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arXiv · 1902.00401

Non-local effects and size-dependent properties in Stefan problems with Newton cooling

Marc Calvo-Schwarzwälder
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Abstract

We model the growth of a one-dimensional solid by considering a modified Fourier law with a size-dependent effective thermal conductivity and a Newton cooling condition at the interface between the solid and the cold environment. In the limit of a large Biot number, this condition becomes the commonly used fixed-temperature condition. It is shown that in practise the size of this non-dimensional number is very small. We study the effect of a small Biot number on the solidification process with numerical and asymptotic solution methods. The study indicates that non-local effects become less important as the Biot number decreases.

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Marc Calvo-Schwarzwälder. 2019-02-01. Non-local effects and size-dependent properties in Stefan problems with Newton cooling. https://doi.org/10.1016/j.apm.2019.06.008

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