A study of dual phage lag model of heat transfer for solidification of binary eutectic alloy

Abstract

In this paper, we developed a generalized non-Fourier model of energy transfer for solidification of a binary eutectic system (Al-Cu alloy). The mathematical model is divided into three stages: stage I (liquid region), II (liquid and mushy region), and III (liquid, mushy and solid region). The analysis of the model has been done in dimensionless form. This model is a boundary value problem of the system of second-order hyperbolic partial differential equations for Stage I, the moving boundary problem of the System of second-order hyperbolic partial differential equations for Stage II and III. For the solution, we applied Laplace transform technique in Stage I and Legendre wavelet spectral Galerkin method in Stage II and III. The effect of unit-less parameters: Relaxation time, Predvoditelev numbers, dimensionless thermal conductivity, Fourier numbers, Stefan number, solid fraction on temperature, and position of moving interface are discussed in detail. © 2023