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

Purpose 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. Design/methodology/approach 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. Findings 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. Originality/value 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.

Analysis of a Hyperbolic Heat Conduction-Radiation Problem With Temperature Dependent Thermal Conductivity

This article deals with the analysis of a hyperbolic conduction and radiation heat transfer problem in a planar participating medium. Thermal conductivity of the medium is temperature dependent. Hyperbolic conduction is due to non-Fourier effect. The boundaries of the medium can be either at prescribed temperatures and/or fluxes. With both boundaries insulated, effects of a short pulse internal heat source in the medium are also considered. The problem is analyzed using the lattice Boltzmann method. The finite volume method is employed to compute the radiative information required. Transient temperature distributions in the medium are studied for the effects of various parameters.

New Interpretation of Non-Fourier Heat Conduction in Processed Meat

This work uses the “dual phase lag” (DPL) model of heat conduction to offer a new interpretation for experimental evidence of non-Fourier conduction in processed meat that was interpreted previously with hyperbolic conduction. Specifically, the DPL model combines the wave features of hyperbolic conduction with a diffusion-like feature of the evidence not captured by the hyperbolic case. In addition, comparing the new interpretation to Fourier-based alternatives suggests that further study of all the interpretations could help advance the understanding of conduction in the processed meat and other biological materials such as human tissue.