Improved lumped-differential formulations in hyperbolic heat conduction

The present work aims at applying the ideas in the so-called Coupled Integr al Equations Approach (CIEA) to the one-dimensional thermal wave propagatio n problem in a finite solid medium, leading to improved lump ed-differentia l formulations through Hermite-type approximations for integrals. The appli cation of CIEA methodology makes it possible to reduce the partial differen tial equation governing the hyperbolic heat conduction problem to a simple system consisting of two or three ordinary differential equations for the a verage and surface temperatures, depending on the choice of the Hermite-typ e approximation. The Runge-Kuta method, enclosed in the IVPRK routine from IMSL Library [1], is used to solve the system of ordinary differential equa tions. Results for the average and surface temperatures are computed for di fferent thermal relaxation times. (C) 2000 Elsevier Science Ltd.