Unsteady hydromagnetic channel flow of dusty fluid with temperature dependent viscosity and thermal conductivity

In the present paper the unsteady flow and heat transfer of a dusty conducting fluid between two parallel plates with temperature dependent viscosity and thermal conductivity are studied. A constant pressure gradient and an external uniform magnetic field is applied. The governing coupled momentum and energy equations are solved numerically using finite differences. The effect of the variable viscosity and thermal conductivity of the fluid and the uniform magnetic field on the velocity and temperature fields for both the fluid and dust particles is discussed.On leave from Department of Mathematics and Physics, Faculty of Engineering, El-Fayoum University, Egypt     

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     

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.     

The effects of variable properties on MHD unsteady natural convection heat and mass transfer over a vertical wavy surface

A mathematical model will be analyzed in order to study the effects of variables viscosity and thermal conductivity on unsteady heat and mass transfer over a vertical wavy surface in the presence of magnetic field numerically by using a simple coordinate transformation to transform the complex wavy surface into a flat plate. The fluid viscosity is assumed to vary as a exponential function of temperature and thermal conductivity is assumed to vary linearly with temperature. An implicit marching Chebyshev collocation scheme is employed for the analysis. Numerical solutions are obtained for different values of variable viscosity, variable thermal conductivity and MHD variation parameter. Numerical results show that, variable viscosity, variable thermal conductivity and MHD variation parameter have significant influences on the velocity, temperature and concentration profiles as well as for the local skin friction, Nusselt number and Sherwood number.     

Temperature dependent viscosity and thermal conductivity effects on combined heat and mass transfer in MHD three-dimensional flow over a stretching surface with Ohmic heating

An analysis has been carried out to obtain the flow, heat and mass transfer characteristics of a viscous electrically conducting fluid having temperature dependent viscosity and thermal conductivity past a continuously stretching surface, taking into account the effect of Ohmic heating. The flow is subjected to a uniform transverse magnetic field normal to the plate. The resulting governing three-dimensional equations are transformed using suitable three-dimensional transformations and then solved numerically by using fifth order Runge–Kutta–Fehlberg scheme with a modified version of the Newton–Raphson shooting method. Favorable comparisons with previously published work are obtained. The effects of the various parameters such as magnetic parameter M, the viscosity/temperature parameter θ _r , the thermal conductivity parameter S and the Eckert number Ec on the velocity, temperature, and concentration profiles, as well as the local skin-friction coefficient, local Nusselt number, and the local Sherwood number are presented graphically and in tabulated form.     

Dual solutions in mixed convection with variable physical properties

Assisting and opposing flows in a mixed convection boundary layer flow over an isothermal vertical plate are studied for the case of variable physical properties and uniform free stream. Fluid viscosity and thermal conductivity are assumed to be linear functions of temperature. Using local similarity the flow and heat transfer quantities are found to be functions of four parameters, i.e. Richardson number, Prandtl number, a viscosity variation parameter and a thermal conductivity variation parameter. Numerical solutions are obtained by two methods, a shooting technique and Nachtsheim-Swigert technique, for selected values of parameters appropriate for the fluids considered and specific temperatures of the plate and ambient fluid. For assisting flows, there exist solutions for all values of Richardson number while for opposing flows solutions exist only for a finite set of its values and, in addition, there also exist dual solutions. Important flow and heat transfer quantities of practical interest are determined and the influence of different parameters is discussed.     

Effect of magnetic Reynolds number on the two‐dimensional hydromagnetic flow around a cylinder

Numerical experiments have been conducted to study the effect of magnetic Reynolds number on the steady, two‐dimensional, viscous, incompressible and electrically conducting flow around a circular cylinder. Besides usual Reynolds number Re, the flow is governed by the magnetic Reynolds number R_m and Alfvén number β. The flow and magnetic field are uniform and parallel at large distances from the cylinder. The pressure Poisson equation is solved to find the pressure fields in the entire flow region. The effects of the magnetic field and electrical conductivity on the recirculation bubble, drag coefficient, standing vortex and pressure are presented and discussed. For low interaction parameter (N<1), the suppression of the flow‐separation is nearly independent of the conductivity of the fluid, whereas for large interaction parameters, the conductivity of the fluid strongly influences the control of flow‐separation. Copyright © 2008 John Wiley & Sons, Ltd.     

The Effect of Magnetic Field Dependent Viscosity on Thermosolutal Convection in a Ferromagnetic Fluid Saturating a Porous Medium

The effect of magnetic field dependent viscosity on thermosolutal convection in a ferromagnetic fluid saturating a porous medium is considered for a fluid layer heated and soluted from below in the presence of uniform magnetic field. Using linearized stability theory and normal mode analysis, an exact solution is obtained for the case of two free boundaries. For case of stationary convection, medium permeability has a destabilizing effect, whereas a stable solute gradient and magnetic field dependent viscosity have a stabilizing effect on the system. In the absence of magnetic field dependent viscosity, the destabilizing effect of non-buoyancy magnetization is depicted but in the presence of magnetic field dependent viscosity non-buoyancy magnetization may have a destabilizing or stabilizing effect on the onset of instability. The critical wave number and the critical magnetic thermal Rayleigh number for the onset of instability are also determined numerically for sufficiently large values of buoyancy magnetization parameter M₁ and the results are depicted graphically. The principle of exchange of stabilities is found to hold true for the ferromagnetic fluid saturating a porous medium heated from below in the absence of stable solute gradient. The oscillatory modes are introduced due to the presence of the stable solute gradient, which were non-existent in its absence. A sufficient condition for the non-existence of overstability is also obtained. The paper also reaffirms the qualitative findings of earlier investigations which are, in fact, limiting cases of the present study.     

Locally similar solutions for hydromagnetic and thermal slip flow boundary layers over a flat plate with variable fluid properties and convective surface boundary condition

This paper presents heat transfer process in a two-dimensional steady hydromagnetic convective flow of an electrically conducting fluid over a flat plate with partial slip at the surface of the boundary subjected to the convective surface heat flux at the boundary. The analysis accounts for both temperature-dependent viscosity and temperature dependent thermal conductivity. The local similarity equations are derived and solved numerically using the Nachtsheim-Swigert iteration procedure. Results for the dimensionless velocity, temperature and ambient Prandtl number within the boundary layer are displayed graphically delineating the effect of various parameters characterizing the flow. The results show that momentum boundary layer thickness significantly depends on the surface convection parameter, Hartmann number and on the sign of the variable viscosity parameter. The results also show that plate surface temperature is higher when there is no slip at the plate compared to its presence. For both slip and no-slip cases surface temperature of the plate can be controlled by controlling the strength of the applied magnetic field. In modelling the thermal boundary layer flow with variable viscosity and variable thermal conductivity, the Prandtl number must be treated as a variable irrespective of flow conditions whether there is slip or no-slip at the boundary to obtain realistic results.     

On the stability of a thermally stratified conducting fluid under the action of aligned magnetic field

The stability of a thermally stable stratified viscous electrically conducting shear flow is investigated in the presence of an impressed uniform aligned magnetic field. Only two-dimensional disturbances are studied in this paper because Squire's theorem does not apply in general, owing to the presence of the aligned magnetic field. The analysis is partly analytical and partly numerical. The asymptotic solutions for non-viscous fluid are first obtained analytically and they are then improved by introducing viscous and thermal diffusion terms (but only for =1) to get a uniformly valid solution. The neutral stability curves are numerically computed for a range of values of Richardson and Stuart numbers, which show that the flow is completely stabilized when a Stuart number exceeds a certain value for a given R _i>0. It is shown that the combined effects of magnetic field and stratification is to make the system stable to two-dimensional disturbances at lower Stuart number than the one given by Stuart (1954) in the absence of thermal stratification.     

An investigation on internal thermal flow of non-Newtonian fluid

In the present paper an unsteady thermal flow of non-Newtonian fluid is investigated which is of the fiow into axisymmetric mould cavity. In the second part an unsteady thermal flow of upper-convected Maxwell fluid is studied, For the flow into mould cavity the constitutive equation of power-law fluid is used as a rheological model of polymer fluid. The apparent viscosity is considered as a function of shear rate and temperature. A characteristic viscosity is introduced in order to avoid the nonlinearity due to the temperature dependence of the apparent viscosity. As the viscosity of the fluid is relatively high the flow of the thermal fluid can be considered as a flow of fully developed velocity field. However, the temperature field of the fluid fiow is considered as an unsteady one. The governing equations are constitutive equation, momentum equation of steady flow and energy conservation equation of non-steady form. The present system of equations has been solved numerically by the splitting differen     

A numerical study of unsteady gas-solid flow between parallel porous plates submitted to a magnetic field

This paper studies unsteady laminar flow of dusty conducting fluid between parallel porous plates with temperature dependent viscosity and the Network Simulation Method (NSM) is used to solve the governing nonlinear partial differential equations. The fluid is acted upon by a constant pressure gradient and an external uniform magnetic field is applied perpendicular to the plates that are assumed to be porous. The NSM is applied to solve 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. The velocity and temperature are studied for different values of the viscosity and magnetic field parameters.     

Numerical study on a vertical plate with variable viscosity and thermal conductivity

Free convection over an isothermal vertical plate immersed in a fluid with variable viscosity and thermal conductivity is studied in this paper. We consider the two-dimensional, laminar and unsteady boundary layer equations. Using the appropriate variables, the basic governing equations are transformed to non-dimensional governing equations. These equations are then solved numerically using a very efficient implicit finite difference scheme known as Crank–Nicolson scheme. The fluid considered in this study is of viscous incompressible fluid of temperature dependent viscosity and thermal conductivity. The effect of varying viscosity and thermal conductivity on velocity, temperature, shear stress and heat transfer rate are discussed. The velocity and temperature profiles are compared with previously published works and are found to be in good agreement.     

Impact of thermal radiation on MHD slip flow over a flat plate with variable fluid properties

The influence of partial slip, thermal radiation and temperature dependent fluid properties on the hydro-magnetic fluid flow and heat transfer over a flat plate with convective surface heat flux at the boundary 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. Using the similarity transformation, the governing system of non-linear partial differential equations are transformed into similarity non-linear ordinary differential equations and are solved numerically using symbolic software MATHEMATICA 7.0. The numerical values obtained within the boundary layer for the dimensionless velocity, temperature, 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 from the physical point of view.     

Experimental investigation on heat transfer characteristics of magnetic fluid flow around a fine wire under the influence of an external magnetic field

Experimental investigation is conducted to get insight into convective heat transfer features of the aqueous magnetic fluid flow over a fine wire under the influence of an external magnetic field. The convective heat transfer coefficient of the aqueous magnetic fluid flow around the heated wire is measured in both the uniform magnetic field and the magnetic field gradient. The effects of the external magnetic field strength and its orientation on the thermal behaviors of the magnetic fluids are analyzed. The experimental results show that the external magnetic field is a vital factor that affects the convective heat transfer performances of the magnetic fluids and the control of heat transfer processes of a magnetic fluid flow can be possible by applying an external magnetic field.     

Magnetohydrodynamic Rayleigh problem for magnetic prandtl number close to one

Summary In this paper the solutions for indicial motion of an infinite flat plate are discussed. It is assumed that the fluid is incompressible and has constant viscosity and electric conductivity. It is also assumed that both the solid and fluid are semi-infinite or that the solid is thin with fluids on both sides. The conductivity of the wall is assumed in one case to be much greater than the conductivity of the fluid and in a second case to be much less than that of the fluid. In the limit the first case corresponds to a perfectly conducting wall; the second, to a perfectly insulated wall. The distributions of the velocity, magnetic field current, and vorticity are calculated. In the case where the magnetic diffusivity becomes larger than the viscous diffusivity, we show that there is a spreading of the layer in which the magnetic field changes and also a shrinking of the viscous layer. Both layers are very thick in comparison with the non-magneto-hydrodynamic case. This is due to diffusion of the Alfvén wave carrying the vorticity and the current.     

Radiation Effect on MHD Free Convection Flow of a Gas Past a Semi-infinite Vertical Plate with Variable Viscosity

The radiation effect in the presence of a uniform transverse magnetic field on steady free convection flow with variable viscosity is investigated. The fluid viscosity is assumed to vary as the reciprocal of a linear function of temperature. Boundary layer equations are derived. The resulting approximate non-linear ordinary differential equations are solved linearly and nonlinearly by shooting methods. The velocity and temperature profiles are shown, and the skin friction on the plate and heat transfer coefficient are presented and discussed. The results of the present study show that in the presence of magnetic field, as the radiation parameter increases the temperature increases, but the velocity decreases.     

Effect of rotation on ferromagnetic porous convection with a thermal non-equilibrium model

The effect of rotation on the onset of thermal convection in a horizontal layer of ferrofluid saturated Brinkman porous medium is investigated in the presence of a uniform vertical magnetic field using a local thermal non-equilibrium (LTNE) model. A two-field model for temperature representing the solid and fluid phases separately is used for energy equation. The condition for the occurrence of stationary and oscillatory convection is obtained analytically. The stability of the system has been analyzed when the magnetic and buoyancy forces are acting together as well as in isolation and the similarities as well as differences between the two are highlighted. In contrast to the non-rotating case, it is shown that decrease in the Darcy number Da and an increase in the ratio of effective viscosity to fluid viscosity Λ is to hasten the onset of stationary convection at high rotation rates and a coupling between these two parameters is identified in destabilizing the system. Asymptotic solutions for both small and large values of scaled interphase heat transfer coefficient H _t are presented and compared with those computed numerically. Besides, the influence of magnetic parameters and also parameters representing LTNE on the stability of the system is discussed and the veracity of LTNE model over the LTE model is also analyzed.     

Effects of variable fluid properties on natural convection of MHD fluid from a heated vertical wavy surface

In the present paper, the influence of temperature-dependent fluid properties, density, viscosity and thermal conductivity on MHD natural convection flow from a heated vertical wavy surface is studied. It is assumed that, the fluid density and the thermal conductivity vary as exponential and linear functions of temperature, respectively. However, the fluid viscosity is assumed to vary as a reciprocal of a linear function of temperature. The model analysis used here is more relevant to liquid flow. Using the appropriate variables, the wavy surface are transformed into a flat one. The transformed boundary layer equations are solved numerically, using implicit-Chebyshev pseudospectral method, for several sets of values of the physical parameters, namely, the temperature dependent fluid properties parameters, the magnetic parameter, the amplitude-wavelength ratio parameter, and the Prandtl number. The numerical values obtained for the velocity, temperature, shearing stress, and the Nusselt number are presented through graphs and tables for several sets of values of the parameters. The effects of the physical parameters on the flow and heat transfer characteristics are discussed. The results were compared with numerical solutions of previous works. The present results are found to be in good agreement.     

Free convection effects on a vertical cone with variable viscosity and thermal conductivity

The present paper deals with a flow of a viscous incompressible fluid along a heated vertical cone, with due allowance for variations of viscosity and thermal diffusivity with temperature. The fluid viscosity is assumed to be an exponential function of temperature, and the thermal diffusivity is assumed to be a linear function of temperature. The governing equations for laminar free convection of the fluid are transformed into dimensionless partial differential equations, which are solved by a finite difference method with the Crank–Nicolson implicit scheme. Dependences of the flow parameters on the fluid viscosity and thermal conductivity are obtained.