Mass transfer and free convective MHD flow past an accelerated vertical porous plate

The effects of variable suction/injection on the unsteady two-dimensional free convective flow with mass transfer of an electrically conducting fluid past a vertical accelerated plate in presence of a transverse magnetic field is considered. Solutions of the equations governing the flow are obtained with the help of the power series. The paper is concluded with a discussion of the results obtained.

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Stofftransport und MHD-Strömung bei freier Konvektion an einer beschleunigten senkrechten porösen Platte

Zusammenfassung In dieser Arbeit werden die Wirkungen verÄnderlicher Absaugung/Ausblasung auf die instationÄre zweidimensionale freie Strömung mit Stoffübertragung eines elektrisch leitenden Fluids an einer senkrecht beschleunigten Wand mit magnetischem Querfeld betrachtet. Lösungen erhÄlt man mit Hilfe von PotenzansÄtzen. Die Ergebnisse werden diskutiert.

     

Dissipation effects on MHD free convection flow past a semi-infinite vertical plate

Viscous and Joule dissipation effects are considered on MHD free convection flow past a semi-infinite isothermal vertical plate under a uniform transverse magnetic field. Series solutions in powers of a dissipation number (=gx/c _p) have been employed and the resulting ordinary differential equations have been solved numerically. The velocity and temperature profiles are shown on graphs and the numerical values of ₁(0)/₀(0) (, temperature function) have been tabulated. It is observed that the dissipation effects in the MHD case become more dominant with increasing values of the magnetic field parameter (=M ²/(Gr _x /4)^1/2) and the Prandtl number.     

Soret and Dufour effects on unsteady MHD flow past an infinite vertical porous plate with thermal radiation

The objective of the present study is to investigate the effect of flow parameters on the free convection and mass transfer of an unsteady magnetohydrodynamic flow of an electrically conducting, viscous, and incompressible fluid past an infinite vertical porous plate under oscillatory suction velocity and thermal radiation. The Dufour （diffusion thermo） and Soret （thermal diffusion） effects are taken into account. The problem is solved numerically using the finite element method for the velocity, the temperature, and the concentration field. The expression for the skin friction, the rate of heat and mass transfer is obtained. The results are presented numerically through graphs and tables for the externally cooled plate （Gr 〉 0） and the externally heated plate （Gr 〈 0） to observe the effects of various parameters encountered in the equations.     

Hall effect on MHD free convection boundary layer flow past a vertical flat plate

Effects of Hall current on MHD free convection boundary layer flow of a viscous incompressible electrically conducting fluid past a heated vertical flat plate of finite dimension in the presence of a uniform transverse magnetic field have been studied. An exact solution of the governing equations describing the flow has been obtained. The velocity field, induced magnetic field and bulk temperature distributions in the boundary layer flow have been discussed. It is found that the velocity components increase with an increase in Hall parameter. It is noticed that the induced magnetic field components are radically influenced by the Hall parameter. It is also found that the magnitude of bulk temperature in the x-direction decreases with an increase in either Hall parameter or magnetic parameter. On the other hand, the magnitude of the bulk temperature in the z-direction increases with an increase in Hall parameter whereas it decreases with an increase in magnetic parameter.     

Visco-elastic fluid flow past an infinite vertical porous plate in the presence of first-order chemical reaction

An analysis has been developed to study the unsteady free convection flow of an incompressible visco-elastic fluid on a continuously moving vertical porous plate in the presence of a first-order chemical reaction. The governing equations are solved numerically using an implicit finite difference technique. The obtained numerical solutions are compared with the analytical solutions. The velocity profiles are presented. A parametric analysis is performed to illustrate the influences of the visco-elastic parameter, the dimensionless chemical reaction parameter, and the plate moving velocity on the steady state velocity profiles, the time dependent friction coefficient, the Nusselt number, and the Sherwood number.     

Effects of MHD free convection and mass transfer on the flow past an oscillating infinite coaxial vertical circular cylinder

The effects of MHD free convection and mass transfer are taken into account on the flow past oscillating infinite coaxial vertical circular cylinder. The analytical expressions for velocity, temperature and concentration of the fluid are obtained by using perturbation technique.

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Einwirkungen von freier MHD-Konvektion und Stoffübertragung auf eine Strömung nach einem schwingenden unendlichen koaxialen vertikalen Zylinder

Zusammenfassung Die Einwirkungen der freien MHD-Konvektion und Stoffübertragung auf eine Strömung nach einem schwingenden, unendlichen, koaxialen, vertikalen Zylinder wurden untersucht. Die analytischen Ausdrücke der Geschwindigkeit, Temperatur und Fluidkonzentration sind durch die Perturbationstechnik erhalten worden.

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Nomenclature C _p Specific heat at constant temperature - C the species concentration near the circular cylinder - C _w the species concentration of the circular cylinder - C the species concentration of the fluid at infinite - * dimensionless species concentration - D chemical molecular diffusivity - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - K thermal conductivity - Pr Prandtl number - r _a ,r _b radius of inner and outer cylinder - a, b dimensionless inner and outer radius - r,r coordinate and dimensionless coordinate normal to the circular cylinder - Sc Schmidt number - t time - t dimensionless time - T temperature of the fluid near the circular cylinder - T _w temperature of the circular cylinder - T temperature of the fluid at infinite - u velocity of the fluid - u dimensionless velocity of the fluid - U ₀ reference velocity - z,z coordinate and dimensionless coordinate along the circular cylinder - coefficient of volume expansion - * coefficient of thermal expansion with concentration - dimensionless temperature - H ₀ magnetic field intensity - coefficient of viscosity - _e permeability (magnetic) - kinematic viscosity - electric conductivity - density - M Hartmann number - dimensionless skin-friction - frequency - dimensionless frequency     

Heat and mass transfer on a MHD third grade fluid with partial slip flow past an infinite vertical insulated porous plate in a porous medium

The influence of third grade, partial slip and other thermophysical parameters on the steady flow, heat and mass transfer of viscoelastic third grade fluid past an infinite vertical insulated plate subject to suction across the boundary layer has been investigated. The space occupying the fluid is porous. The momentum equation is characterized by a highly nonlinear boundary value problem in which the order of the differential equation exceeds the number of available boundary conditions. An efficient numerical scheme of midpoint technique with Richardson’s extrapolation is employed to solve the governing system of coupled nonlinear equations of momentum, energy and concentration. Numerical calculations were carried out for different values of various interesting non-dimensional quantities in the slip flow regime with heat and mass transfer and were shown with the aid of figures. The values of the wall shear stress, the local rate of heat and mass transfers were obtained and tabulated. The analysis shows that as the fluid becomes more shear thickening, the momentum boundary layer decreases but the thermal boundary layer increases; the magnetic field strength is found to decrease with an increasing temperature distribution when the porous plate is insulated. The consequences of increasing the permeability parameter and Schmidt number decrease both the momentum and concentration boundary layer thicknesses respectively whereas an increase in the thermal Grashof number gives rise to the thermal boundary layer thickness.     

Combined forced and free convection MHD row past a semi-infinite vertical plate

Effects of a transversely applied magnetic field on the forced and free convective flow of an electrically conducting fluid past a vertical semi-infinite plate, on taking into account dissipative heat and stress work, have been presented. Without magnetic field, it has been discussed by the authors [1] in an earlier paper. The effects of Gr (Grashof number, Gr>0 cooling of the plate by free convection currents, Gr<0 heating of the plate by free convection currents), Pr (Prandtl number), F (Froude number) and M² (the magnetic field parameter) are discussed. It is observed that reverse type of flow of air exists near the plate when Gr<0.

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Gemischte erzwungene und freie Konvektions-MHD-Strömung an einer halbunendlichen senkrechten Platte

Zusammenfassung Die Wirkung eines transversalen Magnetfeldes auf die erzwungene und freie Konvektion einer elektrisch leitenden Flüssigkeit an einer halbunendlichen senkrechten Platte wurde unter Berücksichtigung der Dissipationswärme und der Kompressionsarbeit mitgeteilt. Das Problem wurde ohne Magnetfeld schon früher [1] behandelt. Diskutiert wurde die Wirkung der Grashof-Zahl Gr (Gr>0 Kühlung der Platte durch freie Konvektion), der Prandtl-Zahl Pr, der Froude-Zahl F und des magnetischen Feldparameters M₂. Bei Gr<0 wird Umkehr strömung in Plattennähe betrachtet.

     

Effects of MHD free convection and mass transfer on the flow past a vibrating infinite vertical circular cylinder

The effects of MHD free convection and mass transfer are taken into account on the flow past a vibrating infinite isothermal and constant heat flux vertical circular cylinder. The expressions for velocity, temperature, concentration and skin-friction of the fluid are obtained in closed form by using Laplace transform technique. The effects ofPr (Prandtl number),Sc (Schmidt number),Gr (Grashof number,Gr>0 implies cooling andGr<0 heating of the cylinder),Gm (modified Grashof number),M (magnetic field parameter) and variation of time on velocity distribution have been studied graphically. The results presented in this paper agree with the results of Lien and Chen when magnetic parameter approaches zero.

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Effekte der freien MHD Konvektion und der Stoffübertragung auf die Strömung längs eines vibrierenden unendlich langen vertikalen Kreiszylinders

Zusammenfassung Es werden die Effekte der freien MHD Konvektion und der Stoffübertragung auf die Strömung längs eines vibrierenden unendlich langen vertikalen isothermen Kreiszylinders mit konstanter Wärmestromdichte untersucht. Es werden geschlossene Ausdrücke für die Geschwindigkeit, Temperatur, Konzentration und Wandreibung des Fluides mittels der Laplace-Transformation erhalten. Die Effekte der Prandtl-ZahlPr, Schmidt-ZahlSc, Grashof-ZahlGr (Gr>0 bedeutet kühlen,Gr<0 heizen), der modifizierten Grashof-ZahlGm, des ParametersM für das magnetische Feld und das zeitliche Verhalten der Geschwindigkeitsverteilung wurden graphisch untersucht. Die Ergebnisse dieser Untersuchung stimmen mit denen von Lien und Chen überein, wenn der Parameter für das magnetische Feld nahe bei 0 liegt.

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Nomenclature C _p Specific heat at constant temperature - C the species concentration near the circular cylinder - C _w the species concentration of the circular cylinder - C the species concentration of the fluid at infinite - * dimensionless species concentration - D chemical molecular diffusivity - g acceleration due to gravity - Gr Grashof number - Gm modified Grashof number - K thermal conductivity - Pr Prandtl number - r ₀ radius of the circular cylinder - r ₀ dimensionless radius - r, r coordinate and dimensionless coordinate normal to the circular cylinder - Sc Schmidt number - t time - t dimensionless time - T temperature of the fluid near the circular cylinder - T _w temperature of the circular cylinder - T temperature of the fluid at infinite - u velocity of the fluid - u dimensionless velocity of the fluid - U ₀ reference velocity - z, z coordinate and dimensionless coordinate along the circular cylinder - coefficient of volume expansion - * coefficient of thermal expansion with concentration - dimensionless temperature - H ₀ magnetic field intensity - coefficient of viscosity - _e permeability (magnetic) - kinematic viscosity - electric conductivity - density - M Hartmann number - dimensionless skin-friction - frequency - dimensionless frequency     

An exact solution for the flow of a non-newtonian fluid past an infinite porous plate

Summary The flow of an incompressible fluid of second grade past an infinite porous plate subject to either suction or blowing at the plate is studied. It is found that existence of solutions is tied in with the sign of material moduli and in marked contrast to the Classical Newtonian, fluid solutions can be exhibited for the blowing problem.

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Sommario Si studia la corrente di un fluido incomprimibile di secondo grado che lambisce una lastra porosa da cui è succhiato o soffiato. Si trova che l'esistenza delle soluzioni è legata al segno dei moduli del materiale e, in netto contrasto col fluido newtoniano classico, si possono trovare soluzioni per il problema del soffiamento.

     

An existence theorem for the flow of a non-newtonian fluid past an infinite porous plate

Non-Newtonian fluid mechanics affords an excellent opportunity for studying many of the mathematical methods which have been developed to analyse non-linear problems in mechanics. The flow of an incompressible fluid of grade three past an infinite porous flat plate, subject to suction at the plate, is governed by a non-linear differential equation that is particularly well suited to demonstrate the power and usefulness of three such techniques. We establish an existence theorem using shooting methods. Next, we investigate the problem using a perturbation analysis. It is not clear that the perturbation solution converges and thus may not be the appropriate solution for a certain range of a material constant (which is not the perturbation parameter). Finally, we employ a numerical method which is particularly suited to the problem in question.     

Mixed convection of an incompressible viscous fluid in a porous medium past a hot vertical plate

This paper analyses steady two-dimensional mixed convection of an imcompressible viscous fluid in a porous medium past a hot vertical plate. Assuming Darcy-Brinkman model for the flow in a porous medium, the boundary layer equations are integrated numerically to obtain the non-similar solution for the velocity and temperature distribution for several values of the permeability and viscous dissipation parameters. It is shown that for a fixed value of Prandtl number Pr and dissipation parameter E, the skin-friction at the plate decreases with increase in the permeability parameter K₁. However for the same value or Pr and E, the heat transfer rate at the plate increases with increasing K₁. The dimensionlcss velocity and temperature functions in the flow are plotted for several values of E and K₁ with Pr = 0.73. It is also shown that for fixed values of K₁, and KPr, the skin-friction increases with increase in the dissipation parameter E.     

Magnetogasdynamic flow past an infinite porous flat plate in slip flow regime

This paper presents an exact solution for the flow of a rarefied ionized gas over an infinite porous plate in the presence of a transverse magnetic field, by using the well known continuum approach. An attempt is made to bring out the salient features of the interaction between the applied magnetic field and the flow of a rarefied conducting gas. The analysis reveals that the skin friction, and the heat transfer into the plate are reduced due to gas rarefaction.     

MHD mixed convection for viscoelastic fluid past a porous wedge

A magnetic hydrodynamic (MHD) mixed convective heat transfer problem of a second-grade viscoelastic fluid past a wedge with porous suction or injection has been studied. Governing equations include continuity equation, momentum equation and energy equation of the fluid. It has been analyzed by a combination of a series expansion method, the similarity transformation and a second-order accurate finite-difference method. Solutions of wedge flow on the wedge surface have been obtained by a generalized Falkner-Skan flow derivation. Some important parameters have been discussed by this study, which include the Prandtl number (Pr), the elastic number (E), the free convection parameter (G) and the magnetic parameter (M), the porous suction and injection parameter (C) and the wedge shape factor (β). Results indicated that elastic effect (E) in the flow could increase the local heat transfer coefficient and enhance the heat transfer of a wedge. In addition, similar to the results from Newtonian fluid flow and conduction analysis of a wedge, better heat transfer is obtained with a larger G and Pr.     

Numerical solutions for the flow of a fluid of grade three past an infinite porous plate

This paper presents a numerical study of the flow of an incompressible fluid of grade three past an infinite porous flat plate, subject to suction at the plate. This flow is governed by a non-linear differential equation that is particularly well suited to demonstrate the power and usefulness of different numerical techniques. In this work, the numerical solutions are obtained using a Runge-Kutta method of fourth order. The accuracy of the method for this problem is demonstrated.     

Magnetohydrodynamic unsteady free convection past a hot vertical plate

The free convection flow of an electrically conducting liquid from an infinite plate has been studied in the presence of a uniform magnetic field. General expressions for the velocity field, induced magnetic field, skin-friction and temperature distribution have been obtained when the plate is a perfect conductor and its temperature varies with the law t ⁿ e ^at . The results have been presented through some graphs and tables with the magnetic Prandtl number unity as its value.