The effect of variable properties on the unsteady Couette flow with heat transfer considering the Hall effect

The influence of temperature dependent viscosity and thermal conductivity on the transient Couette flow with heat transfer is studied. An external uniform magnetic field is applied perpendicular to the parallel plates and the Hall effect is taken into consideration. The fluid is acted upon by a constant pressure gradient. 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 non-linear equations of motion and the energy equation is obtained. The effect of the Hall term and the temperature dependent viscosity and thermal conductivity on both the velocity and temperature distributions is examined.     

Effect of Hall current on transient hydromagnetic Couette–Poiseuille flow of a viscoelastic fluid with heat transfer

The unsteady Couette–Poiseuille flow of an electrically conducting incompressible non-Newtonian viscoelastic fluid between two parallel horizontal non-conducting porous plates is studied with heat transfer considering the Hall effect. A sudden uniform and constant pressure gradient, an external uniform magnetic field that is perpendicular to the plates and uniform suction and injection through the surface of the plates are applied. The two plates are kept at different but constant temperatures while the Joule and viscous dissipations are taken into consideration. Numerical solutions for the governing momentum and energy equations are obtained using finite difference approximations. The effect of the Hall term, the parameter describing the non-Newtonian behavior, and the velocity of suction and injection on both the velocity and temperature distributions is examined.     

Effects of hall current and heat transfer on MHD flow of a Burgers’ fluid due to a pull of eccentric rotating disks

The effect of Hall current and heat transfer on the magnetohydrodynamics (MHD) flow of an electrically conducting, incompressible Burgers’ fluid between two infinite disks rotating about non-coaxial axes perpendicular to the disks is studied. The flow is due to a pull with constant velocities of eccentric rotating infinite disks and an external uniform magnetic field normal to the disks is applied. Exact solutions are obtained for the governing momentum and energy equations. The effects of Hartmann number M, Prandtl number Pr, Eckert number Ec and Hall parameter η are studied.     

A quasilinearization approach to heat transfer in MHD visco-elastic fluid flow

The paper deals with the study of the flow of an incompressible electrically conducting visco-elastic fluid referred to as Walter’s liquid B over a porous non-isothermal stretching sheet using quasilinearization technique adopting a numerical approach. The sheet is assumed to stretch uni-directionally and the fluid above the sheet is at rest if there were no stretching. The temperature profiles are obtained numerically and these are displayed through graphs for diverse values of Prandtl number, visco-elastic parameter, magnetic parameter, source/sink parameter, wall temperature parameter and wall heat flux parameter. The results are compared with those available in literature obtained through analytical procedures and are seen to be in good agreement.     

Rotating disk flow and heat transfer through a porous medium of a non-Newtonian fluid with suction and injection

The steady flow of an incompressible viscous non-Newtonian fluid above an infinite rotating porous disk in a porous medium is studied with heat transfer. A uniform injection or suction is applied through the surface of the disk. Numerical solutions of the non-linear differential equations which govern the hydrodynamics and energy transfer are obtained. The effect of the porosity of the medium, the characteristics of the non-Newtonian fluid and the suction or injection velocity on the velocity and temperature distributions is considered. The inclusion of the three effects, the porosity, the non-Newtonian characteristics, and the suction or injection velocity together has shown some interesting effects.     

NSM solution for unsteady MHD Couette flow of a dusty conducting fluid with variable viscosity and electric conductivity

The effects of dependence on temperature of the viscosity and electric conductivity, Reynolds number and particle concentration on the unsteady MHD flow and heat transfer of a dusty, electrically conducting fluid between parallel plates in the presence of an external uniform magnetic field have been investigated using the network simulation method (NSM) and the electric circuit simulation program Pspice. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field perpendicular is applied to the plates. We solved the steady-state and transient problems of flow and heat transfer for both the fluid and dust particles. With this method, only discretization of the spatial co-ordinates is necessary, while time remains as a real continuous variable. Velocity and temperature are studied for different values of the viscosity and magnetic field parameters and for different particle concentration and upper wall velocity.     

MHD oblique stagnation-point flow of a micropolar fluid

The steady two-dimensional oblique stagnation-point flow of an electrically conducting micropolar fluid in the presence of a uniform external electromagnetic field (E₀, H₀) is analysed and some physical situations are examined. In particular, if E₀ vanishes, H₀ lies in the plane of the flow, with a direction not parallel to the boundary, and the induced magnetic field is neglected, it is proved that the oblique stagnation-point flow exists if, and only if, the external magnetic field is parallel to the dividing streamline. In all cases it is shown that the governing nonlinear partial differential equations admit similarity solutions and the resulting ordinary differential problems are solved numerically. Finally, the behaviour of the flow near the boundary is analysed; this depends on the three dimensionless material parameters, and also on the Hartmann number if H₀ is parallel to the dividing streamline.     

计及Hall和离子滑移电流的旋转流体在与时间相关初值条件下的MHDCouette流动

考虑Hall和离子滑移电流的影响,在旋转系统中研究导电流体非稳定的MHD Couette流动．在小数值磁场Reynolds数假定下,推导出基本的控制方程,使用著名的Laplace变换技术,数值地求解该基本方程．分两种情况:磁场相对于流体或者移动平板固定时,得到速度和表面摩擦力统一的闭式表达式．用图形讨论了问题的不同参数,对速度和表面摩擦力的影响．所得结果显示,主流速度u和次生速度v随着Hall电流而增大．离子滑移电流的增大,也会导致主流速度u的增大,但会使次生速度v减小．还给出了旋转、Hall和离子滑移参数的综合影响,确定了次生运动对流体流动的贡献．     

Effect of heat transfer on the peristaltic flow of an electrically conducting fluid in a porous space

This work is aimed at describing the heat transfer on the peristaltic motion in a porous space. An incompressible and magnetohydrodynamic (MHD) viscous fluid is taken in an asymmetrical channel. Expressions of dimensionless stream function and temperature are obtained analytically by employing long wavelength and low Reynolds number assumptions. The influence of various parameters of interest is seen through graphs on pumping and trapping phenomena and temperature profile.     

Three-dimensional Couette flow of a dusty fluid with heat transfer

This work is focused on the mathematical modeling of three-dimensional Couette flow and heat transfer of a dusty fluid between two infinite horizontal parallel porous flat plates. The problem is formulated using a continuum two-phase model and the resulting equations are solved analytically. The lower plate is stationary while the upper plate is undergoing uniform motion in its plane. These plates are, respectively, subjected to transverse exponential injection and its corresponding removal by constant suction. Due to this type of injection velocity, the flow becomes three dimensional. The closed-form expressions for velocity and temperature fields of both the fluid and dust phases are obtained by solving the governing partial differential equations using the perturbation method. A selective set of graphical results is presented and discussed to show interesting features of the problem.     

Series solution for unsteady axisymmetric flow and heat transfer over a radially stretching sheet

This paper deals with the unsteady axisymmetric flow and heat transfer of a viscous fluid over a radially stretching sheet. The heat is prescribed at the surface. The modelled non-linear partial differential equations are solved using an analytic approach namely the homotopy analysis method. Unlike perturbation technique, this approach gives accurate analytic approximation uniformly valid for all dimensionless time. The explicit expressions for velocity, temperature and skin friction coefficient are developed. The influence of time on the velocity, temperature and skin friction coefficient is discussed.     

Combined effect of magnetic field and heat absorption on unsteady free convection and heat transfer flow in a micropolar fluid past a semi-infinite moving plate with viscous dissipation using element free Galerkin method

The fully developed electrically conducting micropolar fluid flow and heat transfer along a semi-infinite vertical porous moving plate is studied including the effect of viscous heating and in the presence of a magnetic field applied transversely to the direction of the flow. The Darcy-Brinkman-Forchheimer model which includes the effects of boundary and inertia forces is employed. The differential equations governing the problem have been transformed by a similarity transformation into a system of non-dimensional differential equations which are solved numerically by element free Galerkin method. Profiles for velocity, microrotation and temperature are presented for a wide range of plate velocity, viscosity ratio, Darcy number, Forchhimer number, magnetic field parameter, heat absorption parameter and the micropolar parameter. The skin friction and Nusselt numbers at the plates are also shown graphically. The present problem has significant applications in chemical engineering, materials processing, solar porous wafer absorber systems and metallurgy.     

Convective heat transfer in a conducting fluid over a permeable stretching surface with suction and internal heat generation/absorption

We consider a convective flow in a porous medium of an incompressible viscous conducting fluid impinging on a permeable stretching surface with suction, and internal heat generation/absorption. Using a similarity transformation the governing equations of the problem are reduced to a coupled third-order nonlinear ordinary differential equations. We first examine a number of special cases for which we may obtain exact solutions. We then obtain analytical solutions (by the Homotopy Analysis Method) and numerical solutions (by a boundary value problem solver), in order to further study the behavior of the nonlinear differential equations, for various values of the physical parameters. Our numerical solutions are shown to agree with the available results in the literature. We then employ the numerical results to bring out the effects of the suction parameter, heat source/sink parameter, stretching parameter, porosity parameter, the Prandtl number and the free convection parameter on the flow and heat transfer characteristics. In the absence of suction and free convection, our findings are in agreement with the corresponding numerical results of Attia [H.A. Attia, On the effectiveness of porosity on stagnation point flow towards a stretching surface with heat generation, Comput. Mater. Sci. 38 (2007) 741-745].     

The effects of MHD and temperature dependent viscosity on the flow of non-Newtonian nanofluid in a pipe: Analytical solutions

This article examines the magnetohydrodynamic (MHD) flow of non-Newtonian nanofluid in a pipe. The temperature of the pipe is assumed to be higher than the temperature of the fluid. In particular two temperature dependent viscosity models, have been considered. The nonlinear partial differential equations along with the boundary conditions are first cast into a dimensionless form and then the equations are solved by homotopy analysis method (HAM). Explicit analytical expressions for the velocity field, the temperature distribution and nano concentration have been derived analytically. The effects of various physical parameters on velocity, temperature and nano concentration are discussed by using graphical approach.     

The influence of Hall current and heat transfer on the flow of a fourth grade fluid

In this article, a mathematical model is analyzed to investigate the effects of Hall current and heat transfer on the flow of a fourth grade fluid between two heated and rotating disks. The corresponding problem of velocity and temperature are solved analytically by homotopy analysis method. Comparison is given between the results of velocity in fourth grade, third grade, second grade, and viscous fluids. The variation of pertinent parameters are graphed and discussed. © 2010 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq 2010     

Heat transfer in a peristaltic flow of MHD fluid with partial slip

In the present note, we have discussed the effects of partial slip on the peristaltic flow of a MHD Newtonian fluid in an asymmetric channel. The governing equations of motion and energy are simplified using a long wave length approximation. A closed form solution of the momentum equation is obtained by Adomian decomposition method and an exact solution of the energy equation is presented in the presence of viscous dissipation term. The expression for pressure rise is calculated using numerical integration. The trapping phenomena is also discussed. The graphical results are presented to interpret various physical parameter of interest. It is found that the temperature field decreases with the increase in slip parameter L, and magnetic field M, while with the increase in P_r and E_c, the temperature field increases.     

Effect of Hall current on the unsteady MHD flow due to a rotating disk with uniform suction or injection

The unsteady flow of a viscous conducting fluid due to the rotation of an infinite, non-conducting, porous disk in the presence of an axial uniform steady magnetic field is studied without neglecting the Hall effect. The fluid is acted upon by a uniform injection or suction through the disk. The relevant equations are solved numerically with a special technique to resolve the conflict between the initial and boundary conditions. The solution shows that the inclusion of the injection or suction through the surface of the disk in addition to the Hall current gives some interesting results.     

Heat transfer in unsteady axisymmetric second grade fluid

This work looks at the heat transfer effects on the flow of a second grade fluid over a radially stretching sheet. The axisymmetric flow of a second grade fluid is induced due to linear stretching of a sheet. Mathematical analysis has been carried out for two heating processes, namely (i) with prescribed surface temperature (PST case) and (ii) prescribed surface heat flux (PHF case). The modelled non-linear partial differential equations in two dependent variables are reduced into a partial differential equation with one dependent variable. The resulting non-linear partial differential equations are solved analytically using homotopy analysis method (HAM). The series solutions are developed and the convergence is properly discussed. The series solutions and graphs of velocity and temperature are constructed. Particular attention is given to the variations of emerging parameters such as second grade parameter, Prandtl and Eckert numbers.     

Exact solution of thermal radiation on MHD flow over a stretching porous sheet

The effect of radiation on MHD steady asymmetric flow of an electrically conducting fluid past a stretching porous sheet in the presence of radiation has been analyzed. Exact solutions for the velocity and temperature fields have been derived and the effects of radiation, magnetic, Prandtl number, wall temperature and suction (or injection) parameters have been studied with the help of graphs.