Non-Fourier heat conduction in a hollow sphere with periodic surface heat flux

摘要

Presented is the analysis of non-Fourier effect in a hollow sphere exposed to a periodic boundary heat flux. The problem is studied by deriving an analytical solution of the hyperbolic heat conduction equation. Using the obtained analytical expression, the temperature profiles at outer and inner surfaces of the sphere are evaluated for various thermal relaxation times. By comparing the results of non-Fourier model with those obtained from Fourier heat conduction equation, the transition process from parabolic model to hyperbolic one is shown. The phase difference and amplitude ratio of boundary surfaces are calculated as functions of the thermal relaxation time and the results are depicted graphically.