A new iterative least square Chebyshev wavelet Galerkin FEM applied to dual phase lag model on microwave drying of foods

Abstract

In this paper, we developed a dual-phase-lag (DPL) model of heat and mass transfer in presence of a source term for microwave drying foods of different geometrical configuration like slab, cylinder or sphere under the most generalized boundary conditions. The particular cases of present model are the diffusion model, Luikov model, Weng-Chang model and Andarwa-Tabrizi model. The proposed model is the most generalized boundary value problem of a coupled system of two hyperbolic second order partial differential equations. Stability analysis of present model is provided. A new iterative least square Chebyshev wavelet Galerkin finite element method provided for solution. The discretization in space and then application of Chebyshev wavelet Galerkin method converts our problem into a coupled system of two most generalized Sylvester equations. The iterative least square method provide solution of coupled system of Sylvester equations. Convergence and stability analysis of present method is discussed in detail. In a particular case of DPL model, the solution obtained by present method is compared with exact solution (Laplace transform technique) and are approximately same. Effect of relaxation time, Fourier number, phase change coefficient, thermo-gradient coefficient, heat generation, radius of the food and diffusion coefficient on heat and mass transfer are discussed in detail. This generalized model and its solution play important role in the study of microwave food drying.