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Abstract
In this article, the two-dimensional boundary layer problem of Hiemenz flow (two-dimensional flow of a fluid near a stagnation point) of an incompressible micropolar fluid towards a nonlinear stretching surface placed in a porous medium in the presence of transverse magnetic field is examined. The resulting nonlinear differential equations governing the problem have been transformed by a similarity transformation into a system of nonlinear ordinary differential equations which are solved numerically by the Element Free Galerkin method. The influence of various parameters on the velocity, microrotation, temperature, and concentration is shown. Some of the results are compared with the Finite Element Method. Finally, validation of the numerical results is demonstrated for local skin friction for hydrodynamic micropolar fluid flow on a linearly stretching surface.
NOMENCLATURE
| x, y | = | coordinate system |
| u, v | = | component of velocities along |
| N | = | microrotation in boundary layer x and y direction, respectively |
| T | = | temperature in boundary layer |
| Tw, Cw | = | plate temperature and concentration |
| C | = | concentration in boundary layer |
| T∞ | = | free-stream temperature |
| B0 | = | strength of magnetic field |
| C∞ | = | free-stream concentration |
| μe | = | dynamic viscosity of fluid |
| ρ, j | = | fluid density and gyration parameter |
| ν | = | kinematic viscosity of fluid |
| γ, k | = | spin gradient and vortex viscosity |
| kf | = | thermal conductivity |
| kg | = | molecular diffusivity |
| βT | = | thermal expansion coefficient |
| βC | = | concentration expansion coefficient |
| kp | = | permeability of the porous medium |
| β | = | porosity coefficient medium |
| Q0 | = | heat source coefficient |
| σ | = | electrical conductivity |
| cp | = | specific heat at constant pressure |
| f | = | dimensionless flow stream function |
| ω, θ | = | dimensionless microrotation, temperature |
| φ | = | dimensionless concentration |
| Gr | = | thermal Grashof number |
| Gc | = | species Grashof number |
| K | = | Eringen micropolar parameter |
| M | = | magnetic field parameter |
| Rex | = | local Reynolds number |
| Q | = | heat source parameter |
| = | Prandtl number | |
| Sc | = | Schmidt number |
| Nux | = | Nusselt number |