obtained by using this new technique are compared with those obtained by the conventional Rayleigh-Ritz method (RRM), the finite-difference technique (FDM), the method of Fourier transform (MFT), and the heat balance integral method (HBIM). For the case of a rectangular region in the absence of internal heat generation, the results are also compared with those obtained from an exact solution presented for the first time in this paper. These comparisons indicate that the RSM gives reasonably accurate results in all cases, but that the HBIM is not very accurate when there is internal heat generation. © American Institute of Aeronautics and Astronautics, Inc., 1987. All rights reserved.