Mostafa A. A. Mahmoud

Slip velocity effect on a non-Newtonian power-law fluid over a moving permeable surface with heat generation

The effects of surface slip and heat generation (absorption) on the flow and heat transfer of a non-Newtonian power-law fluid on a continuously moving surface have been examined. The governing nonlinear partial differential equations describing the problem are transformed to nonlinear ordinary differential equations using suitable transformations. The transformed ordinary differential equations are solved numerically using the fourth order Runge-Kutta method with the shooting technique. Graphical solutions for the dimensionless velocity and the dimensionless temperature are presented and discussed for various values of the slip parameter, the heat generation or absorption parameter and the Eckert number. The results show that the local skin-friction coefficient is decreased as the slip parameter increased. Also, it is found that the local Nusselt number is decreased as the slip parameter or the heat generation parameter increased and the heat absorption parameter has the effect of increasing the local Nusselt number.

A note on variable viscosity and chemical reaction effects on mixed convection heat and mass transfer along a semi-infinite vertical plate.

In the present study, an analysis is carried out to study the variable viscosity and chemical reaction effects on the flow, heat, and mass transfer characteristics in a viscous fluid over a semi-infinite vertical porous plate. The governing boundary layer equations are written into a dimensionless form by similarity transformations. The transformed coupled nonlinear ordinary differential equations are solved numerically by using the shooting method. The effects of different parameters on the dimensionless velocity, temperature, and concentration profiles are shown graphically. In addition, tabulated results for the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are presented and discussed.

Hydromagnetic boundary layer micropolar fluid flow over a stretching surface embedded in a non-darcian porous medium with radiation

We have studied the effects of radiation on the boundary layer flow and heat transfer of an electrically conducting micropolar fluid over a continuously moving stretching surface embedded in a non-Darcian porous medium with a uniform magnetic field. The transformed coupled nonlinear ordinary differential equations are solved numerically. The velocity, the angular velocity, and the temperature are shown graphically. The numerical values of the skin friction coefficient, the wall couple stress, and the wall heat transfer rate are computed and discussed for various values of parameters.

Effects of Slip and Heat Generation/Absorption on MHD Mixed Convection Flow of a Micropolar Fluid over a Heated Stretching Surface

A theoretical analysis is performed to study the flow and heat transfer characteristics of magnetohydrodynamic mixed convection flow of a micropolar fluid past a stretching surface with slip velocity at the surface and heat generation (absorption). The transformed equations solved numerically using the Chebyshev spectral method. Numerical results for the velocity, the angular velocity, and the temperature for various values of different parameters are illustrated graphically. Also, the effects of various parameters on the local skin-friction coefficient and the local Nusselt number are given in tabular form and discussed. The results show that the mixed convection parameter has the effect of enhancing both the velocity and the local Nusselt number and suppressing both the local skin-friction coefficient and the temperature. It is found that local skin-friction coefficient increases while the local Nusselt number decreases as the magnetic parameter increases. The results show also that increasing the heat generation parameter leads to a rise in both the velocity and the temperature and a fall in the local skin-friction coefficient and the local Nusselt number. Furthermore, it is shown that the local skin-friction coefficient and the local Nusselt number decrease when the slip parameter increases.

ON STEADY HYDROMAGNETIC BOUNDARY-LAYER FLOW OF A NON-NEWTONIAN POWER-LAW FLUID OVER A CONTINUOUSLY MOVING SURFACE WITH SUCTION

Analytical studies for the problem of flow and heat transfer of an electrically conducting non-Newtonian power-law fluid with low electrical conductivity on a continuously moving infinite porous plate in the presence of viscous dissipation and a uniform transverse magnetic field have been presented. It is found that steady solutions for dimensionless velocity exist only for a fluid in which its power-law index n satisfies 0.5 < n < 1 with suction at the plate. The problem is also solved numerically by using the shooting method. The results show a good agreement between the analytical and the numerical results. The influences of the magnetic parameter, suction parameter, the power-law index, and the Prandtl number on the velocity and temperature profiles are studied. Also the effects of the various parameters on the skin-friction coefficient and the rate of heat transfer at the surface are discussed and displayed in tables.

HYDROMAGNETIC STAGNATION POINT FLOW TOWARDS A POROUS STRETCHING SHEET WITH VARIABLE SURFACE HEAT FLUX IN THE PRESENCE OF HEAT GENERATION

The influence of heat generation or absorption on the steady, two-dimensional flow of an electrically conducting fluid near a stagnation point on a stretching permeable surface with variable surface heat flux in the presence of a magnetic field is investigated. The governing system of partial differential equations describing the problem are converted into highly non-linear ordinary differential equations using similarity transformation. Numerical solutions of these equations are obtained using the fourth-order Runge-Kutta integration scheme with the shooting method. The effects of the heat generation or absorption parameter and the velocity ratio parameter on the velocity and the temperature are displayed graphically and discussed. The numerical values of the local skin-friction coefficient and the local Nusselt number for various values of physical parameters are presented through tables and discussed.

THE EFFECTS OF VARIABLE FLUID PROPERTIES ON MHD MAXWELL FLUIDS OVER A STRETCHING SURFACE IN THE PRESENCE OF HEAT GENERATION/ABSORPTION

An analysis is performed to investigate the effects of variable viscosity and thermal conductivity on the two-dimensional steady flow of an electrically conducting, incompressible, upper-convected Maxwell fluid in the presence of a transverse magnetic field and heat generation or absorption. The governing system of partial differential equations is transformed into a system of coupled nonlinear ordinary differential equations, and is solved numerically. Velocity and temperature fields have been computed and shown graphically for various values of the physical parameters. The local skin-friction coefficient and the local Nusselt number have been tabulated. It is found that fluid velocity decreases with an increase in the viscosity parameter and the Deborah number. It is also observed that increasing the magnetic parameter leads to a fall in the velocity and a rise in the temperature. Furthermore, it is shown that the temperature increases due to increasing the values of the thermal conductivity parameter and the heat generation parameter, while it decreases with an increase of both the absolute value of the heat absorption parameter and the Prandtl number.

Hydromagnetic Hiemenz Slip Flow of Convective Micropolar Fluid Towards a Stretching Plate

This paper is concerned with the effect of slip velocity on the steady two-dimensional flow of a micropolar fluid near a stagnation point at a stretching plate in the presence of a uniform transverse magnetic field and thermal radiation with the bottom surface of the plate is heated by convection from a hot fluid. The governing system of partial differential equations describing the problem is converted into a system of nonlinear ordinary differential equations using similarity transformation, and then solved numerically using the Chebyshev spectral method. Numerical results for the velocity, microrotation, and temperature are shown graphically and discussed for various values of different parameters. Moreover, the numerical values of the local skin-friction coefficient and the local Nusselt number for these parameters are also tabulated and discussed.

Similarity Analysis for Effects of Variable Diffusivity and Heat Generation/Absorption on Heat and Mass Transfer for a MHD Stagnation-Point Flow of a Convective Viscoelastic Fluid over a Stretching Sheet with a Slip Velocity

A mathematical analysis has been carried out for stagnation-point heat and mass transfer of a viscoelastic fluid over a stretching sheet with surface slip velocity, concentration dependent diffusivity, thermal convective boundary conditions, and heat source/sink. The governing partial differential equations are reduced to a system of nonlinear ordinary differential equations using Lie group analysis. Numerical solutions of the resulting ordinary differential equations are obtained using shooting method. The influences of various parameters on velocity, temperature, and mass profiles have been studied. Also, the effects of various parameters on the local skin-friction coefficient, the local Nusselt number, and the local Sherwood number are given in graphics form and discussed.

MHD FLOW AND HEAT TRANSFER IN A VISCOUS FLUID OVER A NON-ISOTHERMAL STRETCHING SURFACE WITH THERMAL RADIATION IN SLIP-FLOW REGIME

The present work is concerned with the effects of surface slip conditions and thermal radiation on an electrically conducting fluid over a non-isothermal stretching surface in the presence of a uniform transverse magnetic field. Similarity transformation is used to transform the partial differential equations describing the problem into a system of nonlinear ordinary differential equations, which is solved analytically. The effects of various parameters on the velocity and temperature profiles as well as on the local skin-friction and the local Nusselt number are discussed in detail and displayed through graphs.