Approximate solutions to three-dimensional unsteady heat conduction through plane flaws within anisotropic media using a perturbation method

Abstract

This paper studies the analytical solution of three-dimensional thermal conduction in an anisotropic medium containing one or several plane flaws. This problem is typical of one or several delaminations within a composite material. The method proposed here consists in applying a Laplace transform on the time variable followed by a Fourier integral transform on space variables (Cartesian geometry). The numerical or semi-analytical true solutions for the integral equations generated by this problem may be very time consuming, especially in a three-dimensional configuration. Therefore, we suggest a modelling reduction using a first order analytical perturbation method, which is subsequently improved by applying Padé's approximant approach. The latter formalism leads to a better tracking of the true solution and increases the validity field of the perturbed approximation.