Numerical solution of hyperbolic heat conduction problems in the cylindrical coordinate system by the hybrid Green’s function method

Abstract

In the present study, we have analyzed the hyperbolic heat conduction problems in the cylindrical coordinate system using a hybrid Green’s function method. The major difficulty encountered in the numerical solutions of hyperbolic heat conduction problems is the suppression of the numerical oscillations in vicinity of sharp discontinuities (Chen and Lin (1993) [11]). The proposed method combines the Laplace transform for the time domain, Green’s function for the space domain and ε-algorithm acceleration method for fast convergence of the series solution. Six different examples included the one-, two- and three-dimensional problems have been analyzed by the present method. It is found from these examples that the present method does not exhibit numerical oscillations at the wave front and the propagation of the two- and three-dimensional thermal wave becomes so complicated because it occur jumping discontinuities, reflections and interactions in these numerical results of the hyperbolic heat conduction problem.