Analytical formulas for calculating the thermal diffusivity of cylindrical shell and spherical shell samples

TL;DR

This paper develops new analytical formulas to calculate the thermal diffusivity of cylindrical and spherical shell samples under radial heat flow, extending previous work on flat samples, with code implementation provided.

Contribution

It generalizes existing formulas to cylindrical and spherical shells for radial heat flow, offering analytical solutions and verification code.

Findings

Derived formulas for cylindrical and spherical shells

Validated formulas with implementation code

Applicable to different heat pulse configurations

Abstract

Calculating the thermal diffusivity of solid materials is commonly carried out using the laser flash experiment. This classical experiment considers a small (usually thin disc-shaped) sample of the material with parallel front and rear surfaces, applying a heat pulse to the front surface and recording the resulting rise in temperature over time on the rear surface. Recently, Carr and Wood [Int J Heat Mass Transf, 144 (2019) 118609] showed that the thermal diffusivity can be expressed analytically in terms of the heat flux function applied at the front surface and the temperature rise history at the rear surface. In this paper, we generalise this result to radial unidirectional heat flow, developing new analytical formulas for calculating the thermal diffusivity for cylindrical shell and spherical shell shaped samples. Two configurations are considered: (i) heat pulse applied on the inner surface and temperature rise recorded on the outer surface and (ii) heat pulse applied on the outer surface and temperature rise recorded on the inner surface. Code implementing and verifying the thermal diffusivity formulas for both configurations is made available.