Numerical solution of hyperbolic heat conduction in cylindrical and spherical systems

Abstract

Hyperbolic heat conduction problems in cylindrical and spherical coordinate systems are investigated numerically. Unlike the classical Fourier heat flux model, the thermal wave of such problems propagates with a finite speed. The major difficulty in dealing with such problems is the suppression of numerical oscillations in the vicinity of a jump discontinuity. The proposed numerical method combines the Laplace transform technique for the time domain and the control volume formulation for the space domain. The transformed nodal temperatures are inverted to the physical quantities by using numerical inversion of the Laplace transform. Due to the application of a hyperbolic shape function, it can be seen from the illustrated examples that the present numerical solutions are stable and accurate. The application of the hyperbolic shape function can successfully suppress the numerical oscillations in the vicinity of jump discontinuities. Comparisons with the results obtained from the Fourier law are also presented for some basic problems.