Construction and Analysis of a Discrete Heat Equation Using Dynamic Consistency: The Meso-Scale Limit

Mickens, Ronald, Clark Atlanta University
Washington, Talitha, Clark Atlanta University

2023-01

2020-2029

We present and analyze a new derivation of the meso-level behavior of a discrete microscopic model of heat transfer. This construction is based on the principle of dynamic consistency. Our work reproduces and corrects, when needed, all the major previous expressions which provide modications to the standard heat PDE. However, unlike earlier efforts, we do not allow the microscopic level parameters to have zero limiting values. We also give insight into the difficulties of constructing physically valid heat equations within the framework of the general mathematically inequivalent of difference and differential equations.

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arXiv

Clark Atlanta University

http://hdl.handle.net/20.500.12322/cau.ir:2023_washington_talitha

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