High order numerical simulation of non-Fourier heat conduction: An application of numerical Laplace transform inversion

Non-Fourier heat conduction phenomenon in a finite slab with insulated boundaries is investigated in the present paper. Since solving the hyperbolic heat conduction equation analytically requires considerable effort, a new high-order numerical approach has been implemented to achieve comparable exactitude. This method solves the considered equation in Laplace space and numerical inversion is employed with the intention of transformation to temporal domain. In order to examine numerical accuracy of this method, Dirac delta heat flux is applied to the assumed medium and results were compared with those of the analytical solution. It was observed that numerical values follow exact ones, at least up to the seventh order of accuracy. In addition, Step and Triangular heat pulses in the medium were studied to reveal temporal and spatial non-Fourier heat conduction characteristics. It was found that in large values of Ve number, for various kinds of heat fluxes carrying the same amount of energy, temperature distribution varies conspicuously through the medium; nevertheless, at each pass of heat wave, a specific point experiences a definite rise of temperature regardless of the type of heat flux provided that the same conditions are present.