Analytical Solution of a Generalized Two-Dimensional Model for Laser-Flash Thermal Diffusivity Measurements

• Published in: Journal of thermophysics and heat transfer 2019-04, Vol.33 (2), p.300-308
• Main Author: Milošević, Nenad D
• Format: Article
• Language: English
• Subjects: Conduction heating; Conductive heat transfer; Diffusivity; Exact solutions; Initial conditions; Integrals; Laser beam heating; Lasers; Mathematical models; Numerical analysis; Penetration depth; Pulse duration; Pulse heating; Sensitivity analysis; Thermal diffusivity; Two dimensional analysis; Two dimensional models
• ISSN: 0887-8722; 1533-6808
• DOI: 10.2514/1.T5436

This paper presents a two-dimensional model that generalizes the use of the laser flash method for thermal diffusivity measurements of homogeneous, opaque, and two-dimensional (2-D) anisotropic solid materials in the form of thin disk-shaped samples. The model employs partial central or annular pulse heating of the front sample side and a temperature detection over a generally decentralized circular surface on the rear or front sample side. A general analytical solution of related 2-D heat conduction problem with boundary and initial conditions that may exist in reality (such as radiation heat transfer between specimen surfaces and the environment, nonuniform pulse heating, finite pulse duration, and laser pulse penetration) is presented in a partial integral form. The solution for the transient temperature over the decentralized detection surface is transformed from a double integral to a single integral, which reduces the processing time in numerical computation. A simplified solution is given for the partial uniform pulse heating, rectangular pulse duration, and negligible laser pulse penetration depth. Following the simplified solution, four different applications of the presented model for the case of the rear-side temperature detection are described, together with an example of a related sensitivity analysis for the selected set of parametric values. The influence of the size and position of the detection surface on the transient temperature response is separately analyzed, and the results are presented in the last section of the paper.