Flow and heat transfer of an electrically conducting third grade fluid past an infinite plate with partial slip

The effects of partial slip on the steady flow and heat transfer of an electrically conducting, incompressible, third grade fluid past a horizontal plate subject to uniform suction and blowing is investigated. Two distinct heat transfer problems are studied. In the first case, the plate is assumed to be at a higher temperature than the fluid; and in the second case, the plate is assumed to be insulated. 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. Numerical solutions for the governing nonlinear equations are obtained over the entire range of physical parameters. The effects of slip, magnetic parameter, non-Newtonian fluid characteristics on the velocity and temperature fields are discussed in detail and shown graphically. It is interesting to find that the velocity and the thermal boundary layers decrease with an increase in the slip, and as the slip increases to infinity, the flow behaves as though it were inviscid.     

MHD free convection flow of visco-elastic fluid past an infinite vertical porous plate

 This work provides a comprehensive theoretical analysis of a two-dimensional unsteady free convection flow of an incompressible, visco-elastic fluid past an infinite vertical porous plate. Solutions for the zero order perturbation velocity profile, the first order perturbation velocity and temperature profiles in closed form are obtained with the help of Laplace transform technique. The numerical solutions are carried out for the Prandtl number 0.1, 0.72, 1.0, 1.5 and 2.0 which are appropriate for different types of liquid metals and for different values of magnetic field parameter, M. Received on 1 September 1999     

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.

     

Oscillating plate temperature effects on a flow past an infinite vertical porous plate with constant suction and embedded in a porous medium

 An approximate solution to the problem of flow of a viscous incompressible dissipative fluid past an infinite vertical porous plate embedded in a porous medium is presented here. The plate temperature is assumed to be oscillating about a constant mean temperature. Mean velocity and mean temperature, the transient velocity and temperature profiles are shown graphically. The mean skin-friction and the mean rate of heat transfer are also shown graphically. The expressions for the amplitude and the phase of the skin-friction and the rate of heat transfer are derived and their numerical values are listed in Tables. The effects of different parameters governing the unsteady flow are discussed. Received on 23 November 1998     

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.     

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 axisymmetric flow of third grade fluid between porous disks with heat transfer

The magnetohydrodynamic(MHD) flow of the third grade fluid between two permeable disks with heat transfer is investigated.The governing partial differential equations are converted into the ordinary differential equations by suitable transformations.The transformed equations are solved by the homotopy analysis method(HAM).The expressions for square residual errors are defined,and the optimal values of convergencecontrol parameters are selected.The dimensionless velocity and temperature fields are examined for various dimensionless parameters.The skin friction coefficient and the Nusselt number are tabulated to analyze the effects of dimensionless parameters.     

On hydromagnetic fluctuating flow past an infinite porous plate in slip flow regime

The effect of a uniform external magnetic field on the laminar, incompressible rarefied gas flow along an infinite porous flat plate is studied under the following conditions: 1) there is uniform suction, 2) the external flow velocity varies periodically with time in magnitude but not in direction, 3) the magnetic Reynolds number is small and 4) the current occurs under slip flow boundary conditions. Expressions for the velocity and temperature fields in the boundary layer are obtained. The response of skin friction, and heat transfer to the fluctuating stream is studied for variations in the rarefaction parameter h ₁, the magnetic field parameter M, and the frequency of the fluctuating stream.Nomenclature c _p specific heat of the gas - f ₁ Maxwells reflection coefficient - f ₂ thermal accommodation coefficient - G as defined in (36) - h ₁ rarefaction parameter (L ₁ v ₀/) - h ₂ nondimensional temperature jump coefficient (L ₂ v ₀/) - H amplitude of the skin friction - k thermal conductivity - K _n Knudsen number - L mean free path - L ₁ (2–f ₁/f ₁) L - L ₂ - M magnetic field parameter ( ₀ B ₀ ² /v ₀ ² ) - m 1/2[1+(1+4M+4i)^1/2], m _r+im _i - n ₁ 1/2[1+(1+4M)^1/2] - q heat flux - R suction Reynolds number - T temperature - x, y coordinates along and perpendicular to the plates - u, v velocity components along x, y-directions - density - kinematic viscosity - ₀ electrical conductivity - Prandtl number - frequency of the fluctuating stream - nondimensional frequency parameter (/v ₀ ² ) - nondimensional distance from wall (v ₀ y/) - phase lead - U _{0 0} mean velocity in the boundary layer - U _{0 1}, U _{0 2} amplitude of the velocity fluctuation in the boundary layer - specific heat ratio     

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.     

Effects of partial slip on flow of a third grade fluid

This paper is an analytical study of the rotating flow of a third grade fluid past a porous plate with partial slip effects. It serves as a flow model for the study of polymers. The analytic solution has been determined using homotopy analysis method (HAM).The English text was polished by Yunming Chen.     

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.     

Heat and mass transfer by MHD mixed convection stagnation point flow toward a vertical plate embedded in a highly porous medium with radiation and internal heat generation

This paper examined the hydromagnetic mixed convection stagnation point flow towards a vertical plate embedded in a highly porous medium with radiation and internal heat generation. The governing boundary layer equations are formulated and transformed into a set of ordinary differential equations using a local similarity approach and then solved numerically by shooting iteration technique together with Runge-Kutta sixth-order integration scheme. A representative set of numerical results are displayed graphically and discussed quantitatively to show some interesting aspects of the pertinent parameters on the dimensionless axial velocity, temperature and the concentration profiles, local skin friction, local Nusselt number and local Sherwood number, the rate of heat and mass transfer. Good agreement is found between the numerical results of the present paper with the earlier published works under some special cases.     

Heat transfer on peristaltic flow of fourth grade fluid in inclined asymmetric channel with partial slip

In this paper, the effects of slip and heat transfer are studied on the peristaltic transport of a magnetohydrodynamic (MHD) fourth grade fluid. The governing equations are modeled and solved under the long wavelength approximation by using a regular perturbation method. Explicit expressions of solutions for the stream function, the velocity, the pressure gradient, the temperature, and the heat transfer coefficient are presented. Pumping and trapping phenomena are analyzed for increasing the slip parameter. Further, the temperature profiles and the heat transfer coefficient are observed for various increasing parameters. It is found that these parameters considerably affect the considered flow characteristics. Comparisons with published results for the no-slip case are found in close agreement.     

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     

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     

Mass transfer effects on flow past an impulsively started infinite vertical plate with constant mass flux — an exact solution

An exact solution to the problem of flow past an impulsively started infinite vertical plate in the presence of a foreign mass and constant mass flux at the plate is presented by the Laplace-transform technique. The velocity, the temperature and the concentration profiles are shown on graphs. The skin-friction and the Sherwood number are also shown on graphs. The effects of different parameters likeG (the Grashof number),Gc (the modified Grashof number),Pr (the Prandtl number) andSc (the Schmidt number) are discussed.     

Finite difference analysis of mass transfer effects on flow past an impulsively started infinite vertical plate in dissipative fluid and constant heat flux

A finite-difference solution to the flow past an impulsively started infinite vertical plate is derived by assuming 1) presence of species concentration like water vapour, CO₂ etc. and 2) constant heat flux at the plate. The velocity and the temperature profiles, the skin-friction and the rate of heat transfer are shown graphically. The effects of the modified Grashof number,Gm, the Eckert numberE, the Schmidt numberSc on the flow of air are discussed.