Thermal Resonance in Hyperbolic Heat Conduction in Porous Media due to Periodic Ohm’s Heating

Abstract

The effect of periodic Ohm’s heating on hyperbolic heat conduction in porous media is studied analytically with the objective of identifying the thermal resonance conditions. Local thermal equilibrium conditions are assumed to apply. The paper focuses initially on the temperature solution and looks at the conditions required for resonating the temperature signal. The heat flux solution is then evaluated. While a discrete infinite set of modes can be resonated, it is shown that in practice the resonance in the temperature signal is felt starting from moderately small values of Fourier numbers and becomes too small to be noticed if the Fourier number is extremely small. The temperature solution is shown to represent a standing wave the amplitude of which is strongly affected by the Fourier number. While the heat flux solution is shown to differ from the one obtained for the temperature, it also shows similar features such as the standing wave behavior the amplitude of which is strongly affected by the Fourier number.