Fadzilah Md. Ali

MHD Mixed Convection Boundary Layer Flow Toward a Stagnation Point on a Vertical Surface With Induced Magnetic Field

In this paper, the steady magnetohydrodynamic (MHD) mixed convection stagnation point flow of an incompressible, viscous, and electrically conducting fluid over a vertical flat plate is investigated. The effect of induced magnetic field is taken into account. Numerical results are obtained using an implicit finite-difference scheme. Both assisting and opposing flows are considered. The results for skin friction, heat transfer, and induced magnetic field coefficients are obtained and discussed for various parameters. The velocity, temperature, and induced magnetic field profiles are also presented. For the case of the opposing flow, it is found that dual solutions exist for a certain range of the buoyancy parameter. Dual solutions are also obtained for the assisting flow.

Dual solutions in MHD flow on a nonlinear porous shrinking sheet in a viscous fluid

In this paper, the problem of magnetohydrodynamic (MHD) flow of a viscous fluid on a nonlinear porous shrinking sheet is studied. The boundary layer partial differential equations are first transformed into an ordinary differential equation, which is then solved numerically by the shooting method. The features of the flow for various governing parameters are presented and discussed in detail. It is found that dual solutions only exist for positive values of the controlling parameter.MSC: 34B15, 76D10.

DUAL SOLUTIONS ON THERMOSOLUTAL MARANGONI FORCED CONVECTION BOUNDARY LAYER WITH SUCTION AND INJECTION

This paper considers the extended problem of the thermosolutal Marangoni forced convection boundary layer by Pop et al. (2001) when the wall is permeable, namely, there is a suction or injection effect. The governing system of partial differential equations is transformed into a system of ordinary differential equations, and the transformed equations are solved numerically using the shooting method. The effects of suction or injection parameter 𝑓0 on the velocity, temperature, and concentration profiles are illustrated and presented in tables and figures. It is shown that dual solutions exist for the similarity parameter 𝛽 less than 0.5.

Unsteady viscous MHD flow over a permeable curved stretching/shrinking sheet

Purpose The purpose of this paper is to theoretically study the problem of the unsteady boundary layer flow past a permeable curved stretching/shrinking surface in the presence of a uniform magnetic field. The governing nonlinear partial differential equations are converted into ordinary differential equations by similarity transformation, which are then solved numerically. Design/methodology/approach The transformed system of ordinary differential equations was solved using a fourth-order Runge-Kutta integration scheme. Results for the reduced skin friction coefficient and velocity profiles are presented through graphs and tables for several sets of values of the governing parameters. The effects of these parameters on the flow characteristics are thoroughly examined. Findings Results show that for the both cases of stretching and shrinking surfaces, multiple solutions exist for a certain range of the curvature, mass suction, unsteadiness, stretching/shrinking parameters and magnetic field parameter. Originality/value The paper describes how multiple (dual) solutions for the flow reversals are obtained. It is shown that the solutions exist up to a critical value of the shrinking parameter, beyond which the boundary layer separates from the surface and the solution based upon the boundary layer approximations is not possible.

MHD stagnation-point flow and heat transfer over a permeable stretching/shrinking sheet

The steady magnetohydrodynamic (MHD) two-dimensional stagnation-point boundary layer flow and heat transfer of a viscous, incompressible and electrically conducting fluid over a permeable flat stretching/shrinking sheet in the presence of an externally applied magnetic field of constant strength is studied. The governing partial differential equations are first transformed into a system of ordinary differential equations, which is then been solved numerically using a shooting method built in Maple software. It is found that the heat transfer rate at the surface reduces with the Eckert number and it is also found that dual solutions exist for certain values of the mass flux parameter and the stretching/shrinking parameter.

Dual solutions in magnetohydrodynamic (MHD) flow on a nonlinear porous shrinking sheet: A stability analysis

The problem of the steady two dimensional MHD flow of an incompressible electrically conducting fluids towards a nonlinear porous shrinking surface is studied. The similarity transformations is use...

A stability analysis on unsteady mixed convection stagnation-point flow over a moving plate along the flow impingement direction

The unsteady mixed convection stagnation-point flow over a moving plate along the flow impingement direction is numerically studied. The governing partial differentiation equations are transformed into ordinary differential equations using a similarity transformation, and then solved numerically by a shooting technique method. Dual solutions are observed in a certain range of opposing flow and regarding on these numerical solutions, we prepared a stability analysis to identify which solution is stable between non-unique solutions by bvp4c solver in Matlab. Further we obtain numerical results which enable us to discuss the features of the respective solutions.

The effect of convective boundary condition on MHD mixed convection boundary layer flow over an exponentially stretching vertical sheet

A theoretical study that describes the magnetohydrodynamic mixed convection boundary layer flow with heat transfer over an exponentially stretching sheet with an exponential temperature distribution has been presented herein. This study is conducted in the presence of convective heat exchange at the surface and its surroundings. The system is controlled by viscous dissipation and internal heat generation effects. The governing nonlinear partial differential equations are converted into ordinary differential equations by a similarity transformation. The converted equations are then solved numerically using the shooting method. The results related to skin friction coefficient, local Nusselt number, velocity and temperature profiles are presented for several sets of values of the parameters. The effects of the governing parameters on the features of the flow and heat transfer are examined in detail in this study.

Boundary layer flow and heat transfer over a stretching cylinder in a copper-water nanofluid

The problem of boundary layer flow and heat transfer over a stretching cylinder in a Copper-water nanofluid is considered in this study. The governing partial differential equations in cylindrical form are transformed into ordinary differential equations by a similarity transformation. Then, the transformed equations are solved numerically using a shooting method with Prandtl number Pr=6.2. The results of skin friction coefficient, local Nusselt number, velocity profiles and temperature profiles for different values of the governing parameters are presented graphically. The effects of the curvature parameter, suction parameter, skin friction coefficient and local Nusselt number on the flow and heat transfer characteristics are discussed. The study indicates that dual solutions exist for the stretching cylinder. It is observed that the surface shear stress at the surface decrease while the heat transfer rate at the surface increase as the curvature parameter increases.

Effects of non-uniform heat source and magnetic field on the flow and heat transfer over a nonlinearly stretching sheet with suction

A theoretical study has been presented to describe the flow and heat transfer in the boundary layers on a nonlinearly stretching sheet with a variable wall temperature and suction, in the presence of magnetic field and non-uniform heat source. The governing partial differential equations are converted into ordinary differential equations by similarity transformation, which is then solved numerically using the shooting method. Results for the skin friction coefficient, local Nusselt number, velocity profiles as well as temperature profiles are presented through graphs and table for several sets of values of the parameters. The effects of the parameters on the flow and heat transfer characteristics are thoroughly examined.