MHD Couette two-fluid flow and heat transfer in presence of uniform inclined magnetic field

The MHD Couette flow of two immiscible fluids in a parallel plate channel in the presence of an applied electric and inclined magnetic field is investigated in the paper. One of the fluids is assumed to be electrically conducting, while the other fluid and the channel plates are assumed to be electrically insulating. Separate solutions with appropriate boundary conditions for each fluid are obtained and these solutions are matched at the interface using suitable matching conditions. The partial differential equations governing the flow and heat transfer are transformed to ordinary differential equations and closed-form solutions are obtained in both fluid regions of the channel. The results for various values of the Hartmann number, the angle of magnetic field inclination, the loading parameter and the ratio of the heights of the fluids are presented graphically to show their effect on the flow and heat transfer characteristics.     

Unsteady magnetohydrodynamic stagnation point flow — closed-form analytical solutions

This paper investigates the unsteady stagnation point flow and heat transfer of magnetohydrodynamic(MHD) fluids over a moving permeable flat surface. The unsteady Navier-Stokes(NS) equations are transformed into a similarity nonlinear ordinary differential equation, and a closed form solution is obtained for the unsteadiness parameter of 2. The boundary layer energy equation is transformed into a similarity equation,and is solved for a constant wall temperature and a time-dependent uniform wall heat flux case. The solution domain, velocity, and temperature profiles are calculated for different combinations of parameters including the Prandtl number, mass transfer parameter, wall moving parameter, and magnetic parameter. Two solution branches are obtained for certain combinations of the controlling parameters, and a stability analysis demonstrates that the lower solution branch is not stable. The present solutions provide an exact solution to the entire unsteady MHD NS equations, which can be used for validating the numerical code of computational fluid dynamics.     

Steady MHD Couette flow with temperature-dependent physical properties

The influence of variation in physical variables on the steady magnetohydrodynamic (MHD) Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the fluid is acted upon by a constant pressure gradient. The viscosity and the thermal as well as electric conductivities are assumed to be temperature dependent. The two plates are kept at two constant but different temperatures, and the viscous and Joule dissipations are considered in the energy equation. A numerical solution for the governing nonlinear coupled equations of motion and the energy equation is obtained. The effect of the temperature-dependent viscosity, thermal conductivity, and electrical conductivity on both the velocity and temperature distributions is examined. H.A. Attia - On leave from: Dept. of Eng. Mathematics and physics, El-Fayoum University, El-Fayoum, Egypt     

MHD flow and heat transfer over a stretching surface with variable thermal conductivity and partial slip

In this paper we analyze the flow and heat transfer of an MHD fluid over an impermeable stretching surface with variable thermal conductivity and non-uniform heat source/sink in the presence of partial slip. The governing partial differential equations of the problem are reduced to nonlinear ordinary differential equations by using a similarity transformation. The temperature boundary conditions are assumed to be linear functions of the distance from the origin. Analytical solutions of the energy equations for Prescribed Surface Temperature (PST) and Prescribed Heat Flux (PHF) cases are obtained in terms of a hypergeometric function, without applying the boundary-layer approximation. The effects of the governing parameters on the flow and heat transfer fields are presented through tables and graphs, and they are discussed. Furthermore, the obtained numerical results for the skin friction, wall-temperature gradient and wall temperature are analyzed and compared with the available results in the literature for special cases.     

Effects of radiation and heat source on MHD flow of a viscoelastic liquid and heat transfer over a stretching sheet

We study the MHD flow and also heat transfer in a viscoelastic liquid over a stretching sheet in the presence of radiation. The stretching of the sheet is assumed to be proportional to the distance from the slit. Two different temperature conditions are studied, namely (i) the sheet with prescribed surface temperature (PST) and (ii) the sheet with prescribed wall heat flux (PHF). The basic boundary layer equations for momentum and heat transfer, which are non-linear partial differential equations, are converted into non-linear ordinary differential equations by means of similarity transformation. The resulting non-linear momentum differential equation is solved exactly. The energy equation in the presence of viscous dissipation (or frictional heating), internal heat generation or absorption, and radiation is a differential equation with variable coefficients, which is transformed to a confluent hypergeometric differential equation using a new variable and using the Rosseland approximation for the radiation. The governing differential equations are solved analytically and the effects of various parameters on velocity profiles, skin friction coefficient, temperature profile and wall heat transfer are presented graphically. The results have possible technological applications in liquid-based systems involving stretchable materials.     

Effects of thermal radiation on MHD viscous fluid flow and heat transfer over nonlinear shrinking porous sheet

This paper investigates the effects of thermal radiation on the magnetohy-drodynamic (MHD) flow and heat transfer over a nonlinear shrinking porous sheet. The surface velocity of the shrinking sheet and the transverse magnetic field are assumed to vary as a power function of the distance from the origin. The temperature dependent viscosity and the thermal conductivity are also assumed to vary as an inverse function and a linear function of the temperature, respectively. A generalized similarity transformarion is used to reduce the governing partial differential equations to their nonlinear coupled ordinary differential equations, and is solved numerically by using a finite difference scheme. The numerical results concern with the velocity and temperature profiles as well as the local skin-friction coefficient and the rate of the heat transfer at the porous sheet for different values of several physical parameters of interest.     

Numerical simulation of MHD stagnation point flow and heat transfer of a micropolar fluid towards a heated shrinking sheet

A comprehensive study of magneto hydrodynamics two‐dimensional stagnation flow with heat transfer characteristics towards a heated shrinking sheet immersed in an electrically conducting incompressible micropolar fluid in the presence of a transverse magnetic field is analyzed numerically. The governing continuity, momentum, angular momentum and heat equations together with the associated boundary conditions are first reduced to a set of self similar nonlinear ordinary differential equations using a similarity transformation and are then solved by a method based on finite difference discretization. Some important features of the flow and heat transfer in terms of normal and streamwise velocities, microrotation and temperature distributions for different values of the governing parameters are analyzed, discussed and presented through tables and graphs. The results indicate that the reverse flow caused due to shrinking of the sheet can be stopped by applying a strong magnetic field. The magnetic field enhances the shear stresses and decreases the thermal boundary layer thickness. The heat loss per unit area from the sheet decreases with an increase in the shrinking parameter. Micropolar fluids exhibit reduction in shear stresses and heat transfer rate as compared with Newtonian fluids, which may be beneficial in the flow and thermal control of polymeric processing. Copyright © 2011 John Wiley & Sons, Ltd.     

Flow of an oldroyd fluid in a circular pipe with time dependent pressure gradient

The problem of pulsating flow superimposed on the steady laminar flow in a circular tube is investigated for the fluid characterized by the Oldroyd's constitutive equations. The governing equations are solved in an exact manner and the solution is obtained in terms of two non-dimensional fluid parameters. Several interesting illustrations are provided comparing the behaviour of Newtonian fluid and Oldroyd fluids regarding the velocity field, sectional mean velocity, surface friction and balance of force. The flow for small and large frequencies of vibration are obtained as special cases. For Oldroyd fluids also the flow is basically parabolic for small frequencies while it possesses a boundary layer character at large frequencies. The solution for second order fluids and Maxwell fluids can be obtained by appropriately choosing the two fluid parameters.     

Combined heat and mass transfer by mixed convection MHD flow along a porous plate with chemical reaction in presence of heat source

An exact and a numerical solutions to the problem of a steady mixed convective MHD flow of an incompressible viscous electrically conducting fluid past an infinite vertical porous plate with combined heat and mass transfer are presented.A uniform magnetic field is assumed to be applied transversely to the direction of the flow with the consideration of the induced magnetic field with viscous and magnetic dissipations of energy.The porous plate is subjected to a constant suction velocity as well as a uniform mixed stream velocity.The governing equations are solved by the perturbation technique and a numerical method.The analytical expressions for the velocity field,the temperature field,the induced magnetic field,the skin-friction,and the rate of heat transfer at the plate are obtained.The numerical results are demonstrated graphically for various values of the parameters involved in the problem.The effects of the Hartmann number,the chemical reaction parameter,the magnetic Prandtl number,and the other parameters involved in the velocity field,the temperature field,the concentration field,and the induced magnetic field from the plate to the fluid are discussed.An increase in the heat source/sink or the Eckert number is found to strongly enhance the fluid velocity values.The induced magnetic field along the x-direction increases with the increase in the Hartmann number,the magnetic Prandtl number,the heat source/sink,and the viscous dissipation.It is found that the flow velocity,the fluid temperature,and the induced magnetic field decrease with the increase in the destructive chemical reaction.Applications of the study arise in the thermal plasma reactor modelling,the electromagnetic induction,the magnetohydrodynamic transport phenomena in chromatographic systems,and the magnetic field control of materials processing.     

Transient free convection of non-Newtonian fluids along a wavy vertical plate including the magnetic field effect

A Prandtl transformation method is applied to study the transient free convection of non-Newtonian fluids along a wavy vertical plate in the presence of a magnetic field. A simple transformation is proposed to transform the governing equations into the boundary-layer equations and solved numerically by the cubic spline approximation. A simple coordinate transformation is employed to transform the complex wavy surface to a vertical flat plate for a constant wall temperature by the numerical method. The effects of the magnetic field parameter, the wavy geometry and the non-Newtonian nature of the fluids on the flow characteristics and heat transfer are discussed in detail.     

Thermodynamic optimization of conjugate convection from a finned channel using genetic algorithms

For the first time, this study reports the results of numerical investigation of conjugate convection from a finned channel. The computational domain of investigation consists of a horizontal channel with vertical rectangular fins being mounted on outside of the channel. The equations governing two-dimensional, steady, incompressible, constant property laminar flow have been solved for the fluid flowing outside the channel. In doing this, Boussinesq assumption is assumed to be valid for the fluid flowing outside the channel along the fins. For the fluid flowing inside the channel, flow is assumed to be turbulent with forced convection as the mode of heat transfer. From a large volume of numerically generated data correlations have been proposed for (1) Nusselt number and (2) Entropy generated by the system. These correlations are finally used to obtain thermodynamic optimum where in we seek a solution with minimum total entropy generation rate for varying heat duties, by using the state-of-the art Genetic algorithms.     

Generalised Couette flow of two immiscible viscous fluids with heat transfer using Brinkman model

The present study deals with generalised Couette flow of two viscous, incompressible, immiscible fluids with heat transfer in presence of heat source through two straight parallel horizontal walls. The lower wall is bounded below, by a naturally permeable material of high porosity and the flow inside the porous medium is assumed to be of moderate permeability, modelled by Brinkman equation. The flow domain is divided into three zones to obtain analytical solutions of the momentum and energy equations. To link various flow regions, appropriate matching conditions have been used. The effects of permeability parameter, Reynolds number and viscous parameter on velocity field and the effects of Reynolds number, viscous parameter, permeability parameter, constant heat source and Brinkman number on temperature distribution in different zones are discussed graphically. The mass flow rate, skin-friction factor and rates of heat transfer at the upper boundary and porous interface are discussed with the help of tables.     

MHD effects on a thermo-solutal stratified nanofluid flow on an exponentially radiating stretching sheet

This study is focused on the heat and mass transfer effects in a magnetohydrodynamic (MHD) flow of a viscous nanofluid saturating a porous medium past an exponentially radiating stretching sheet. The governing differential equations are transformed to a system of nonlinear ordinary differential equations by suitable transformations. It is noted that stratification affects the local Nusselt and Sherwood numbers.     

The Effect of MHD on a Porous Fin Attached to a Vertical Isothermal Surface

The effect of MHD on the total heat transfer from a porous fin attached to a vertical isothermal surface has been investigated. The Maxwell equations have been used, and also Rosseland approximation for radiation heat transfer and Darcy model for simulating the flow in porous medium have been adapted. The governing equations are reduced to a nonlinear ODE. The fin is supposed to be an infinite fin, which is exposed to a magnetic field. The dimensionless temperature profile, and the average Nusselt number profiles have been obtained for different Rayleigh numbers and porosities. Validation is carried out by comparing the results obtained in this study with those predicted by Darcy–Brinkman–Forchheimer model.     

Hydromagnetic flow and heat transfer adjacent to a stretching vertical sheet with prescribed surface heat flux

The similarity solution for the problem of mixed convection boundary layer flow adjacent to a stretching vertical sheet in an incompressible electrically conducting fluid in the presence of a transverse magnetic field is presented. It is assumed that the sheet is stretched with a power-law velocity and is subjected to a variable surface heat flux. The governing partial differential equations are first transformed into a system of non-linear ordinary differential equations, before being solved numerically by the Keller-box method. The numerical results obtained are then compared with previously reported cases available in the literature as well as the series solution for certain values of parameters, to support their validity. The effects of the governing parameters on the flow field and heat transfer characteristics are obtained and discussed.     

A similarity solution for the flow and heat transfer over a moving permeable flat plate in a parallel free stream

This paper presents both a numerical and analytical study in connection with the steady boundary layer flow and heat transfer induced by a moving permeable semi-infinite flat plate in a parallel free stream. Both the velocities of the flat plate and the free stream are proportional to x ^1/3. The surface temperature is assumed to be constant. The governing partial differential equations are converted into ordinary differential equations by a new similarity transformation. Numerical results for the flow and heat transfer characteristics are obtained for various values of the moving parameter, transpiration parameter and the Prandtl number. Approximate analytical solutions are also obtained when the suction or injection parameter is very large. It is found that dual solutions exist for the case when the fluid and the plate move in the opposite directions.     

Combined influence of wall conductance,pressure work,viscous dissipation and joule heating on MHD channel flow heat transfer

To investigate the combined influence of viscous dissipation, pressure work, Joule heating, arbitrary voltage ratio, unequal wall conductances and wall heat fluxes on the fully developed laminar MHD channel flow heat transfer, the exact solution of the energy equations for fluid and channel walls are derived assuming the Hartmann velocity profile. It is concluded that there can be a substantial difference, depending upon Hartmann number, electric field and Brinkman number, between the Nusselt number considering the wall conductance and that neglecting it. Representative results are presented in diagrams.     

Mixed convection boundary layer flow near stagnation-point on vertical surface with slip

This paper considers the steady mixed convection boundary layer flow of a viscous and incompressible fluid near the stagnation-point on a vertical surface with the slip effect at the boundary. The temperature of the sheet and the velocity of the external flow are assumed to vary linearly with the distance from the stagnation-point. The governing partial differential equations are first transformed into a system of ordinary differential equations, which are then solved numerically by a shooting method. The features of the flow and heat transfer characteristics for different values of the governing parameters are analyzed and discussed. Both assisting and opposing flows are considered. The results indicate that for the opposing flow, the dual solutions exist in a certain range of the buoyancy parameter, while for the assisting flow, the solution is unique. In general, the velocity slip increases the heat transfer rate at the surface, while the thermal slip decreases it.     

Transient analysis of diffusive chemical reactive species for couple stress fluid flow over vertical cylinder

The unsteady natural convective couple stress fluid flow over a semi-infinite vertical cylinder is analyzed for the homogeneous first-order chemical reaction effect. The couple stress fluid flow model introduces the length dependent effect based on the material constant and dynamic viscosity. Also, it introduces the biharmonic operator in the Navier-Stokes equations, which is absent in the case of Newtonian fluids. The solution to the time-dependent non-linear and coupled governing equations is carried out with an unconditionally stable Crank-Nicolson type of numerical schemes. Numerical results for the transient flow variables, the average wall shear stress, the Nusselt number, and the Sherwood number are shown graphically for both generative and destructive reactions. The time to reach the temporal maximum increases as the reaction constant K increases. The average values of the wall shear stress and the heat transfer rate decrease as K increases, while increase with the increase in the Sherwood number.     

MHD axisymmetric flow of third grade fluid between porous disks with heat transfer

The magnetohydrodynamic(MHD) flow of the third grade fluid between two permeable disks with heat transfer is investigated.The governing partial differential equations are converted into the ordinary differential equations by suitable transformations.The transformed equations are solved by the homotopy analysis method(HAM).The expressions for square residual errors are defined,and the optimal values of convergencecontrol parameters are selected.The dimensionless velocity and temperature fields are examined for various dimensionless parameters.The skin friction coefficient and the Nusselt number are tabulated to analyze the effects of dimensionless parameters.