Nasser S. Elgazery

Chebyshev finite difference method for MHD flow of a micropolar fluid past a stretching sheet with heat transfer

In this paper, the problem of heat transfer to MHD flow of a micropolar fluid from a stretching sheet with suction and blowing through a porous medium is studied numerically by using Chebyshev finite difference method (ChFD). A similarity solution to governing momentum, angular momentum and energy equations is derived. The effects of surface mass transfer, Prandtl number, magnetic field and porous medium on the velocities and temperature profiles have been studied. The numerical results indicate that, the velocity and the angular velocity increase as the permeability parameter increases but they decrease as the magnetic field increases. Also, the temperature decreases as the permeability parameter increases but it increases as the magnetic field increases.

Effect of inclined magnetic field on magneto fluid flow through a porous medium between two inclined wavy porous plates (numerical study)

In this paper, the problem of an incompressible viscous fluid moving through a porous medium (Brinkmain model) between two inclined wavy porous plates under the effects of a constant inclined magnetic field that makes an angle with the vertical axis and constant suction (or injection) is studied numerically by a method related to that of Takabatake-Ayukawa in 1982. The present approach is not restricted by any of the parameters appearing in the problem such as Reynolds number, Froude number, magnetic parameter, suction (or injection) parameter, permeability parameter, wave number and amplitude ratio. The effects of the above variable parameters on the velocity, stream function and pressure gradient profiles have been studied. Moreover, the effect of varying the Froude number and the inclined angle on the pressure gradient and pressure rise is studied.

Effects of Viscous Dissipation and Joule Heating on Natural Convection Flow of a Viscous Fluid from Heated Vertical Wavy Surface

A mathematical model will be analyzed in order to study the effects of viscous dissipation and Ohmic heating (Joule heating) on magnetohydrodynamic (MHD) natural convection flow of a temperature dependent viscosity from heated vertical wavy surface. The present physical problem is studied numerically by using the appropriate variables, which reduce the complex wavy surface into a flat one. An implicit marching Chebyshev collocation scheme is employed for the analysis. Numerical solutions are obtained for velocity, temperature, local skin friction, and Nusselt number for a selection of parameter sets consisting of Eckert number, Prandtl number, MHD variation, and amplitude-wavelength ratio parameter. Numerical results show that these parameters have significant influences on the velocity and the temperature profiles as well as for the local skin friction and Nusselt number

THE EFFECT OF VARIABLE THERMAL CONDUCTIVITY ON MICRO-POLAR FLUID FLOW BY CHEBYSHEV COLLOCATION METHOD

In this article, the authors analyzed the effect of thermal conductivity on unsteady magnetohydrodynamic (MHD) free convection in a micro-polar fluid past a semi-infinite vertical porous plate. The fluid thermal conductivity is assumed to vary as a linear function of temperature. By using the Chebyshev collocation method in the spatial direction and the Crank-Nicolson method in the time direction, the boundary layer equations are transformed into a linear algebraic system. There are several material parameters whose affect on the flow have been studied, for instance, thermal conductivity, radiation, magnetic, micro-polar, suction (or injection) parameters, and Prandtl number. Boundary layer and Boussineq approximations have been introduced together to describe the flow field. The domain of the problem is discretized according to the Chebyshev collocation scheme. The numerical results show that, the values of velocity, angular velocity and temperature profiles approach to the steady state when the time reach to infinity. However, the friction factor has been found to increase as micro-polar and thermal conductivity parameters increase. But it decreases as magnetic parameter increases. Meanwhile, Nusselt number increases as thermal conductivity parameter increases, and vice versa with the micro-polar parameter. Moreover, the local couple stress has been found to decrease as micro-polar and thermal conductivity parameters increase. On the other hand, it increases as magnetic parameter increases.

Numerical Study of a Magneto-fluid Motion Through a Porous Medium Between Two Wavy Plates with Constant Suction

Abstract In this note, the problem of an incompressible viscous fluid moving through a porous medium (Brinkman model) between two wavy plates under the effects of a constant inclined magnetic field that makes an angle with the vertical axis and constant suction, are studied numerically by a method related to the method of Takabatake and Ayukawa in 1982. The present approach is not restricted by any of the parameters appearing in the problem such as Reynolds number, magnetic parameter, suction parameter, the wave number and amplitude ratio. The variations in velocity, flow rate and pressure gradient with the above governing parameters are presented. Moreover, the effect of varying the porous medium and the inclined angle is also studied.