Finite volume solution of 2-D hyperbolic conduction with contact resistance

The purpose of this paper is to present a numerical methodology for the solution of non-Fourier conduction in two-dimensional (2-D) heterogeneous materials with contact resistance.

Energy and heat flux equations with time lagging constant are combined to form a 2-D hyperbolic conduction equation in conservational form, and the resulting equation is solved by finite volume method.

The magnitude of contact resistance is inversely proportional to the temperature jump at the contact surface and phonon transmission coefficient between heterogeneous medium. Numerical results show that higher the contact resistance, lower the heat flux through the interface, lower the strength of transmitted wave and higher the strength of reflected wave at the interface. These results are in agreement with physical expectations. Temperature profiles show expected discontinuity at the interface while the heat fluxes are continuous, demonstrating the accuracy of the proposed methodology.

In most available numerical methods for hyperbolic conduction with contact resistance, contact resistances are treated as internal boundaries at which boundary conditions are specified. In the present formulation, contact resistance between two heterogeneous materials is treated as a part of interface transport properties not as an added boundary condition. This approach makes the formulation much simpler and straightforward for multidimensional applications. This approach is never used previously and is original.