On the Well-Posedness Problem of the Anisotropic Porous Medium Equation with a Variable Diffusion Coefficient

The initial-boundary value problem of an anisotropic porous medium equation■is studied.Compared with the usual porous medium equation,there are two different characteristics in this equation.One lies in its anisotropic property,another one is that there is a nonnegative variable diffusion coefficient a(x,t)additionally.Since a(x,t)may be degenerate on the parabolic boundary∂Ω×(0,T),instead of the boundedness of the gradient|∇u|for the usual porous medium,we can only show that∇u∈L^(∞)(0,T;L^(2)_(loc)(Ω)).Based on this property,the partial boundary value conditions matching up with the anisotropic porous medium equation are discovered and two stability theorems of weak solutions can be proved naturally.

Galerkin Finite Element Study on the Effects of Variable Thermal Conductivity and Variable Mass Diffusion Conductance on Heat and Mass Transfer

This article investigates the effects of variable thermal conductivity and variable mass diffusion coefficient on the transport of heat and mass in the flow of Casson fluid. Numerical simulations for two-dimensional flow induced by stretching surface are performed by using Galerkin finite element method(GFEM) with linear shape functions. After assembly process, nonlinear algebraic equations are linearized through Picard method and resulting linear system is solved iteratively using Gauss Seidal method with simulation tolerance 10^(-8). Maximum value of independent variableη is searched through numerical experiments. Grid independent study was carried out and error analysis is performed.Simulated results are validated by comparing with already published results. Parametric study is carried out to explore the physics of the flow. The concentration increases when mass diffusion coefficient is increased. The concentration and thermal boundary layer thicknesses increase when ?_1 and ? are increased. The effect of generative chemical reaction on concentration is opposite to the effect of destructive chemical reaction on the concentration.