Variable mass and thermal properties in three-dimensional viscous flow: Application of Darcy law

This article concentrates on the properties of three-dimensional magneto-hydrodynamic flow of a viscous fluid saturated with Darcy porous medium deformed by a nonlinear variable thickened surface.Analysis of flow is disclosed in the neighborhood of stagnation point.Features of heat transport are characterized with Newtonian heating and variable thermal conductivity.Mass transport is carried out with first order chemical reaction and variable mass diffusivity.Resulting governing equations are transformed by implementation of appropriate transformations.Analytical convergent series solutions are computed via homotopic technique.Physical aspects of numerous parameters are discussed through graphical data.Drag force coefficient,Sherwood and Nusselt numbers are illustrated through graphs corresponding to various pertinent parameters.Graphical discussion reveals that conjugate and constructive chemical reaction parameters enhance the temperature and concentration distributions,respectively.

Space-Fractional Diffusion with Variable Order and Diffusivity:Discretization and Direct Solution Strategies

We consider the multidimensional space-fractional diffusion equations with spatially varying diffusivity and fractional order.Significant computational challenges are encoun-tered when solving these equations due to the kernel singularity in the fractional integral operator and the resulting dense discretized operators,which quickly become prohibitively expensive to handle because of their memory and arithmetic complexities.In this work,we present a singularity-aware discretization scheme that regularizes the singular integrals through a singularity subtraction technique adapted to the spatial variability of diffusiv-ity and fractional order.This regularization strategy is conveniently formulated as a sparse matrix correction that is added to the dense operator,and is applicable to different formula-tions of fractional diffusion equations.We also present a block low rank representation to handle the dense matrix representations,by exploiting the ability to approximate blocks of the resulting formally dense matrix by low rank factorizations.A Cholesky factorization solver operates directly on this representation using the low rank blocks as its atomic com-putational tiles,and achieves high performance on multicore hardware.Numerical results show that the singularity treatment is robust,substantially reduces discretization errors,and attains the first-order convergence rate allowed by the regularity of the solutions.They also show that considerable savings are obtained in storage(O(N^(1.5)))and computational cost(O(N^(2)))compared to dense factorizations.This translates to orders-of-magnitude savings in memory and time on multidimensional problems,and shows that the proposed methods offer practical tools for tackling large nonlocal fractional diffusion simulations.

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.