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This paper presents an application of the spectral homotopy analysis method (SHAM) to solve a problem of darcy-forcheimer mixed convection flow in a porous medium in the presence of magnetic field, viscous dissipation and thermopherisis. A mathematical model governed the flow is analyzed in order to study the effects of chemical reaction, magnetic field, viscous dissipation and thermophoresis on mixed convection boundary layer flow of an incompressible, electrically conducting fluid past a heated vertical permeable flat plate embedded in a uniform porous medium. The similarity variable is used to transform the governing equations into a boundary valued problem of coupled ordinary differential equations which are then solved using spectral homotopy Analysis Method. The spatial domains are discretized using Chebyshev-Gauss-Lobatto points and numerical computations are carried out for the non-dimensional physical parameters. A parametric study of selected parameters is conducted and the results for the velocity, temperature and concentration are illustrated graphically and physical aspects of the problem are discussed.

In this article, a comparative analysis of free convective Blasius and Sakiadis flows of a viscous fluid over a vertical porous surface is presented. The relationship between the flow rate and pressure drop as the Newtonian fluid flows past a porous medium is linear; hence Darcy model is adopted. Suitable similarity variables are employed to transform the governing non-linear partial differential equations into a set of coupled non-linear ordinary differential equations. An approximate analytical solution of the coupled ordinary differential equation is obtained using Optimal Homotopy Analysis method (OHAM). The computational results for velocity and temperature profiles are shown graphically for various flow parameters and analyzed. The results show that an increase in convective parameter leads to increase in velocity and temperature profiles. Also, increasing buoyancy parameter increases the velocity profile and decreases the temperature profiles for both Sakiadis and Blasius flow. The temperature distribution at the maximum value of Prandtl in Sakiadis case is greater than the temperature distribution at the maximum value of Prandtl even in Blasius case.

Boundary layer flow has great importance in engineering applications such as oil bed recovery, filtration, thermal insulations, heat exchangers, geothermal analysis and so on. This paper investigated the effects of heat radiation, soret and dufour in the presence of suction or injection on a boundary layer flow over a porous wedge. The governing equations with the boundary conditions are non-dimensionalized by introducing some non-dimensional variables. The flow model is described in terms of a highly coupled and nonlinear system of partial differential equations as the method of solution seeks to decouple the original system to form a sequence of equations corresponding to the momentum, energy and concentration equations that is solved in a computationally efficient manner. The resulting equations are solved using a numerical technique called Bivariate Spectral Relaxation Method (BSRM). Numerical calculations are carried out for different values of dimensionless parameters and the analysis of the physical parameters of engineering applications are investigated. Effects of these major parameters on transport behaviors are investigated and typical results are illustrated to reveal the effect of pertinent parameter on the velocity, temperature, concentration profiles of the flow. The effects on the local skin friction, local nusselt and Sherwood number are also presented in the tables.

An approximate analysis of the problem of the transient free convective transfer flow of a Newtonian non-gray optically thin fluid past an isothermal vertical oscillating porous plate in the presence of chemical reaction and heat generation/absorption is studied. The dimensionless governing coupled linear partial differential equations are solved using a spectral relaxation method. The essence of the method of the solution-spectral relaxation method SRM is to linearize and decouple the original system of PDEs to form a sequence of independent linear equations that can be solved iteratively. The SRM approach applies the spectral collocation method and a finite different method independently in all underlying independent variables to obtain approximate solutions of the problem. Detailed computations on the influence of the chemical reaction parameter A 2 , the thermal radiation parameter R, the number Sc, the heat absorption/generation parameter Q 1 , and the Prandtl number on the flow velocity, temperature, and concentration distributions are illustrated graphically and in table format. It is observed that the flow velocity increases with the increase in either thermal radiation or thermal Grashof number. The temperature profile increases with the increase in either the thermal radiation parameter or the heat absorption/generation parameter. The rate of heat transfer decreases with the increase in the thermal radiation parameter, whereas it increases with increasing value of the heat generation/absorption parameter.