Highly Accurate Compact Difference Scheme for SPL Heat Conduction Model of General Body

Abstract

Abstract Heat transport based on SPL model is of vital importance in microtechnological applications. The heat transport equation is different from the traditional heat conduction equation due to the presence of lagging parameter. In this article, the heat transport in the general body based on SPL heat conduction model under Neumann (insulated) boundary condition is solved by high-order compact difference scheme. The solution is obtained by extending the idea of Dai for discretising Neumann (insulated) boundary condition of heat conduction to the SPL heat conduction model and avoid the need of discretising Neumann boundary conditions. The stability of the numerical scheme has been discussed and observed that the present scheme is unconditionally stable. Model is validated for the thin film of silicon and found that SPL model give the satisfactory results in the macro- and microtemporal scales and up to microspatial scale. A numerical example of particular interest has been studied and discussed in details.