Green's functions, temperature and heat flux in the rectangle

Steady heat conduction in the rectangle is treated with the method of Green 's functions. Single-sum series for the Green's functions are reported in t erms of exponentials which have better numerical properties than hyperbolic functions. Series expressions for temperature and heat flux caused by spat ially uniform effects are presented. The numerical convergence of these ser ies is improved, in some cases by a factor of 1000, by replacing slowly con verging portions of the series with fully summed forms. This work is motiva ted by high-accuracy verification of finite-difference and finite-element c odes. (C) 2001 Elsevier Science Ltd. All rights reserved.