Effects of mass transfer and free convection on the unsteady mhd flow past a vertical porous plate with variable suction

In this paper we investigate the effects of mass transfer on the unsteady free convective flow of an electrically conducting and viscous incompressible fluid past an infinite vertical plate subjected to variable suction, in the presence of transverse magnetic field, when the free-stream velocity oscillates with time in magnitude but not in direction. In this analysis, the effects of the induced magnetic field is neglected. Approximate solutions to the transient flow, the amplitude and phase of skin-friction and the rate of heat transfer have been derived. During the course of the discussion, the effects of Gr, Gc, Sc, Ec, M and ω have been presented.     

Effects of mass transfer and free convection on the unsteady mhd flow past a vertical porous plate with constant suction

Effects of free convection currents and mass transfer on the unsteady flow of an electrically conducting and viscous incompressible fluid past an infinite vertical porous plate subjected to uniform suction, in the presence of transverse magnetic field, have been studied taking into account that the external flow velocity varies periodically with time in magnitude but not in direction. The effect of the induced magnetic field has been neglected. Approximate solutions to the transient flow, the amplitude and the phase of the skin-friction and the rate of heat transfer have been derived. During the course of the discussion, the effects of the Grashoff number Gr, the modified Grashoff number Gc (depending on the concentration difference), the Schmidt number Sc, the Eckert number Ec, the magnetic field parameter M, and the frequency ω have been discussed.     

Mass transfer and free convection flow through A porous medium

A theoretical analysis of the steady free convective and mass transfer flow is presented, when a viscous and incompressible fluid flows through a porous medium occupying a semi-infinite region of the space bounded by an infinite vertical porous plate. The fluid is subjected to a normal suction velocity, and the heat flux at the plate is constant. The free-stream velocity is assumed constant.     

Free convection heat and mass transfer to steady flow in a semi-infinite vertical porous medium

Analytical solutions are derived for flow in a semi-infinite vertical porous medium with heat and mass transfer. When the temperature and mass concentration are uniform a constant pressure is possible and sustains a fully developed flow. Thereafter there is a small perturbation of the wall temperature and concentration, and the subsequent two-dimensional problem is tackled for large Prandtl number and free convection parameters and small Reynolds number. The heat transfer rate at the wall is discussed quantitatively.     

Oscillatory flow in a stratified medium past an infinite porous plate with constant suction

An approximate solution to oscillatory flow past a porous horizontal plate was carried out under the following conditions

• (i) Constant suction
• (ii) Stratification of the medium due to change in density, viscosity and thermal conductivity
• (iii) Free-stream oscillation about a nonzero constant mean.

Solutions have been derived for the transient velocity, the transient temperature, the amplitude and the phase of skin friction and the amplitude and phase of the first and second harmonics of the rate of heat transfer. These are shown on the graphs. The effects of the suction parameter S, the stratification parameter λ, the frequency λ and the Eckert number E are discussed.     

Hall effects on the hydromagnetic free convective flow and mass transfer through a porous medium bounded by an infinite vertical porous plate with constant heat flux

Effects of Hall current on free convection and mass transfer flow through a porous medium bounded by a vertical surface when a uniform magnetic field acts in a plane which makes an angle x with the plane transverse to the plate have been analysed. An analytic solution of the problem is obtained and the effects of the Hall parameter and the permeability parameter, as well as the other parameters entering into the problem, are discussed and shown graphically.     

A note on heat transfer to MHD oscillatory flow in an asymmetric wavy channel

This note deals with the MHD oscillatory flow of an optically thin fluid in an asymmetric wavy channel filled with porous medium. Based on some simplifying assumptions, the governing momentum and energy equations are solved and analytical solutions for fluid velocity, temperature distribution, Nusselt number and skin friction are constructed. The effects of radiation parameter, Peclet number, Hartmann number, porous medium shape factor and geometric parameters on flow and heat transfer characteristics have been examined in detail.     

Analysis of MHD micropolar nanofluid flow and heat transfer between a porous plate and a nonporous plate filled with porous medium

This article presents an analytical study on magnetohydrodynamic micropolar nanofluid flow through parallel, coaxial discs filled with a porous medium with uniform blowing from the upper plate. Three different types of nanoparticles, namely copper, aluminum oxide, and titanium dioxide are considered with water and used as base fluids. The governing equations are solved via Differential Transformation Method. The validity of this method has been verified with the results of numerical solution (fourth‐order Runge‐Kutta scheme). The analytical investigation is carried out for different governing parameters. The results indicate that skin friction coefficient has a direct relationship with Hartmann number and the micropolar parameter. It is also found that Nusselt number is increased with increment in Prandtl number and Eckert number. Additionally, this analysis concluded that an increase in volume fraction of nanofluid increases the Nusselt number on the top plate and decreases it on the lower plate.     

MHD effect on flow structures and heat transfer characteristics of liquid metal-gas annular flow in a vertical pipe

The magnetohydrodynamic (MHD) effect on the flow structures and heat transfer characteristics was studied numerically for a liquid metal-gas annular flow under a transverse magnetic field. The side layers, in which the velocity was increased, appeared near the eastern and western sidewalls in an annular MHD flow as in a single-phase liquid metal MHD flow. Temperature distribution in the liquid film, and the Nusselt number distribution in the angular direction were influenced by the flow structures with the side layers. Consequently heat transfer rate was higher at the eastern/western sidewalls than that at the southern/northern walls. The pressure drop in the MHD annular flow is of the same order of magnitude as in the single-phase MHD pipe flow under similar liquid metal flow condition.     

Heat transfer in fluctuating flow past an infinite plate with suction and constant heat flux

An analysis of unsteady heat transfer in a two-dimensional flow past an infinite porous plate has been carried out under the following conditions: (1) constant or variable suction; (2) free-stream oscillating in time about a non-zero constant mean; and (3) constant heat flux at the plate. Approximate solutions to the temperature field have been derived. the transient temperature, the amplitude and phase of the Nusselt number are shown on graphs.     

Effects of chemical reaction, heat and mass transfer along a wedge with heat source and concentration in the presence of suction or injection

An approximate numerical solution for the steady laminar boundary-layer flow over a wall of the wedge with suction or injection in the presence of species concentration and mass diffusion has been obtained by solving the governing equations using numerical technique. The fluid is assumed to be viscous and incompressible. Numerical calculations up to third level of truncation are carried out for different values of dimensionless parameters and an analysis of the results obtained shows that the flow field is influenced appreciably by the chemical reaction, heat source and suction or injection at the wall of the wedge.     

Heat transfer in the magnetohydrodynamic flow of a power-law fluid past a porous flat plate with suction or blowing

An analysis is made of the steady magnetohydrodynamic flow of a power-law fluid past an infinite porous flat plate subjected to suction or blowing. A uniform transverse magnetic field is applied normal to the plate. It is shown that for small magnetic field parameter M, the steady solutions for velocity distribution exist for a pseudoplastic (shear-thinning) fluid for which the power-law index n satisfies 1/2 < n ≤ 1 provided that there is suction at the plate. For blowing at the plate the steady solutions for velocity distribution exist only when n is of the form p/q, where p is an odd positive integer and q is an even positive integer provided 1/2 < n < 1. Velocity at a point is found to increase with increase in M. The solution of the energy equation governing temperature distribution in the flow of a pseudoplastic fluid past an infinite porous plate subjected to uniform suction reveals that the temperature at a given point increases with increase in M.     

Effects of hall current and wall temperature oscillation on free convective and mass transfer flow in a rotating porous medium with constant heat source

The combined effects of Hall current and a constant heat source on the hydromagnetic free convective and mass transfer flow past an infinite vertical porous plate in a rotating porous medium are considered, when the temperature of the plate varies with time about a nonzero constant mean and the temperature of the free stream is constant. The problem is solved analytically and the velocity profiles are shown on graphs. Effects of m (Hall parameter) and α (heat source parameter) on velocity are discussed extensively.     

Local similarity solution for combined free-forced convective and mass transfer flow past a semi-infinite vertical plate

An analysis is presented of the effects of buoyancy forces in a laminar uniform forced-convective flow with mass transfer along a semi-infinite vertical plate. A family of solutions to the coupled nonlinear equations is numerically obtained. The velocity, temperature and concentration profiles are shown for different values of the dimensionless parameters g_r =Gr/Re_x² and g_c =Gc/Ref_x² (Gr =Grashof number, Gc =modified Grashof number, Re_x =Local Reynolds number). The numerical values of the skin friction and the rate of heat transfer for different values of Gr and Gc are also tabulated. The flow field is greatly influenced by the dimensionless ratio Gr/Re_x², which means that the effects of the free convection currents and mass transfer flow on the flow field, are important.     

MHD mass transfer flow past an inclined plate with variable temperature and plate velocity embedded in a porous medium

An exact solution of unsteady MHD free convective mass transfer flow past an infinite inclined plate embedded in a saturated porous medium with variable plate velocity, temperature, and mass diffusion has been presented. An attempt has been made to analyze the Soret effect and the influence of the angle of inclination on the flow and transport properties, in the presence of thermal radiation, heat source, and chemical reaction. The equations governing the flow, heat, and mass transfer are solved by employing the Laplace transform technique, in closed form. The variations in fluid velocity, temperature, and concentration profiles are shown graphically whereas the numerical values of shear stress, the rate of heat transfer, and the rate of mass transfer from the plate to the fluid are presented in tabular form for various values of the flow parameters. The results show that the flow is accelerated due to the Soret effect while the angle of inclination sustains a retarding effect on fluid velocity. Further it is observed that the viscous drag at the plate and the mass diffusion from the plate to the fluid decrease under the influence of thermal diffusion.     

Radiation and mass transfer effects on two-dimensional flow past an impulsively started infinite vertical plate

The interaction of free convection with thermal radiation of a viscous incompressible unsteady flow past an impulsively started vertical plate with heat and mass transfer is analyzed. The fluid is gray, absorbing-emitting but non-scattering medium and the Rosseland approximation is used to describe the radiative flux in the energy equation. The dimensionless governing equations are solved using an implicit finite-difference method of Crank–Nicolson type. Numerical results for the velocity, the temperature, the concentration, the local and average skin-friction, the Nusselt number and Sherwood number are shown graphically. It is observed that, when the radiation parameter increases, the velocity and temperature decrease in the boundary layer. The local and average skin-friction increases with the increase in radiation parameter. For increasing values of radiation parameter the local as well as average Nusselt number increases.     

Simultaneous heat and mass transfer on oscillatory free convection boundary layer flow

The problem of simultaneous heat and mass transfer in two-dimensional free convection from a semi-infinite vertical flat plate is investigated. An integral method is used to find a solution for zero wall velocity and for a mass transfer velocity at the wall with small-amplitude oscillatory wall temperature. Low- and high-frequency solutions are developed separately and are discussed graphically with the effects of the parameters Gr (the Grashof number for heat transfer), Gc (the Grashof number for mass transfer) and Sc (the Schmidt number) for Pr = 0–71 representing aid at 20°C.     

Unsteady hydromagnetic free convection flow with hall current mass transfer and variable suction through a porous medium near an infinite vertical porous plate with constant heat flux

The effects of Hall current on unsteady free convection flow of an MHD viscous incompressible fluid along an infinite vertical porous plate are investigated in the presence of a uniformly applied magnetic field acting in a plane which makes an angle α with the plane transverse to the plate. A similarity parameter, taken to be a function of time, is introduced, and the suction velocity is considered to be inversely proportional to this parameter. Similarity equations are then derived and solved numerically. The effects of the Hall parameter, the magnetic parameter and the permeability are discussed and shown graphically.     

Interfacial suction effects of a porous layer on filmwise condensation heat transfer enhancement

Considering the liquid transverse suction effect at the porous layer interface, a mathematical model was presented to investigate the influence of the porous layer characteristic parameters on condensation heat transfer. The results revealed that the enhancement ratio increased with the increase of the porous layer thickness and permeability. The effective thermal conductivity of the porous layer was, however, of little significance for condensation heat transfer enhancement. Also, the enhancement mechanism was analyzed by comparing the thermal resistances within the external condensate film and the porous layer. © 2002 Wiley Periodicals, Inc. Heat Trans Asian Res, 31(7): 568–577, 2002; Published online in Wiley InterScience ( www.interscience.wiley.com ). DOI 10.1002/htj.10058     

Analysis of flow and heat transfer inside oscillatory squeezed thin films subject to a varying clearance

The flow and heat transfer inside a non-isothermal and incompressible thin film having its upper plate slightly inclined from the horizontal and undergoing an oscillatory squeezing motion is investigated in this work. Two models are analyzed: low and large Reynolds number flow models. The corresponding governing equations for each model are properly non-dimensionalized and solved numerically. The main controlling parameters for the dynamic and thermal behavior of the inclined thin film are found to be the amplitude of the upper plate motion, squeezing Reynolds number, squeezing number, thermal squeezing parameter and the dimensionless slope of the upper plate. It is found that fluctuations in the axial and normal velocities are greater for convergent thin films than for divergent thin films. Furthermore, Nusselt numbers and their amplitudes are found to decrease with an increase in the dimensionless slope of the upper plate. Finally correlations are obtained for Nusselt numbers and their corresponding amplitudes for two different thermal conditions: constant wall temperature and uniform wall heat flux.