Hyperbolic heat propagation in a spherical solid medium under extremely high heating rates

摘要

Thermal wave propagation in a spherical medium with a sudden temperature change or a uniform and time-varying heat flux prescribed on its surface is considered.The non-stationary heat conduction problem involving a high rate of change of temperature is studied by assuming a non-vanishing value of the thermal relaxation time for solid medium,i.e. by employing the hyperbolic heat conduction equation.The analytical expressions of the temperature field in the sphere under these two different cases are determined respectively.The variations of non-Fourier temperature profiles under different conditions are calculated and analyzed.Comparisons with the solutions obtained for parabolic heat conduction are also performed.