Two-Dimensional Analysis of Solids Subjected to Exponential Heating and Surface Convection Using Thermal Diffusion and Propagation Models

摘要

Thermal diffusion and wave phenomena in a two-dimensional solid subjected to convective cooling and an internal exponential heat source are investigated. Both diffusion and Cattaneo-Vernotte (C-V) heat conduction models are solved using the superposition principle in conjunction with the solution structure theorems. For comparison purposes, both models are solved to demonstrate the flexibility of the technique and to show differences between the results. With cooling at the exposed surface, peak temperatures occur in the interior of the medium instead of at exposed surfaces. Peak temperatures predictions from the C-V model are higher than those from a conventional diffusion model due to the thermal lagging phenomenon. Because of the inherent thermal relaxation characteristic in the C-V model, energy transport takes the form of wave propagation rather than instantaneous energy transport at a non-physical infinite speed as seen in the diffusion model. The study demonstrates the flexibility of the solution structure theorems in solving conduction heat transfer problems in two-dimensional solids with complex boundary conditions and heat loads.