Thermal Diffusivity Measurement Based on Thermal/Cooling Excitation: Theory and Experiments

Photothermal methods for measuring thermal diffusivity inherently involve an illposed inverse problem influenced by multiple factors, including sample thickness, heating or cooling duration, and excitation energy. Measurement accuracy becomes particularly challenging under nonimpulsive pulsed excitation when the observation timescale is comparable to the pulse duration. This difficulty arises from poorly defined pulse profiles, broadened thermal responses, and the lack of clear boundary condition criteria - especially under significant interfacial temperature gradients where natural convection dominates (Grashof number Gr gg 2000 ). Although the classic Parker solution is widely used, it is physically unrealistic because it assumes adiabatic heat flux and shallow-region heat absorption. In this study, we demonstrate that Parker's assumption is mathematically equivalent to a Dirac pulse boundary condition. We then derive comprehensive analytical solutions for both thermal and cooling responses under Dirac and rectangular pulse excitations. By comparing these with eigenfunction-based solutions under well-posed boundary conditions, we reveal that Parker's model is valid only before the thermal peak occurs. Through dimensionless analysis, we further show that Parker's solution represents the limiting case of the rectangular pulse model as the heating duration approaches zero. Finally, we propose a novel excitation approach - evaporative cryocooling - for thermal diffusivity measurements. This technique provides a compact, low-cost, and easily implemented alternative to conventional excitation schemes. The theoretical model is further validated through comparison with experimental results.