Hall effect on MHD free convection boundary layer flow past a vertical flat plate

Effects of Hall current on MHD free convection boundary layer flow of a viscous incompressible electrically conducting fluid past a heated vertical flat plate of finite dimension in the presence of a uniform transverse magnetic field have been studied. An exact solution of the governing equations describing the flow has been obtained. The velocity field, induced magnetic field and bulk temperature distributions in the boundary layer flow have been discussed. It is found that the velocity components increase with an increase in Hall parameter. It is noticed that the induced magnetic field components are radically influenced by the Hall parameter. It is also found that the magnitude of bulk temperature in the x-direction decreases with an increase in either Hall parameter or magnetic parameter. On the other hand, the magnitude of the bulk temperature in the z-direction increases with an increase in Hall parameter whereas it decreases with an increase in magnetic parameter.     

Dissipation effects on MHD free convection flow past a semi-infinite vertical plate

Viscous and Joule dissipation effects are considered on MHD free convection flow past a semi-infinite isothermal vertical plate under a uniform transverse magnetic field. Series solutions in powers of a dissipation number (=gx/c _p) have been employed and the resulting ordinary differential equations have been solved numerically. The velocity and temperature profiles are shown on graphs and the numerical values of ₁(0)/₀(0) (, temperature function) have been tabulated. It is observed that the dissipation effects in the MHD case become more dominant with increasing values of the magnetic field parameter (=M ²/(Gr _x /4)^1/2) and the Prandtl number.     

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field. It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field. The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF). The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method. Moreover, the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method, for the whole range of the local transpiration parameter ζ. Consideration is also given to the regions where the local transpiration parameter ζ is small or large enough. However, in these particular regions, solutions are acquired with the aid of a regular perturbation method. The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (= 0.005, 0.01, 0.05). Furthermore, the velocity and temperature profiles are also drawn from various values of the local transpiration parameter ζ.     

Effect of Hall current on MHD natural convection flow from vertical permeable flat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numer...     

MHD free convective flow past semi-infinite vertical permeable wall

In this paper,the basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical permeable plate in the form of partial differential equations are reduced to a set of non-linear ordinary differential equations by applying a suitable similarity transformation.Approximate solutions of the transformed equations are obtained by employing the perturbation method for two cases,i.e.,small and large values of the suction parameter.From the numerical evaluations of the solution,it can be seen that the velocity field at any point decreases as the values of the magnetic and suction parameters increase.The effect of the magnetic parameter is to increase the thermal boundary layer.It is also found that the velocity and temperature fields decrease with the increase in the sink parameter.     

MHD free convection flow of visco-elastic fluid past an infinite vertical porous plate

 This work provides a comprehensive theoretical analysis of a two-dimensional unsteady free convection flow of an incompressible, visco-elastic fluid past an infinite vertical porous plate. Solutions for the zero order perturbation velocity profile, the first order perturbation velocity and temperature profiles in closed form are obtained with the help of Laplace transform technique. The numerical solutions are carried out for the Prandtl number 0.1, 0.72, 1.0, 1.5 and 2.0 which are appropriate for different types of liquid metals and for different values of magnetic field parameter, M. Received on 1 September 1999     

Radiation effect on MHD mixed convection flow about a permeable vertical plate

This study investigates mixed convection heat transfer about a permeable vertical plate in the presence of magneto and thermal radiation effects. The effects of the mixed convection parameter, the radiation–conduction parameter, the surface temperature parameter, the magnetic parameter and the suction/injection parameter on the local skin friction and local heat transfer parameters are presented and analyzed.     

Combined forced and free convection MHD row past a semi-infinite vertical plate

Effects of a transversely applied magnetic field on the forced and free convective flow of an electrically conducting fluid past a vertical semi-infinite plate, on taking into account dissipative heat and stress work, have been presented. Without magnetic field, it has been discussed by the authors [1] in an earlier paper. The effects of Gr (Grashof number, Gr>0 cooling of the plate by free convection currents, Gr<0 heating of the plate by free convection currents), Pr (Prandtl number), F (Froude number) and M² (the magnetic field parameter) are discussed. It is observed that reverse type of flow of air exists near the plate when Gr<0.

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Gemischte erzwungene und freie Konvektions-MHD-Strömung an einer halbunendlichen senkrechten Platte

Zusammenfassung Die Wirkung eines transversalen Magnetfeldes auf die erzwungene und freie Konvektion einer elektrisch leitenden Flüssigkeit an einer halbunendlichen senkrechten Platte wurde unter Berücksichtigung der Dissipationswärme und der Kompressionsarbeit mitgeteilt. Das Problem wurde ohne Magnetfeld schon früher [1] behandelt. Diskutiert wurde die Wirkung der Grashof-Zahl Gr (Gr>0 Kühlung der Platte durch freie Konvektion), der Prandtl-Zahl Pr, der Froude-Zahl F und des magnetischen Feldparameters M₂. Bei Gr<0 wird Umkehr strömung in Plattennähe betrachtet.

     

Unsteady natural convection from a vertical flat plate with suction

Summary Exact solutions of the Navier-Stokes equations and the energy equation neglecting dissipation terms for natural convection from a porous vertical flat plate have been obtained in the following two cases: (i) when the plate is suddenly raised to a uniform higher temperature, (ii) when the plate suddenly begins to generate a uniform heat flux at its surface. Expressions for the skin friction and coefficient of heat transfer at the plate have been obtained. Skin friction decreases with suction in both cases.     

General series solution for free convection past a non-isothermal vertical flat plate

Summary Free convection past a vertical plate is studied theoretically for a general class of nonlinear wall temperature distributions. Due to the broad approach it is possible in some cases to find two series solutions applying to the same wall temperature distribution which are valid in different parts of the x region. Through graphical joining of both solutions an overall valid solution is obtained. This is illustrated by examples.     

Numerical solution of natural convection flow past a non-isothermal vertical flat plate

The problem of natural convection over a semi-infinite flat plate with non-uniform wall temperature is studied by using a numerical method. The local rates of heat transfer as a function of the distance along the plate are tabulated for a range of Prandtl numbers (0.01 to 100) and for a few cases of wall temperature distributions. Such tabulations serve as a reference against which other approximate solutions can be compared in the future.     

Unsteady MHD mixed convection flow over an impulsively stretched permeable vertical surface in a quiescent fluid

The unsteady mixed convection flow of an incompressible laminar electrically conducting fluid over an impulsively stretched permeable vertical surface in an unbounded quiescent fluid in the presence of a transverse magnetic field has been investigated. At the same time, the surface temperature is suddenly increased from the surrounding fluid temperature or a constant heat flux is suddenly imposed on the surface. The problem is formulated in such a way that for small time it is governed by Rayleigh type of equation and for large time by Crane type of equation. The non-linear coupled parabolic partial differential equations governing the unsteady mixed convection flow under boundary layer approximations have been solved analytically by using the homotopy analysis method as well as numerically by an implicit finite difference scheme. The local skin friction coefficient and the local Nusselt number are found to decrease rapidly with time in a small time interval and they tend to steady-state values for t*≥5. They also increase with the buoyancy force and suction, but decrease with injection rate. The local skin friction coefficient increases with the magnetic field, but the local Nusselt number decreases. There is a smooth transition from the unsteady state to the steady state.     

MHD flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge

The steady flow and heat transfer of a hybrid nanofluid past a permeable stretching/shrinking wedge with magnetic field and radiation effects are studied. The governing equations of the hybrid nanofluid are converted to the similarity equations by techniques of the similarity transformation. The bvp4c function that is available in MATLAB software is utilized for solving the similarity equations numerically. The numerical results are obtained for selected different values of parameters. The resul...     

Effect of Hall current on MHD natural convection flow from vertical permeable fiat plate with uniform surface heat flux

The effect of the Hall current on the magnetohydrodynamic (MHD) natural convection flow from a vertical permeable flat plate with a uniform heat flux is analyzed in the presence of a transverse magnetic field.It is assumed that the induced magnetic field is negligible compared with the imposed magnetic field.The boundary layer equations are reduced to a suitable form by employing the free variable formulation (FVF) and the stream function formulation (SFF).The parabolic equations obtained from FVF are numerically integrated with the help of a straightforward finite difference method.Moreover,the nonsimilar system of equations obtained from SFF is solved by using a local nonsimilarity method,for the whole range of the local transpiration parameter ζ.Consideration is also given to the regions where the local transpiration parameter ζis small or large enough.However,in these particular regions,solutions are acquired with the aid of a regular perturbation method.The effects of the magnetic field M and the Hall parameter m on the local skin friction coefficient and the local Nusselt number coefficient are graphically shown for smaller values of the Prandtl number Pr (=0.005,0.01,0.05).Furthermore,the velocity and temperature profiles are also drawn from various values of the local transpiration parameterζ.     

MHD boundary-layer flow of a non-Newtonian nanofluid past a stretching sheet with a heat source/sink

The goal of the present paper is to examine the magnetohydrodynamic effects on the boundary layer flow of the Jeffrey fluid model for a non-Newtonian nanofluid past a stretching sheet with considering the effects of a heat source/sink. The governing partial differential equations are reduced to a set of coupled nonlinear ordinary differential equations by using suitable similarity transformations. These equations are then solved by the variational finite element method. The profiles of the velocity, temperature, and nanoparticle volume fraction are presented graphically, and the values of the Nusselt and Sherwood numbers are tabulated. The present results are compared with previously published works and are found to be in good agreement with them.     

Higher approximations to the free convection flow from a heated vertical flat plate

This paper is concerned with the problem of obtaining higher approximations for the free convection from a heated vertical flat plate to that represented by the well known solution of Schmidt and Beckmann. For large Grashof number, the perturbation problem is a singular one and the method of matched asymptotic expansions is used to construct inner and outer expansions for the velocity and temperature distributions. The small perturbation parameterε is the inverse of the fourth root of the Grashof number and the expansions are shown to involve only integral powers ofε. The first three terms in the expansion are calculated and numerical results are presented for the velocity, temperature, skin friction and heat transfer. The agreement with experiment is found to be excellent, and the theory fully explains the discrepancies which exist between boundary layer theory and experiment.     

Unsteady flow past an impulsively started vertical plate with heat and mass transfer

Finite difference solution of the transient free-convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with heat and mass transfer is presented here. The steady state velocity, temperature and concentration profiles are shown graphically. Velocity profiles are compared with exact solution. It has been observed that there is a rise in the velocity due to the presence of a mass diffusion. An increase in Schmidt number, leads to a fall in the velocity. Stability and the convergence of the finite difference scheme are established. Received on 7 January 1998     

Entropy generation effects in a hydromagnetic free convection flow past a vertical oscillating plate

An unsteady free convective flow of a viscous fluid past an oscillating plate is considered, and the effects of entropy generation are investigated. The governing partial differential equations are normalized by using suitable transformations, and an exact solution of the problem is obtained by using the Laplace transformation technique. The expressions for the velocity and temperature are then used to compute the skin friction, Nusselt number, local entropy generation number, and Bejan number.