Infinite Vertical Plate Research Articles

Analysis of Free Convective Jeffery’s Fluid with Periodic Permeability and Cattaneo-Christov Heat Transfer

Abstract In this study a free convective three-dimensional flow of an incompressible Jeffery’s fluid through a highly porous medium bounded by an infinite vertical porous plate subjected to a constant suction is modeled and analyzed theoretically. The permeability of the medium is assumed to be periodic while free stream velocity is assumed to be uniform. The assumption of either constant or time dependent permeability of a porous medium leads to two-dimensional flows, however, the flow becomes three-dimensional due to variable permeability of the porous medium. Cattaneo-Christov approach is used for the transfer of heat in fluid flow. Analytic solutions for velocity field, pressure, skin friction components and temperature distribution are obtained. The effects of physical parameters emerging in the mathematical model of the physical phenomenon on these physical quantities are discussed and visualized graphically. It is noted that main flow velocity component decreases due to enhancement in non-Newtonian parameter, however, pressure rises due to thickening of the fluid.

MHD Free Convective Boundary Layer Flow through Porous medium Past a Moving Vertical Platewith Heat Source and Chemical Reaction

In this paper, we have considered the unsteady magnetohydrodynamic (MHD) free convection in a boundary layer flow of an electrically conducting fluid through porous medium subject to uniform transverse magnetic field over a moving infinite vertical plate in the presence of heat source and chemical reaction. The equations for governing flow through porous medium based on Brinkman’s model. The non-linear partial differential equations have been transformed into a two point boundary value problem using similarity variables and then solved numerically by Runge-Kutta fourth order method with the help of shooting technique. Computational results are discussed for velocity, temperature and concentration profiles while numerical values of the skin friction, Nusselt number and Sherwood number are tabulated for different values of governing parameters controlling the flow system.

Heat and Mass Transfer Analysis of an Unsteady MHD Flow Past an Impulsively Started Vertical Plate in Presence of Thermal Radiation

The present paper aims at investigating the boundary layer flow of an unsteady MHD free convection heat and mass transfer flow of a viscous, incompressible and electrically conducting fluid over an impulsively started infinite vertical plate in presence of thermal radiation. The magnetic Reynolds number is considered to be so small that the induced magnetic field can be neglected. Exact solution of the governing equations is obtained in closed form by Laplace transform technique. Expression for skin friction, Nusselt number and Sherwood number are derived. The numerical values of fluid velocity, fluid temperature and species concentration are displayed graphically whereas the numerical values of skin friction, the Nusselt number and the Sherwood number are presented in tabular form for various values of pertinent flow parameters. It is being found that the mass diffusion tends to reduce the fluid velocity whereas thermal radiation has reverse effect on the fluid velocity throughout the boundary layer region. Mass diffusion tends to reduce the species concentration whereas time has reverse effect on the species concentration throughout the boundary layer region. The radiation parameter and mass diffusion decreases the skin friction whereas Prandtl number has reverse effect on it. The radiation parameter reduces the rate of heat transfer whereas as time progress the rate of heat transfer is getting accelerated.

Unsteady MHD natural convection flow of a rotating viscoelastic fluid over an infinite vertical porous plate due to oscillating free-stream

PurposeThe purpose of this paper is to present an analytical study on an unsteady magnetohydrodynamic (MHD) boundary layer flow of a rotating viscoelastic fluid over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream taking Hall and ion-slip currents into account. The unsteady MHD flow in the rotating fluid system is generated due to the buoyancy forces arising from temperature and concentration differences in the field of gravity and oscillatory movement of the free-stream.Design/methodology/approachThe resulting partial differential equations governing the fluid motion are solved analytically using the regular perturbation method by assuming a very small viscoelastic parameter. In order to note the influences of various system parameters and to discuss the important flow features, the numerical results for fluid velocity, temperature and species concentration are computed and depicted graphically vs boundary layer parameter whereas skin friction, Nusselt number and Sherwood number at the plate are computed and presented in tabular form.FindingsAn interesting observation is recorded that there occurs a reversal flow in the secondary flow direction due to the movement of the free stream. It is also noted that a decrease in the suction parameter gives a rise in momentum, thermal and concentration boundary layer thicknesses.Originality/valueVery little research work is reported in the literature on non-Newtonian fluid dynamics where unsteady flow in the system arises due to time-dependent movement of the plate. The motive of the present analytical study is to analyse the influences of Hall and ion-slip currents on unsteady MHD natural convection flow of a rotating viscoelastic fluid (non-Newtonian fluid) over an infinite vertical porous plate embedded in a uniform porous medium with oscillating free-stream.

The Effect of MHD on Free Convection with Periodic Temperature and Concentration in the Presence of Thermal Radiation and Chemical Reaction

This paper studies the effect of magneto hydrodynamics on unsteady free convection between a pair of infinite vertical Couette plates. The temperature of the plates and concentration between the plates vary with time. Convection between the plates is considered in the presence of thermal radiation and chemical reaction. The solution is obtained using perturbation techniques. These techniques are used to transform nonlinear coupled partial differential equations to a system of ordinary differential equations. The resulting equations are solved analytically. The solution is expressed in terms of power series with some small parameter. The effect of various parameters, viz., velocity, temperature and concentration, has been discussed. Mat lab code simulation study is carried out to support the theoretical results. The result shows that as the thermal radiation parameter R increases, the temperature decreases near the moving porous plate while it approaches to a zero in the region close to the boundary layer of the stationary plate. Moreover, as the modified Grashof number, i.e., based on concentration difference, increases, the velocity of the fluid flow increases hence the concentration decreases. An increase in both the chemical reaction parameter and Schmidt number results in decreased concentration.

A Study of Chemically Reactive Species and Thermal Radiation Effects on an Unsteady MHD Free Convection Flow Through a Porous Medium Past a Flat Plate with Ramped Wall Temperature

An investigation of the effects of a chemical reaction and thermal radiation on unsteady MHD free convection heat and mass transfer flow of an electrically conducting, viscous, incompressible fluid past a vertical infinite flat plate embedded in a porous medium is carried out. The flow is induced by a general time-dependent movement of the vertical plate, and the cases of ramped temperature and isothermal plates are studied. An exact solution of the governing equations is obtained in closed form by the Laplace Transform technique. Some applications of practical interest for different types of plate motions are discussed. The numerical values of fluid velocity, temperature and species concentration are displayed graphically whereas the numerical values of skin friction, Nusselt number and Sherwood number are presented in a tabular form for various values of pertinent flow parameters for both ramped temperature and isothermal plates.

Initial Unsteady Free Convective Flow Past an Infinite Vertical Plate with Radiation and Mass Transfer Effects

An exact solution and analysis of an initial unsteady two dimensional free convection flow, heat and mass transfer in the presence of thermal radiation along an infinite fixed vertical plate when the plate temperature is instantaneously raised, is presented. The fluid considered is a gray, absorbing emitting radiation but a nonscattering medium. Three cases have been discussed, in particular, namely, (i) when, the plate temperature is instantaneously raised to a higher constant value, (ii) when, the plate temperature varies linearly with time and (iii) when, the plate temperature varies non-linearly with time. A close form general solution for all the cases has been obtained in terms of repeated integrals of error functions. In two particular cases, the solutions in terms of the repeated integrals of error functions have been further simplified to forms containing only error functions. It is observed that for an increase in the radiation parameter N or a decrease in the Grashof number Gr or Gm, there is a fall in the velocity or temperature, but compared to the no radiation case or no diffusing species, there is a rise in the velocity and temperature of the fluid.

Heat and Mass Transfer on unsteady MHD free convective flow through a porous medium over an infinite vertical plate with time dependent permeability and oscillatory suction

Heat and Mass Transfer on unsteady MHD free convective flow through a porous medium over an infinite vertical plate with time dependent permeability and oscillatory suction

Hydro magnetic heat and mass transfer flow in a porous plate with varying temperature

Objectives: To study the unsteady hydro magnetic naturally convicting flow with heat and mass flux in the presence of chemical reaction, fluid past an infinite vertical porous plate with varying temperature and concentration. Statistical Analysis: An analysis is carried out to study the heat transfer in unsteady two dimensional Mass transfer flow of a magneto hydrodynamic over a porous medium. The flow is subjective in the action of uniform transverse magnetic field. With the help of dimensionless variable, the governing flow equation are reduced to a system of nonlinear Partial Differential Equation. This system has been solved analytically using Perturbation Approximation. Findings: The influence of the temperature distribution, concentration distribution, Skin friction coefficient, BrandtNumber, Magnetic Parameter, chemical Reaction Parameter, Gash of number, Modified Gash of Number, Schmidt Number, Heat source Parameter, Radiation Parameter are discussed in Graph. In this paper, suppression of velocity on magnetic Parameter and chemical reaction are discussed. The Gash of Number and Modified Gash of Number increase the velocity, whereas in the literature survey, the analytical or numerical solution obtained by assuming that the temperature at the interface was continuous and well defined. The highlights of the results are helpful to variety the ramped temperature and ramped concentration on the wall of the infinite vertical porous plate. Applications: The combined heat and mass transfer problem along with chemical reaction play a prominent role in chemical and hydrometallurgical industries. It is used by different scientific disciplines for different processes and mechanisms. In many practical situations, mass transfer is accomplished in order to bring chemical reagents together so that a reaction can take place. Thus for example reaction can be used to provide more rapid solution of a gas in to a liquid than physical solution. Keywords: Hydro Magnetic, Heat Transfer, Mass Transfer, Chemical Reaction, Porous Medium

General Solutions for Hydromagnetic Free Convection Flow over an Infinite Plate with Newtonian Heating, Mass Diffusion and Chemical Reaction

The problem of hydromagnetic free convection flow over a moving infinite vertical plate with Newtonian heating, mass diffusion and chemical reaction in the presence of a heat source is completely solved. Radiative and porous effects are not taken into consideration but they can be immediately included by a simple rescaling of Prandtl number and magnetic parameter. Exact general solutions for the dimensionless velocity and concentration fields and the corresponding Sherwood number and skin friction coefficient are determined under integral form in terms of error function or complementary error function of Gauss. They satisfy all imposed initial and boundary conditions and can generate exact solutions for any problem with technical relevance of this type. As an interesting completion, uncommon in the literature, the differential equations which describe the thermal, concentration and momentum boundary layer, as well as the exact expressions for the thicknesses of thermal, concentration or velocity boundary layers were determined. Numerical results have shown that the thermal boundary layer thickness decreases for increasing values of Prandtl number and the concentration boundary layer thickness is decreasing with Schmidt number. Finally, for illustration, three special cases are considered and the influence of physical parameters on some fundamental motions is graphically underlined and discussed. The required time to reach the flow according with post-transient solution (the steady-state), for cosine/sine oscillating concentrations on the boundary is graphically determined. It is found that, the presence of destructive chemical reaction improves this time for increasing values of chemical reaction parameter.

Variable mass diffusion effects on free convection flow past an impulsively started infinite vertical plate

An exact analysis of the problem of free convection flow of a viscous incompressible chemically reacting fluid past an infinite vertical plate with the flow due to impulsive motion of the plate with Newtonian heating in the presence of thermal radiation and variable mass diffusion is performed. The resulting governing equations were tackled by Laplace transform technique. Finally the effects of pertinent flow parameters such as the radiation parameter, chemical reaction parameter, buoyancy ratio parameter, thermal Grashof number, Schmidt number, Prandtl number and time on the velocity, temperature, concentration and skin friction for both aiding and opposing flows were examined in detail when Pr=0.71(conducting air) and Pr=7.0(water).

General solution for MHD-free convection flow over a vertical plate with ramped wall temperature and chemical reaction

The aim of the article is to study the unsteady magnetohydrodynamic-free convection flow of an electrically conducting incompressible viscous fluid over an infinite vertical plate with ramped temperature and constant concentration. The motion of the plate is a rectilinear translation with an arbitrary time-dependent velocity. Closed-form solutions for the temperature, concentration and velocity fields of the fluid are obtained. The influence of transverse magnetic field that is fixed relative either to fluid or plate is studied. Furthermore, the effects of system parameters on the fluid velocity are analyzed through numerical simulations and graphical illustrations.

Free convection flows over a vertical plate that applies shear stress to a fractional viscous fluid

Free convection flow of a fractional viscous fluid over an infinite vertical plate with exponential heating is studied using a fractional derivative with non-singular kernel. Fluid motion is induced by the plate that applies an arbitrary time-dependent shear stress to the fluid. Closed-form solutions for the dimensionless velocity and temperature fields and Nusselt number are established under the usual Boussinesq approximation. The obtained results can generate exact solutions for any motion with technical relevance of this type. Moreover, fluid’s velocity is presented as a sum of its mechanical and thermal components. A semi analytical solution based on the Stehfest’s formula for the inverse Laplace transform is also obtained. Finally, the influence of fractional parameter on the fluid motion as well as the contributions of mechanical and thermal components of velocity are graphically underlined and discussed.

Heat and Mass Transfer on MHD Flow of an incompressible fluid past an infinite vertical porous plate

Heat and Mass Transfer on MHD Flow of an incompressible fluid past an infinite vertical porous plate

Unsteady MHD free convection flow of rotating Jeffrey fluid embedded in a porous medium with ramped wall temperature

The effect of radiative heat transfer on unsteady magnetohydrodynamic (MHD) free convection flow of rotating Jeffrey fluid past an infinite vertical plate saturated in a porous medium with ramped wall temperature is investigated. The incompressible fluid is taken electrically conducting under influence of transverse magnetic field which perpendicular to the flow. An appropriate dimensionless variables are employed to the governing equations and solved analytically by Laplace transform technique. The results of several controlling parameters for both ramped wall temperature and an isothermal plate are presented graphically with comprehensive discussions. It has been observed that, an increase in rotation parameter, reduced the primary velocity, but an opposite behaviour is noticed for the secondary velocity. Moreover, large values of Hartmann number tends to retard the fluid flow due to the Lorentz force.

Effect of thermal radiation on magneto-nanofluids free convective flow over an ac-celerated moving ramped temperature plate

An attempt has been made to explore the effect of thermal radiation on electrically conducting, viscous and incompressible magneto-nanofluids free convective flow in the presence of an inclined magnetic field. Fluid flow is persuaded due to an accelerated movement of an infinite vertical ramped temperature plate. The water based nanofluids with the nanoparticles of alumina (Al2O3), copper (Cu) and titanium oxide (TiO2) have been accounted. In order to model the problem mathematically, the model of nanoparticle volume fraction has been employed. The exact solution of the mathematical model in closed form has been obtained analytically by making use of Laplace transform technique. The amalgamated form expressions are obtained for nanofluid velocity, nanofluid temperature, skin friction and Nusselt number, in both ramped and isothermal conditions. The consequence of various physical parameters affecting the nanofluid velocity and nanofluid temperature have examined by means of various graphs whereas, the numerical values of skin friction and Nusselt number have been reported by different tables. The numerical results have been compared for both ramped and isothermal conditions. It has been noticed that both the nanofluid velocity and temperature are smaller in magnitude in the case of ramped temperature plate than that of isothermal plate.

Heat and Mass Transfer on MHD Free convective flow of Second grade fluid through Porous medium over an infinite vertical plate

In this paper, we have considered the unsteady free convective two dimensional flow of a viscous incompressible electrically conducting second grade fluid over an infinite vertical porous plate under the influence of uniform transverse magnetic field with time dependent permeability, oscillatory suction. The governing equations of the flow field are solved by a regular perturbation method for small amplitude of the permeability. The closed form solutions for the velocity, temperature and concentration have been derived analytically and also its behavior is computationally discussed with reference to different flow parameters with the help of profiles. The skin fiction on the boundary, the heat flux in terms of the Nusselt number and rate of mass transfer in terms of Sherwood number are also obtained and their behavior computationally discussed.

Unsteady MHD Natural Convective Flow of a Rotating Fluid over an Infinite Vertical Plate due to Oscillatory Movement of the Free-Stream with Hall and Ion-Slip Currents

In the present research study a mathematical analysis has been presented for unsteady MHD natural convective flow of a rotating fluid over an infinite vertical plate immersed in a fluid saturated porous medium with oscillating free-stream. The effects of Hall and ion-slip currents also considered on the fluid flow. The unsteady MHD flow over the vertical plate is induced due to thermal and concentration buoyancy forces and oscillatory movement of the free-stream. The partial differential equations governing the motion for the fluid flow are solved analytically. The effects of various pertinent flow parameters on the fluid velocity, fluid temperature and species concentration are presented in graphical form whereas that on skin friction and rate of heat and mass transfer at the plate are presented in tabular form. An interesting observation recorded from the present analysis that there appears reversal flow in the secondary flow direction due to presence of thermal and/or concentration buoyancy forces. However, in the absence of both reversals flow does not exist in the secondary flow direction. It is also noted that the thickness of momentum boundary layer decreases with rise in frequency of oscillations of the free-stream.

Effect of Induced Magnetic Field on MHD Mixed Convection Flow in Vertical Microchannel

The present work presents a theoretical investigation of an MHD mixed convection flow in a vertical microchannel formed by two electrically non-conducting infinite vertical parallel plates. The influence of an induced magnetic field arising due to motion of an electrically conducting fluid is taken into consideration. The governing equations of the motion are a set of simultaneous ordinary differential equations and their exact solutions in dimensionless form have been obtained for the velocity field, the induced magnetic field and the temperature field. The expressions for the induced current density and skin friction have also been obtained. The effects of various non-dimensional parameters such as rarefaction, fluid wall interaction, the Hartmann number and the magnetic Prandtl number on the velocity, the induced magnetic field, the temperature, the induced current density, and skin friction have been presented in a graphical form. It is found that the effect of the Hartmann number and magnetic Prandtl number on the induced current density is found to have a decreasing nature at the central region of the microchannel.

Free convection flow of some fractional nanofluids over a moving vertical plate with uniform heat flux and heat source

Free convection flow of some water based fractional nanofluids over a moving infinite vertical plate with uniform heat flux and heat source is analytically and graphically studied. Exact solutions for dimensionless temperature and velocity fields, Nusselt numbers, and skin friction coefficients are established in integral form in terms of modified Bessel functions of the first kind. These solutions satisfy all imposed initial and boundary conditions and reduce to the similar solutions for ordinary nanofluids when the fractional parameters tend to one. Furthermore, they reduce to the known solutions from the literature when the plate is fixed and the heat source is absent. The influence of fractional parameters on heat transfer and fluid motion is graphically underlined and discussed. The enhancement of heat transfer in such flows is higher for fractional nanofluids in comparison with ordinary nanofluids. Moreover, the use of fractional models allows us to choose the fractional parameters in order to get a very good agreement between experimental and theoretical results.