Oscillatory Couette flow in the presence of an inclined magnetic field

Oscillatory MHD Couette flow of electrically conducting fluid between two parallel plates in a rotating system in the presence of an inclined magnetic field is considered when the upper plate is held at rest and the lower plate oscillates non-torsionally . An exact solution of the governing equations has been obtained by using Laplace transform technique. Asymptotic behavior of the solution is analyzed for M ² ≪1, K ² ≪1 and ω ≪1 and for large M ², K ² and ω. Numerical results of velocities are depicted graphically and the frictional shearing stresses are presented in tables. It is found that a thin boundary layer is formed near the lower plate, for large values of rotation parameter K ², Hartman number M ² and frequency parameter ω. The thickness of this boundary layer increases with increase in inclination of the magnetic field with the axis of rotation.     

Unsteady incompressible Couette flow in a uniform transverse magnetic field

Summary The unsteady plane Couette flow of an incompressible, viscous and infinitely conducting fluid in a uniformly imposed transverse magnetic field is studied. The problem is solved in general in a series form by means of a finite Fourier transform, and explicit solutions for two special cases are worked out.     

MHD mixed convective heat transfer flow about an inclined plate

Mixed convection heat transfer about a semi-infinite inclined plate in the presence of magneto and thermal radiation effects is studied. The fluid is assumed to be incompressible and dense. The nonlinear coupled parabolic partial differential equations governing the flow are transformed into the non-similar boundary layer equations, which are then solved numerically using the Keller box method. The effects of the mixed convection parameter R _i, the angle of inclination α, the magnetic parameter M and the radiation–conduction parameter R _d on the velocity and temperature profiles as well as on the local skin friction and local heat transfer parameters. For some specific values of the governing parameters, the results are compared with those available in the literature and a fairly good agreement is obtained.     

MHD stagnation-point flow and heat transfer towards stretching sheet with induced magnetic field

The problem of the steady magnetohydrodynamic (MHD) stagnation-point flow of an incompressible viscous fluid over a stretching sheet is studied. The effect of an induced magnetic field is taken into account. The nonlinear partial differential equations are transformed into ordinary differential equations via the similarity transformation. The transformed boundary layer equations are solved numerically using the shooting method. Numerical results are obtained for various magnetic parameters and Prandtl numbers. The effects of the induced magnetic field on the skin friction coefficient, the local Nusselt number, the velocity, and the temperature profiles are presented graphically and discussed in detail.     

Analysis of turbulent MHD Couette nanofluid flow and heat transfer using hybrid DTM–FDM

Unsteady turbulent magnetohydrodynamic nanofluid hydrothermal treatment is studied. The zero-equation turbulence model is used to simulate turbulent flow. The modeling results obtained by applying the hybrid differential transformation method–finite difference method to solve this problem confirm its viability. An analytical procedure is used for finding the effects of the problem parameters. Results indicate that the average Nusselt number over the lower plate depends linearly on volume fraction of nanofluid, Hall parameter, turbulent Eckert number, and Reynolds number whereas it is inversely proportional on the Hartmann number and the turbulent parameter.     

MHD liquid metal flow and heat transfer between vertical coaxial cylinders under horizontal magnetic field

Direct numerical simulations are presented of MHD liquid metal flow and heat transfer in vertical annuli. Three annular gaps and four ratios of annular height to annular gap are considered. The walls of the external and internal cylinders are isothermal with the temperature of the outer cylinder being higher and, thus, buoyancy is the driving force. The results show that the fluid motion increases as the aspect ratio and the annular gap become larger. The presence of the magnetic field results to fluid deceleration and, thus, to flow stabilization. Additionally, non symmetric flow patterns develop, due to the magnetic field, resulting in differently sized normal and parallel wall layers, namely the Hartmann and the Roberts layers, respectively. For all annular gaps considered, the highest spatially averaged heat transfer rates are obtained for aspect ratios equal to 1.     

MHD boundary layer flow and heat transfer over a stretching sheet with induced magnetic field

In this paper, the problem of steady magnetohydrodynamic boundary layer flow and heat transfer of a viscous and electrically conducting fluid over a stretching sheet is studied. The effect of the induced magnetic field is taken into account. The transformed ordinary differential equations are solved numerically using the finite-difference scheme known as the Keller-box method. Numerical results are obtained for various values of the magnetic parameter, the reciprocal magnetic Prandtl number and the Prandtl number. The effects of these parameters on the flow and heat transfer characteristics are determined and discussed in detail. When the magnetic field is absent, the closed analytical results for the skin friction are compared with the exact numerical results. Also the numerical results for the heat flux from the stretching surface are compared with the results reported by other authors when the magnetic field is absent. It is found that very good agreement exists.     

MHD flow and heat transfer from continuous surface in uniform free stream of non-Newtonian fluid

An analysis is carried out to study the steady flow and heat transfer charac- teristics from a continuous flat surface moving in a parallel free stream of an electrically conducting non-Newtonian viscoelastic fluid.The flow is subjected to a transverse uni- form magnetic field.The constitutive equation of the fluid is modeled by that for a second grade fluid.Numerical results are obtained for the distribution of velocity and temperature profiles.The effects of various physical parameters like viscoelastic param- eter,magnetic parameter and Prandtl number on various momentum and heat transfer characteristics are discussed in detail and shown graphically.     

Couette flow of a nematic liquid crystal in the presence of a magnetic field

Summary We derive the equations governing helical flow of a nematic liquid crystal in the presence of a magnetic field. These equations are used to investigate Couette flow, and a study is made of the large number of possible solutions.     

Nanofluid flow and heat transfer due to a stretching cylinder in the presence of magnetic field

In this paper, flow and heat transfer of a nanofluid over a stretching cylinder in the presence of magnetic field has been investigated. The governing partial differential equations with the corresponding boundary conditions are reduced to a set of ordinary differential equations with the appropriate boundary conditions using similarity transformation, which is then solved numerically by the fourth order Runge–Kutta integration scheme featuring a shooting technique. Different types of nanoparticles as copper (Cu), silver (Ag), alumina (Al₂O₃) and titanium oxide (TiO₂) with water as their base fluid has been considered. The influence of significant parameters such as nanoparticle volume fraction, nanofluids type, magnetic parameter and Reynolds number on the flow and heat transfer characteristics is discussed. It was found that the Nusselt number increases as each of Reynolds number or nanoparticles volume fraction increase, but it decreases as magnetic parameter increase. Also it can be found that choosing copper (for small of magnetic parameter) and alumina (for large values of magnetic parameter) leads to the highest cooling performance for this problem.     

Unsteady two-fluid flow and heat transfer in a horizontal channel

The problem of unsteady oscillatory flow and heat transfer of two viscous immiscible fluids through a horizontal channel with isothermal permeable walls has been considered. The partial differential equations governing the flow and heat transfer are solved analytically using two-term harmonic and non-harmonic functions in both fluid regions of the channel. Effects of physical parameters such as viscosity ratio, conductivity ratio, Prandtl number and frequency parameter on the velocity and temperature fields are shown graphically. It is observed that the velocity and temperature decrease as the viscosity ratio increases, while they increase with increases in frequency parameter. The effect of increasing the thermal conductivity ratio also suppresses the temperature in both fluid regions. The effect of periodic frequency on the flow is depicted in tabular form. It is predicted that both the velocity and temperature profiles decrease as the periodic frequency increases.     

Burnett simulation of flow and heat transfer in micro Couette flow using second-order slip conditions

The conventional Burnett equations with second-order velocity slip and temperature jump conditions were applied to the steady-state micro Couette flow of a Maxwellian monatomic gas. An analytical approach as well as a relaxation method was used to determine the velocity slip and temperature jump at the wall. Convergent solutions to the Burnett equations were obtained on arbitrary fine numerical grids for all Knudsen numbers (Kn) up to the limit of the equations’ validity. The Burnett equations with second-order slip conditions indicate a much better agreement with DSMC data over the first-order slip conditions at high Kn. The convergent Burnett solutions were obtained in orders of magnitude quicker than that with the corresponding DSMC simulation. The augmented Burnett equations were also introduced to model the flow but no obvious improvement in the results was found.     

Hydromagnetic oscillatory Couette flow in rotating system with induced magnetic field

This paper presents a study of hydromagnetic Couette flow of an incompress- ible and electrically conducting fluid between two parallel rotating plates, one of which is oscillating in its own plane. A uniform transverse magnetic field is used, and the induced magnetic field is taken into account. The exact solution to the governing equations is obtained in a closed form. The solution to the problem in the case of vanishing and small finite magnetic Prandtl numbers is also derived from the general solution. The asymp- totic behavior of the solution for large values of the frequency parameter is analyzed to gain some physical insights into the flow pattern. Expressions for the shear stress at both the oscillatory and stationary plates due to primary and secondary flows and mass flow rate in the primary and secondary flow directions are also obtained. The results of the fluid velocity and the induced magnetic field are presented. The shear stresses on the plates due to the primary and secondary flows and the corresponding mass flow rates are presented in a tabular form.     

Turbulent heat transfer for pipe flow with uniform heat generation

An Analytic solution is presented of the problem of turbulent heat transfer in pipes with internal heat generation and insulated wall by applying a recently-developed eddy conductivity model. The results agree closely with available experimental data for a wide range of Prandtl number (0.02–10.5).     

Buoyancy-induced flow and convective heat transfer in an inclined arc-shape enclosure

Numerical and experimental investigations have been conducted to study the flow and heat transfer characteristics for the buoyancy-induced flow inside an inclined arc-shape enclosure. Mathematical model in form of a stream function-vorticity formulation representing the laws of conservation in mass, momentum, and energy is expressed in a curvilinear coordinate frame and solved by a finite-volume discretization method. Heat transfer and flow pattern are predicted at various Grashof numbers and inclination angles. Meanwhile, an experimental system is developed and a flow-visualization technique using smoke is employed to observe the flow pattern. Results show that only when the Grashof number is higher than 10⁵, the increase in natural convection heat transfer becomes appreciable. Both the strength and the pattern of the buoyancy-induced vortex are found to be greatly dependent on the inclination angle. The range of the Grashof number considered in this study is up to 10⁷ and the inclination angle is varied from 0 to π.     

Stability of MHD Couette flow in a narrow gap annulus

A numerical solution to the MHD stability problem for dissipative Couette flow in a narrow gap is presented under following conditions: (i) the inner cylinder rotating with the outer one stationary, (ii) co-rotating cylinders, (iii) counter-rotating cylinders, (iv) an axially applied magnetic field, and (v) conducting and non-conducting walls.Results for the critical wave number and the critical Taylor number are presented and are compared with those of Chandrasekhar (1953). The agreement is very good. The amplitude of the radial velocity and the cell-pattern are shown on graphs for both the conducting and non-conducting walls and for different values of ± (=₂/₁, ₂-the angular velocity of the outer cylinder, ₁-the angular velocity of the inner cylinder) and Q the magnetic field parameter which is the square of the Hartman number. The effects of ± and Q on the stability of the flow are discussed. It is seen that the effect of the magnetic field is to inhibit the onset of instability, it being more so in the presence of conducting walls than in the presence of non-conducting walls.     

Lie group analysis of viscoelastic MHD aligned flow and heat transfer

Exact solutions for an incompressible, viscoelastic, electrically conducting MHD aligned fluid are obtained for velocity components and temperature profiles. Lie Group method is applied to obtain the solution and the symmetries used are of translational type.The English text was polished by Keren Wang and Yunming Chen.     

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.     

Slip effects on heat and mass transfer in MHD micropolar fluid flow over an inclined plate with thermal radiation and chemical reaction

The influence of partial slip, thermal radiation, chemical reaction and temperature‐dependent fluid properties on heat and mass transfer in hydro‐magnetic micropolar fluid flow over an inclined permeable plate with constant heat flux and non‐uniform heat source/sink is studied. The transverse magnetic field is assumed as a function of the distance from the origin. Also it is assumed that the fluid viscosity and the thermal conductivity vary as an inverse function and linear function of temperature, respectively. With the use of the similarity transformation, the governing system of non‐linear partial differential equations are transformed into non‐linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0 (Wolfram Research, Champaign, IL). The numerical values obtained for the velocity, microrotation, temperature, species concentration, skin friction coefficient and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of various physical parameters on the flow and heat transfer characteristics are discussed.Copyright © 2011 John Wiley & Sons, Ltd.