Stagnation-Point Flow Towards a Heated Porous stretching Sheet Through a Porous Medium with Thermal Radiation and Variable Viscosity

An analysis is made for the steady two-dimensional stagnation-point flow in a porous medium of an incompressible viscous fluid towards a permeable stretching surface with variable viscosity and thermal radiation. The viscosity of the fluid is assumed to be an inverse linear function of the fluid temperature. The stretching velocity and the surface temperature are assumed to vary linearly with the distance from the stagnation point. The governing equations for the problem where changed to dimensionless ordinary differential equations using scaling group of transformations. The transformed governing equations in the present study were solved numerically by using Rung-Kutta and Shooting method. Favorable comparison with previously published work is performed. A comparison between the analytical and numerical solutions has been included. The numerical solutions are presented to illustrate the influence of the various values of the ratio of free stream velocity and stretching velocity, the viscosity variation parameter and the porosity parameter. These effects of the different parameter on the velocity and temperature profiles in the boundary layer as well as the coefficient of heat flux and shearing stress at the surface are presented graphically to show interesting aspects of the solution.

Similarity Solution for Free Convection Flow of a Micropolar Fluid under Convective Boundary Condition via Lie Scaling Group Transformations

The free convective flow of an incompressible micropolar fluid along permeable vertical plate under the convective boundary condition is investigated. The Lie scaling group of transformations is applied to get the similarity representation for the system of partial differential equations and then the resulting systems of equations are solved using spectral quasi-linearisation method. A quantitative comparison of the numerical results is made with previously published results for special cases and the results are found to be in good agreement. The results of the physical parameters on the developments of flow, temperature, concentration, skinfriction, wall couple stress, heat transfer, and mass transfer characteristics along vertical plate are given and the salient features are discussed.

Application of Scaling Group of Transformations to Steady Boundary Layer Flow of Newtonian Fluid over a Stretching Sheet in Presence of Chemically Reactive Species

This investigation analyses application of Lie’s scaling group of transformations to steady flow of a Newtonian fluid over a stretching sheet in presence of chemically reactive species with first order reaction. The governing partial differential equations reduced to self-similar nonlinear ordinary differential equations by the transformations. Obtained momentum equation is solved analytically and the concentration equation is numerically solved applying finite difference method with Thomas algorithm. The plotted results reveal that with the increase of Schmidt number as well as reaction-rate parameter causes a reduction in the thickness of the concentration boundary layer and also the concentration at a point decreases.DOI: http://dx.doi.org/10.3329/jbas.v35i1.7969Journal of Bangladesh Academy of Sciences, Vol.35, No.1, 43-50, 2011

Similarity Solutions of the MHD Stagnation-Point Flow over a Power-Law Stretching Sheet

A similarity analysis is performed for a steady laminar boundary layer stagnation-point flow of an electrically conducting fluid in a porous medium subject to a transverse non-uniform magnetic field past a non-linear stretching sheet. A scaling group of transformations is applied to get the invariants. Using the invariants, a third order ordinary differential equation corresponding to the momentum is obtained. We show the existence and uniqueness of convex and concave solutions for the power law exponent, according to the values of magnetic parameter, permeability parameter and velocity ratio parameter.

SCALING GROUP OF TRANSFORMATIONS FOR BOUNDARY LAYER STAGNATION‐POINT FLOW THROUGH A POROUS MEDIUM TOWARDS A HEATED STRETCHING SHEET

An analysis is performed to investigate the structure of the boundary layer stagnation‐point flow and heat transfer of a fluid through a porous medium over a stretching sheet. A scaling group of transformations is applied to get the invariants. Using the invariants, a third and a second order ordinary differential equations corresponding to the momentum and energy equations are obtained respectively. The equations are then solved numerically. It is found that the horizontal velocity increases with the increasing value of the ratio of the free stream velocity (ax) and the stretching velocity (ax). The temperature decreases in this case. At a particular point of the stretching sheet, the fluid velocity decreases or increases with the increase of the permeability of the porous medium when the free stream velocity is less or grater than the stretching velocity.