Heat Transfer Equation With Delay for Media With Thermal Memory

Abstract

A new model for heat transfer in this paper is proposed. It combines idea of medium with memory and phase-lag model. Equation for a temperature field based on new heat transfer model was obtained and investigated with wave-like solutions. New model was compared with common models for non-stationary heat transfer by its wave-like solutions amplitude attenuation, wave length and phase velocity. It was shown that model with memory is equivalent to a hyperbolic model of heat transfer. While new combined model is equivalent with a phase-lag model for a low frequencies but differs for a high frequencies. Both this models predict possibility of undamped thermal waves, but phase-lag model predict a numerous quantity of undumped thermal waves, while combined model predict undumped wave for a one frequency.