Effective Thermal Diffusivity in Real Solid

TL;DR

This paper evaluates the effective thermal diffusivity of a two-dimensional real solid with a periodic surface, revealing it is always less than the local diffusivity regardless of the model.

Contribution

It introduces a method to compute effective thermal diffusivity considering surface periodicity and provides a universal conclusion about its relation to local diffusivity.

Findings

Effective diffusivity is always less than local diffusivity.

The scale factor for conformal transformation is derived.

The conclusion holds across different models.

Abstract

The effective thermal diffusivity is evaluated for a two dimensional real solid and the real solid is modeled with periodic surface. The result contain the scale factor for the conformal transformation that flattens the surface. We find that the effective thermal diffusivity is always less than the local thermal diffusivity and this conclusion is independent of the model.