Khamisah Jafar

MHD Stagnation-Point Flow over a Nonlinearly Stretching/Shrinking Sheet

AbstractThe steady laminar two-dimensional magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid impinging normal to a nonlinearly stretching/shrinking flat sheet in the presence of a nonuniform magnetic field applied in the positive y-direction normal to the flat sheet is considered. The governing system of partial differential equations is first transformed into ordinary differential equations and solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of the magnetic parameter M, the velocity exponent parameter m, and the stretching/shrinking parameter e on the flow field are discussed. It is found that the magnitude of the skin friction coefficient |f″(0)| increases with both the magnetic parameter M and the velocity exponent parameter m, when the stretching velocity differs from the free-stream velocity (e≠1), and is zero when e=1. For a fixed value of the magnetic parameter M, a unique or dual solutions are found for the ...

MHD boundary layer flow due to a moving wedge in a parallel stream with the induced magnetic field

The present analysis considers the steady magnetohydrodynamic (MHD) laminar boundary layer flow of an incompressible electrically conducting fluid caused by a continuous moving wedge in a parallel free stream with a variable induced magnetic field parallel to the wedge walls outside the boundary layer. Using a similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations in the form of a two-point boundary value problem (BVP) and then solved numerically using a finite difference scheme known as the Keller box method. Numerical results are obtained for the velocity profiles and the skin friction coefficient for various values of the moving parameter λ, the wedge parameter β, the reciprocal magnetic Prandtl number α and the magnetic parameter S. Results indicate that when the wedge and the fluid move in the opposite directions, multiple solutions exist up to a critical value λc of the moving parameter λ, whose value depends on the values of S and β.MSC: 34B15, 76D10.

Stability analysis of flow and heat transfer on a permeable moving plate in a co-flowing nanofluid

In this paper, the stability analysis of the two-dimensional boundary layer flow and heat transfer of a copper (Cu)-water nanofluid past a permeable moving flat plate in the presence of a co-flowing fluid is theoretically investigated. The governing partial differential equations are first transformed into ordinary differential equations before they are solved numerically using bvp4c function in Matlab. The numerical results for the skin friction coefficient, the local Nusselt number and the local Sherwood number, as well as the velocity, temperature and nanoparticle volume fraction profiles are obtained, presented and discussed in detail for a range of various governing parameters. The numerical results indicate that dual solutions exist when the plate and the free stream move in the opposite directions. The time-dependent version of the problem is then considered to produce linearize eigenvalue problem which are then solved numerically using bvp4c function in Matlab. The stability analysis is carried ou...

Numerical solutions of flow and heat transfer on a moving plate in a co-flowing nanofluid

This article presents a numerical investigation on the steady boundary layer flow and heat transfer over a moving impermeable flat plate in the presence of a co-flowing water-based nanofluid containing Cu (copper) nanoparticle. It is assumed that the plate moves in the same or the opposite direction of the free stream. The resulting system of nonlinear ordinary differential equations is solved numerically using a finite-difference scheme along with a shooting method. The effect of the various governing parameters on the flow and heat transfer characteristics is investigated. The results show that dual solutions exist when the plate and the free stream move in the opposite directions.

Boundary-Layer Flow and Heat Transfer of Nanofluids over a Permeable Moving Surface in the Presence of a Coflowing Fluid

The steady boundary-layer flow of a nanofluid past a permeable moving flat plate in the presence of a coflowing fluid is theoretically investigated. The plate is assumed to move in the same or opposite direction of the free stream. The governing partial differential equations are first transformed into ordinary differential (similarity) equations before they are solved numerically using a finite-difference scheme along with a shooting method. Numerical results are obtained for the skin-friction coefficient, the local Nusselt number, and the local Sherwood number as well as the velocity, temperature, and nanoparticle volume fraction profiles for some values of the governing parameters, namely, the plate velocity parameter, the Prandtl number, the Lewis number, the Brownian motion parameter, the thermophoresis parameter, and the nanoparticle volume fraction parameter. The numerical results indicate that dual solutions exist when the plate and the free stream move in the opposite directions.

Magnetohydrodynamic stagnation-point flow and heat transfer over an exponentially stretching/shrinking sheet

This paper considers a numerical investigation on the steady laminar two-dimensional MHD stagnation-point flow and heat transfer of an incompressible viscous fluid impinging normal to an exponentially stretching/shrinking flat sheet in the presence of a non-uniform magnetic field applied in a direction normal to the flat sheet. The sheet surface temperature is assumed to also vary exponentially with the distance from the stagnation-point. The governing system of partial differential equations is first transformed into ordinary differential equations, and solved numerically using an implicit finite-difference scheme known as the Keller-box method. The effects of the stretching/shrinking parameter e and the magnetic parameter on the flow field and heat transfer characteristics are discussed. It is found that the magnitude of the skin friction coefficient |f″(o)|, and the local Nusselt number −θ’(0) increase with both the magnetic parameter M and the stretching/shrinking parameter e. For the shrinking case, ...

Numerical solutions of three-dimensional boundary layer flow and heat transfer past a permeable shrinking surface in a Cu-water nanofluid

This article presents a numerical investigation on the three-dimensional boundary layer flow and heat transfer of a copper, Cu-water nanofluid in the vicinity of a permeable shrinking flat surface in an otherwise quiescent fluid. It is assumed that the nanofluid is incompressible and the flow is laminar. The nanofluid mathematical model proposed by Tiwari and Das is used in which the effect of the nanoparticle volume fraction is considered. The governing nonlinear partial differential equations are transformed into a system of nonlinear ordinary differential equations using a similarity transformation which is then solved numerically using the shooting method. The numerical results for the skin friction coefficient and the local Nusselt number as well as the velocity and temperature profiles are obtained, presented and discussed for a range of various values of the governing parameters.

MHD flow and heat transfer over a moving plate in a parallel stream with induced magnetic field

The present analysis considers a MHD boundary layer flow and heat transfer of an electrically-conducting viscous fluid over a moving flat plate in a parallel stream with a constant magnetic field applied outside the boundary layer parallel to the plate. Using a similarity transformation, the governing system of partial differential equations was transformed to ordinary differential equations. The similarity equations were then solved numerically using a finitedifference scheme known as the Keller-box method. Numerical results were obtained for the velocity, induced magnetic and temperature profiles, the skin friction coefficient and the local Nusselt number for some values of the moving parameter e, magnetic parameter M, the Prandtl number Pr and reciprocal magnetic Prandtl α. The results indicate that dual solutions exist when the plate and the fluid move in the opposite directions, up to a critical value of the moving parameter ec, whose value depends on the value of the magnetic parameter. Furthermore,...

Numerical investigation of MHD stagnation point flow and heat transfer over a permeable shrinking sheet with external magnetic field, viscous dissipation and Joule heating

The present study considers the steady laminar magnetohydrodynamic (MHD) boundary layer flow of a viscous and incompressible electrically conducting fluid near the stagnation point on a horizontal continuously shrinking surface, with variable wall temperature and a constant magnetic field applied normal to the surface of the sheet. The surface is assumed to be permeable, allowing either suction or injection at the wall. By introducing an appropriate similarity transformation, the governing system of partial differential equations is first transformed into a system of ordinary differential equations, which is then solved numerically using an implicit finite-difference scheme known as the Keller-box method for some values of the selected parameters. The effects of the governing parameters, namely the shrinking parameter λ, the suction parameter f0 and the magnetic parameter M on the skin friction coefficient, the local Nusselt number as well as the velocity and temperature profiles are determined and discus...

Magnetohydrodynamic Stagnation Point Flow with a Convective Surface Boundary Condition

Abstract This study analyzes the steady laminar two-dimensional stagnation point flow and heat transfer of an incompressible viscous fluid impinging normal to a horizontal plate, with the bottom surface of the plate heated by convection from a hot fluid. A uniform magnetic field is applied in a direction normal to the flat plate, with a free stream velocity varying linearly with the distance from the stagnation point. The governing partial differential equations are first transformed into ordinary differential equations, before being solved numerically. The analysis includes the effects of the magnetic parameter, the Prandtl number, and the convective parameter on the heat transfer rate at the surface. Results showed that the heat transfer rate at the surface increases with increasing values of these quantities.