Unsteady Flow of Radiating and Chemically Reacting MHD Micropolar Fluid in Slip-Flow Regime with Heat Generation

An analytical study of the problem of unsteady free convection with thermal radiation and heat generation on MHD micropolar fluid flow through a porous medium bounded by a semi-infinite vertical plate in a slip-flow regime has been presented. The Rosseland diffusion approximation is used to describe the radiation heat flux in the energy equation. The homogeneous chemical reaction of first order is accounted for in the mass diffusion equation. A uniform magnetic field acts perpendicular on the porous surface absorbing micropolar fluid with a suction velocity varying with time. A perturbation technique is applied to obtain the expressions for the velocity, microrotation, temperature, and concentration distributions. Expressions for the skin-friction, Nusselt number, and Sherwood number are also obtained. The results are discussed graphically for different values of the parameters entered into the equations of the problem.     

Pulsating flow of a couple stress fluid in a channel with permeable walls

The paper is concerned with an analytical study of the oscillatory flow of a couple stress fluid in a channel, bounded by two permeable walls. The couple stress fluid is considered to be injected into the medium through one of the walls with a given velocity and to be sucked off by the other wall with an equal velocity. The problem is solved by using a perturbation technique. Analytical expressions for the velocity and volumetric flow rate are derived for the oscillatory flow of the couple stress fluid flowing in the channel. By using the method of parametric variation, distribution of the velocity of the couple stress fluid, change in velocity profiles at different instants of time, change in volumetric flow rate with change in frequency and cross-flow Reynolds number are computed, by considering an illustrative example. The study reveals that both the velocity and the volumetric flow rate are quite sensitive to the couple stress parameter, the frequency of oscillation and also to the cross-flow Reynolds number. The study will be immensely useful in resolving different problems associated with oil industries.     

Stratification effects on transient Stokes flow in the presence of a permeable boundary

The transient unbounded flow of a stratified viscous fluid over an oscillating permeable boundary has been considered. The viscosity and the density of the fluid have been assumed to decay exponentially in the direction normal to the bounding permeable wall. The initial value problem associated with the resulting diffusion equation, subject to the Beavers-Joseph boundary condition, has been solved analytically. The solution for the transient velocity has been expressed in terms of error and exponential functions of complex arguments. The effects of fluid stratification and the bounding porous medium on the fluid velocity have been analyzed.     

EMHD free-convection boundary-layer flow from a Riga-plate

The electro-magnetohydrodynamic (EMHD) free-convection flow of a weakly conducting fluid (e.g. seawater) from an electromagnetic actuator is considered. The actuator is a so called Riga-plate which consists of a spanwise aligned array of alternating electrodes and permanent magnets mounted on a plane surface. This array generates a surface-parallel Lorentz force which decreases exponentially in the direction normal to the (horizontal) plate. The free-convection boundary-layer flow induced by this body force is investigated numerically and analytically. It is shown that a certain length and velocity scale exists on which the flow characteristics are independent of the material properties of the fluid, as well as of the structural and functional parameters of the actuator. These universal velocity profiles are calculated numerically at different distances x from the leading edge and are discussed in some detail, both for the impermeable and the permeable Riga-plate when; in the latter case, a uniform lateral suction or injection of the fluid is applied. For the flow characteristics analytical approximations are reported. The asymptotic suction profiles approached for large values of x are given in exact analytical form. From a mathematical point of view the basic equations of the present boundary-value problem resemble those of the classical Blasius problem with an inhomogeneous forcing instead of an external flow and, accordingly, a homogeneous asymptotic condition.     

MHD flow between two parallel plates with heat transfer

Summary In the present paper, the steady flow of an electrically conducting, viscous, incompressible fluid bounded by two parallel infinite insulated horizontal plates and the heat transfe through it are studied. The upper plate is given a constant velocity while the lower plate is kept stationary. The viscosity of the fluid is assumed to vary with temperature. The effect of an external uniform magnetic field as well as the action of an inflow perpendicular to the plates together with the influence of the pressure gradient on the flow and temperature distributions are reported. A numerical solution for the governing non-linear ordinary differential equations is developed.     

Mass transfer effects on impulsively with variable surface heat flux

Numerical Solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite vertical plate with variable surface heat flux and mass transfer is presented here. The governing equations are solved using implicit finite-difference scheme of Crank-Nicolson type. The velocity profiles are compared with exact Solution and are found to be in good agreement. The transient and steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that there is a rise in the velocity due to the presence of a mass diffusion. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.     

Free convection heat and mass transfer along a vertical surface in a porous medium

Summary This study deals with free convection heat and mass transfer from a vertical plate embedded in a fluid saturated porous medium with constant wall temperature and concentration. The temperature and concentration variations across the boundary layer produce a buoyancy effect which gives rise to flow field. Integral method of Von-Karman type is applied to obtain the analytical solution of this fundamental problem.     

Effects of free convection on the oscillatory flow of a polar fluid through a porous medium in the presence of variable wall heat flux

The purpose of this work is to study a laminar two-dimensional free convective oscillatory flow of an incompressible polar fluid through a saturated porous medium occupying a semi-infinite region of the space which is bounded by an infinite vertical permeable plate in the presence of oscillating suction and variable wall heat flux. The governing equations are based on the local volume averaging technique. The generalized Darcy equation accounting for polar effects is employed. Analytical expressions for the linear momentum, angular momentum, and energy fields are obtained by using the two-term perturbation technique. The numerically computed results are shown graphically and compared with the corresponding ones for a viscous (Newtonian) fluid. Distribution of the mean velocity of a polar fluid is found to increase as compared to the Newtonian fluid. The analysis reveals multiple boundary-layer structure for velocity. Published in Inzhenerno-Fizicheskii Zhurnal, Vol. 81, No. 5, pp. 868–884, September–October, 2008.     

On impulsive motion of a vertical plate with heat flux and diffusion of chemically reactive species

Finite-difference solution of the transient natural convection flow of an incompressible viscous fluid past an impulsively started semi-infinite plate with constant heat flux and mass diffusion is presented here, taking into account the homogeneous chemical reaction of first order. The concentration profiles are compared with the exact solution and are found to be in good agreement. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first order chemical reaction, the velocity decreases with increasing values of the chemical reaction parameter. The local as well as average skin-friction, Nusselt number and Sherwood number are shown graphically.     

Viscous flow due to an exponentially shrinking permeable sheet in nanofluid in presence of slip

Classical problem of steady boundary layer flow of nanofluid over an exponentially permeable shrinking sheet in presence of slip is investigated. The model used for nanofluid includes Brownian motion and thermophoresis effects. The governing equations for momentum, energy, and nanofluid solid volume fraction are transformed to ordinary differential equations with the help of similarity transformations and then solved numerically using fourth order Runge–Kutta method with shooting technique. It is found that the governing parameters, viz. the suction/blowing parameter, velocity slip, thermal and mass slip parameters, Brownian motion parameter, thermophoresis parameter, Prandtl number, and Lewis number significantly affect the flow field, heat, and mass transfer. The results obtained indicate that the dual solutions exist for certain values of the mass suction parameter. Velocity increases whereas the temperature and nanoparticle volume fraction decrease due to suction through the porous sheet. It is noted that with the increase in velocity slip fluid velocity increases whereas temperature and concentration decrease. Due to increase in thermal slip and mass slip both temperature and concentration decrease.     

The effect of variable properties on the helical flow and heat transfer of power law fluids

Summary Laminar flow and forced convection heat transfer of the time independent non–Newtonian fluid obeying power law stress-strain relation have been investigated numerically in the annular space between two coaxial rotating cylinders. The problem is considered when the inner cylinder rotates about the common axis with constant angular velocity and the outer cylinder is at rest. The viscosity of the fluid and thermal conductivity are assumed to vary with the temperature. The outer surface of the annulus is considered to be adiabatic, while the inner surface has a uniform temperature. The tangential and axial momentum equations and energy equation have been solved iteratively by using a finite difference method. For the steady fully developed flow, the velocity distributions, temperature profiles, the volumetric flow rate, torque and the average Nusselt number have been obtained for different values of the radius ratio and model parameters.     

Analytical investigation of forced convection from a flat plate enhanced by a porous substrate

Summary This paper deals with an analytical investigation of forced convection from a flat plate enhanced by a porous substrate. The flow occurs in a composite channel, which is partially filled with the porous substrate, and partially with a clear fluid. The substrate is attached to the upper plate in the channel, which is subject to a uniform heat flux. The lower plate of the channel is adiabatic. The flow in the porous region is described by the Brinkman-Forchheimer-extended Darcy equation. Utilizing the boundary layer approximation for the flow in the porous substrate, analytical solutions for the flow velocity, temperature distribution, and the Nusselt number are obtained.     

Radiation and thermal diffusion effects on an unsteady MHD free convection mass-transfer flow past an infinite vertical porous plate with the hall current and a heat source

An analysis is performed to study the effects of radiation and thermal diffusion on an unsteady MHD free convection heat- and mass-transfer flow of an incompressible, electrically conducting, viscous fluid past an infinite vertical porous plate with the Hall current and a heat source. The flow is considered under the influence of a constant suction velocity and a uniform magnetic field applied normally to the flow. The dimensionless governing equations are solved numerically by the Galerkin finite element method. The effects of the flow parameters on the primary and secondary velocities, temperature, species concentration, shearing stresses, Nusselt number, and Sherwood number are calculated and presented in figures and tables. The results obtained show that a decrease in the temperature boundary layer thickness occurs when the Prandtl number and radiation parameter are increased and an increase in the Schmidt number leads to a decrease in the concentration boundary layer thickness.     

Non-Darcian flow and heat transfer along a permeable vertical surface with nonlinear density temperature variation

The non-Darcy free convection flow on a vertical flat plate embedded in a fluid-saturated porous medium in the presence of the lateral mass flux with prescribed constant surface temperature is considered. The coupled nonlinearities generated by the density variation with temperature, inertia, and viscous dissipation are included in the present study. In particular, we analyze a system of nonlinear ODEs describing self-similar solutions to the flow and heat transfer problem. These transformed equations are integrated numerically by a second-order finite difference scheme known as the Keller box method. Furthermore, some analytical results are provided to establish relationships between the physical invariants in the problem, and also to validate the numerical method. One of the important findings of our study is that an increase in the Rayleigh number increases the velocity boundary layer thickness, while the opposite is true for the thermal boundary layer thickness.     

Finite-element method for the effects of chemical reaction, variable viscosity, thermophoresis and heat generation/absorption on a boundary-layer hydromagnetic flow with heat and mass transfer over a heat surface

Summary The effects of variable viscosity, thermophoresis and heat generation or absorption on hydromagnetic flow with heat and mass transfer over a heat surface are presented here, taking into account the homogeneous chemical reaction of first order. The fluid viscosity is assumed to vary as an inverse linear function of temperature. The velocity profiles are compared with previously published works and are found to be in good agreement. The governing fundamental equations are approximated by a system of nonlinear ordinary differential equations and are solved numerically by using the finite element method. The steady-state velocity, temperature and concentration profiles are shown graphically. It is observed that due to the presence of first-order chemical reaction the concentration decreases with increasing values of the chemical reaction parameter. The results also showed that the particle deposition rates were strongly influenced by thermophoresis and buoyancy force, particularly for opposing flow and hot surfaces. Numerical results for the skin-friction coefficient, wall heat transfer and particle deposition rate are obtained and reported graphically for various parametric conditions to show interesting aspects of the solution.     

Finite element analysis of combined heat and mass transfer in hydromagnetic micropolar flow along a stretching sheet

This paper presents a finite element solution of the problem of heat and mass transfer in a hydromagnetic flow of a micropolar fluid past a stretching sheet. The transformed equations for the flow regime are solved numerically by using finite element method. The effect of important parameters namely magnetic field parameter, material parameter, Eckert number and Schmidt number over velocity, microrotation, temperature and concentration functions has been studied. It has been observed that the magnetic field parameter has the effect of reducing the velocity and increasing the microrotation, temperature and concentration while the micropolar parameter has the opposite effect on these functions except temperature function. Temperature increases with the increase in Eckert number and concentration decreases with the increase in Schmidt number.     

Flow and heat transfer of a micropolar fluid in an axisymmetric stagnation flow on a cylinder with variable properties and suction (numerical study)

Summary. In this paper, an analysis is presented to study the effects of variable properties, density, viscosity and thermal conductivity of a micropolar fluid flow and heat transfer in an axisymmetric stagnation flow on a horizontal cylinder with suction, numerically. The fluid density and the thermal conductivity are assumed to vary linearly with temperature. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The similarity solution is used to transform the problem under consideration into a boundary value problem of nonlinear coupled ordinary differential equations which are solved numerically by using the Chebyshev finite difference method (ChFD). Numerical results are carried out for various values of the dimensionless parameters of the problem. The numerical results show variable density, variable viscosity, variable thermal conductivity and micropolar parameters, which have significant influences on the azimuthal and the angular velocities and temperature profiles, shear stress, couple stress and the Nusselt number. The numerical results have demonstrated that with increasing temperature ratio parameter the azimuthal velocity decreases. With increasing variable viscosity parameter the temperature increases, whereas the azimuthal and the angular velocities decrease. Also, the azimuthal and the angular velocities increase and the temperature decreases as the variable conductivity parameter increases. Finally, the pressure increases as the suction parameter increases.     

Combined radiation and mixed convection from a vertical wall with suction/injection in a non–Darcy porous medium

Summary. Mixed convection flow of an absorbing fluid up a uniform non–Darcy porous medium supported by a semi-infinite ideally transparent vertical flat plate due to solar radiation is considered. The external flow field is assumed to be uniform, the effect of the radiation parameter in the boundary layer adjacent to the vertical flat plate with fluid suction/injection through it is analyzed in both aiding and opposing flow situations. It is observed that the similarity solution is possible only when the fluid suction/injection velocity profile varies as x^–1/2. The velocity and temperature profiles in the boundary layer and the heat transfer coefficient are presented for selected values of the parameters. It is observed that the Nusselt number increases with the increase in the radiation parameter and also when the value of the surface mass flux parameter moves from the injection to the suction region.     

Hall effect on MHD flow and heat transfer over a stretching sheet with variable thickness

We investigate the MHD flow and heat transfer of an electrically conducting fluid over a stretching sheet with variable thickness. The wall temperature and the wall velocity are assumed to vary. The effects of external magnetic field along the sheet and the Hall currents are considered. The governing equations are solved numerically using an implicit finite difference scheme. The obtained numerical results are compared with the available results in the literature for some special cases and the results are found to be in very good agreement. The effects of the physical parameters on the velocity and temperature fields are presented graphically and analyzed. The effect of the Hall current gives rise to a cross flow. Moreover, the Hall current and the magnetic field have strong effect on the flow and heat transfer characteristics, i.e., shear stress and the Nusselt number.     

Heat transfer through a porous plate at cooling gas supply in an asymptotic suction regime

The analytical solution is carried out for the one- and two-dimensional problem of the thermal state of a porous plate surrounded by the flow of high-temperature and homogenous cooling gases in a permeable cooling system. Cooling gas flow in a laminar regime of asymptotic suction is considered, which provides effective heat shielding with minimum dependence on the parameters of the permeable wall. Heat exchange from the high-temperature gas is accepted for both laminar and turbulent boundary layers.