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 temperature 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 nonphysical 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.

研究了受对流冷却和内部指数热源的二维固体中的热扩散和波动现象。扩散和 Cattaneo-Vernotte (C-V) 热传导模型均使用叠加原理和解结构定理求解。出于比较的目的，对这两个模型进行求解以证明该技术的灵活性并显示结果之间的差异。在暴露表面冷却时，峰值温度出现在介质内部而不是暴露表面。由于热滞后现象，C-V 模型的峰值温度预测高于传统扩散模型的峰值温度。由于 C-V 模型中固有的热弛豫特性，能量传输采用波传播的形式，而不是在扩散模型中以非物理无限速度的瞬时能量传输。该研究证明了解结构定理在解决具有复杂边界条件和热载荷的二维固体中的传导传热问题方面的灵活性。