Fundamental Solutions of the Equations of Classical and Generalized Heat Conduction Models

A. A. Orekhov, L. N. Rabinskiy, G. Fedotenkov
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引用次数: 0

Abstract

This article presents the mathematical formulations of transient heat conduction problems corresponding to the models of classical heat conduction using the Fourier law and generalized heat conduction based on the Cattaneo–Vernotta–Lykov law (Maxwell–Cattaneo model), as well as the generalized Green–Nagdy type II and III models. The Fourier transforms in spatial coordinates and the Laplace transforms in time were used to obtain the fundamental solutions of the equations of the Maxwell–Cattaneo and Green–Nagdy type II and III models of classical and generalized heat conduction. The results were displayed graphically and analyzed. Differences between the considered heat conduction models were shown, and suggestions for their practical application were given.
经典和广义热传导模型方程的基本解法
本文介绍了与使用傅立叶定律的经典热传导模型和基于 Cattaneo-Vernotta-Lykov 定律的广义热传导模型(Maxwell-Cattaneo 模型)以及广义 Green-Nagdy II 型和 III 型模型相对应的瞬态热传导问题的数学公式。利用空间坐标的傅立叶变换和时间的拉普拉斯变换,获得了经典和广义热传导的 Maxwell-Cattaneo 模型、Green-Nagdy II 型和 III 型模型方程的基本解。结果以图形显示并进行了分析。显示了所考虑的热传导模型之间的差异,并对其实际应用提出了建议。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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