Complexity matters: Highly-accurate numerical models of coupled radiative–conductive heat transfer in a laser flash experiment

Abstract

Opaque and fully dense solids respond to a laser pulse by absorbing its energy, causing non-uniform heating and thus creating a thermal gradient. Thermalisation by thermal conduction acts to minimise that gradient; monitoring this process as a function of time enables to infer the material properties such as thermal diffusivity. For samples with transparency in the near-infrared region (semi-transparent samples), heat within the sample volume is carried both by radiation and conduction, requiring appropriate adjustments to data processing in laser flash analysis. In experiments where a high-emissivity coating is applied to both faces of a semi-transparent sample, an unconstrained diathermic model is conventionally used, allowing to separate conductive and radiative heat fluxes. At high temperatures, materials with strong anisotropic scattering produce a sharp initial peak on the temperature curve, which this simple model fails to reproduce. A more complex coupled radiative–conductive problem needs to be considered instead. Although the general methods for solving radiative transfer problems had been formulated many decades ago, their numerical implementation is not always straightforward. This paper presents the complete set of algorithms for solving the coupled problem allowing to increase the measurement accuracy. The constituent numerical techniques are cross-verified, and the computational method is validated on a set of experimental data collected from a synthetic alumina sample.