Study of hyperbolic heat conduction problem in IC chip

The hyperbolic heat conduction equation is applied to investigate the rapid transient heat conduction in IC chip instead of the classical Fourier equation. The present study applies an analytical method and a hybrid numerical scheme of the Laplace transform technique and the control volume method in conjunction with the hyperbolic shape functions to investigate the present problem. For the numerical scheme, the Laplace transform method is used to remove the time-dependent terms in the governing differential equation and the boundary conditions, and then the transformed equations are discretized by the control volume scheme. The analytical solution is obtained from a simple mathematical analysis. In order to evidence the reliability and accuracy of the present results, a comparison between the present numerical results and the analytical solution is made. The results show that the present numerical results do not exhibit numerical oscillations in the vicinity of the jump discontinuity and agree well with the analytic solution. It can also be observed that the time derivative of the heat generation and the relaxation time play the important role in the present problem and the non-Fourier effects are significant only for short times.