Numerical study of dual-phase-lag heat conduction in a thermal barrier coating with a hybrid method

Abstract

In this study, the dual-phase-lag (DPL) heat conduction model is applied to study the non-Fourier heat transfer in a thermal barrier coating (TBC) structure subjected to heat flux on the exterior of the coating. An efficient numerical scheme involving the hybrid application of the Laplace transform and control volume methods in conjunction with hyperbolic shape functions is used to solve the hyperbolic heat conduction equations in the linearized form of DPL model. The transformed nodal temperatures are inverted to the physical quantities using numerical inversion of the Laplace transform. Parametric studies of properties of the substrate and the coating on the temperature distributions in the TBC are performed. A comparison between the present study and other work in the literature using the thermal wave model is also made. The results also show that the phase lag of heat flux tends to induce thermal waves with sharp wave fronts separating heated and unheated zones in the structure, while the phase lag of temperature gradient results in non-Fourier diffusion-like conduction and smooths the sharp wave fronts by promoting conduction into the medium.