Improved lumped-differential formulations in hyperbolic heat conduction

The present work aims at applying the ideas in the so-called Coupled Integral Equations Approach (CIEA) to the one-dimensional thermal wave propagation problem in a finite solid medium, leading to improved lumped-differential formulations through Hermite-type approximations for integrals. The application of CIEA methodology makes it possible to reduce the partial differential equation governing the hyperbolic heat conduction problem to a simple system consisting of two or three ordinary differential equations for the average and surface temperatures, depending on the choice of the Hermite-type approximation. The Runge-Kuta method, enclosed in the IVPRK routine from IMSL Library [1], is used to solve the system of ordinary differential equations. Results for the average and surface temperatures are computed for different thermal relaxation times.