A mixed approach to finite element analysis of hyperbolic heat conduction problems

Abstract

Using a non‐Fourier heat conduction (NFHC) hypothesis, the governing equations of thermal wave propagation are established. The resulting differential equations are transformed to integral forms using the Galerkin weighted residual method and then are discretized by a finite element technique. The proposed finite element formulation is verified by comparing the results of analytical and numerical solutions to a number of selected 1‐D problems. A couple of 2‐D sample problems are solved and the responses of the system to various input signals are studied. The proposed mixed approach shows superiority to the conventional finite element solution of hyperbolic heat conduction equation, because of the simultaneous determination of heat fluxes and temperature at each nodal point. The mixed approach is also shown to be capable of capturing the sudden temperature jump due to heat pulses.

Citation

Manzari, M.T. and Manzari, M.T. (1998), "A mixed approach to finite element analysis of hyperbolic heat conduction problems", International Journal of Numerical Methods for Heat & Fluid Flow, Vol. 8 No. 1, pp. 83-96. https://doi.org/10.1108/09615539810197952