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Critical times in multilayer diffusion. II: approximate solutions. (English) Zbl 1177.80023

Summary: Traditional averaging methods for multilayer diffusion give inaccurate approximations of critical time behaviour, such as the heating time of a material. In particular, they fail to capture the importance of layer order. We use a perturbation expansion of an exact solution to find a simple approximate solution which accurately describes the critical time for transport across multiple layers. This approximate solution is then used to find a correction for the averaging method which captures the key critical time behaviour.

MSC:

80A20 Heat and mass transfer, heat flow (MSC2010)
80M25 Other numerical methods (thermodynamics) (MSC2010)

Software:

Maple
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References:

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