Singularly Perturbed Solution of Non-Fourier Temperature Field with Mixed Boundary Value Dual-Phase Delay with Thermal Conductivity Jumps

Abstract

Based on the properties of laminates, a class of nonlinear singularly perturbed mixture equations with discontinuous coefficients over bounded domains is constructed by using a dual-phase delayed heat conduction model. First, the singular perturbation expansion method is used, combined with the corresponding boundary conditions, the partial differential equation method and the Laplace transform method are used to obtain the external solution, the boundary layer, and the corner layer. Secondly, the time-varying temperature field at the discontinuity is obtained, which leads to the asymptotic expansion of the solution. Finally, the consistent validity of the asymptotic solution is obtained through residual estimation.