Free convection effects on the oscillatory flow of an incompressible viscous fluid past an infinite,vertical plate with variable suction

An analysis of a two-dimensional flow of an incompressible, viscous fluid past an infinite, vertical porous plate has been carried out under the following conditions: (i) the suction velocity normal to the plate varies periodically with time (ii) the free stream velocity oscillates in time about a constant mean (iii) the temperature difference between the constant plate temperature and the free stream temperature, causing the free convection currents in the boundary layer. Approximate solutions for the transient velocity, the transient temperature, the amplitude and the phase of the skin-friction and the rate of heat transfer are derived. The fluctuating parts of the velocity profiles, the transient velocity, the transient temperature are shown on graphs whereas the numerical values of the amplitude and the phase of the skin-friction and the rate of heat transfer are entered in tables. The results are discussed in a quantitative way.     

Free convection flow of a second order fluid past a hot vertical plate

Laminar free convection flow of a second order fluid past a hot vertical plate with varying wall temperature has been studied in this paper. Exact solutions for the velocity and temperature fields have been obtained. The effects of elastic coefficient on the velocity and temperature fields, rate of heat transfer and the skin-friction have been studied.     

Free convection past a vertical plate

Zusammenfassung Diese kurze Mitteilung zeigt, dass für den Fall natürlicher Konvektion eine Familie von exakten Lösungen gefunden werden kann, welche die regierenden Gleichungen zur Darstellung bringen.

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This work was supported by the Naval Supersonic Laboratory, Department of Aeronautical Engineering, Massachusetts Institute of Technology, ProfessorJohn R. Markham, Director.     

Magnetic field effects on free convection flow of a nanofluid past a vertical semi-infinite flat plate

In this paper, we discuss similarity reductions for problems of magnetic field effects on free convection flow of a nanofluid past a semi-infinite vertical flat plate. The application of a one-parameter group reduces the number of independent variables by 1, and consequently the governing partial differential equation with the auxiliary conditions to an ordinary differential equation with the appropriate corresponding conditions. The differential equations obtained are solved numerically and the effects of the parameters governing the problem are discussed. Different kinds of nanoparticles were tested.     

Hydromagnetic effects on the three-dimensional flow past a porous plate

Hydromagnetic effects on the three-dimensional flow of an electrically conducting viscous incompressible fluid past a porous plate with periodic suction has been analysed. The uniform flow is subjected to a transversely applied magnetic field. The mathematical analysis is presented for the hydromagnetic boundary layer flow neglecting the induced magnetic field. Approximate solutions for the components of velocity field and the skin-frictions due to them are obtained and discussed with the help of a graph and tables.     

Effect of variable density on hydromagnetic mixed convection flow of a non-Newtonian fluid past a moving vertical plate

The effect of temperature-dependent density on MHD mixed convection flow of power-law fluid past a moving semi-infinite vertical plate for high temperature differences between the plate and the ambient fluid is studied. The fluid density is assumed to decrease exponentially with temperature. The usual Boussinesq approximations are not considered due to the large temperature differences. The surface temperature of the moving plate was assumed to vary according to a power-law form, that is, T_w(x) = T_∞ + Ax^γ. The fluid is permeated by a uniform magnetic field imposed perpendicularly to the plate on the assumption of small magnetic Reynolds number. A numerical shooting algorithm for two unknown initial conditions with fourth-order Runge–Kutta integration scheme has been used to solve the coupled non-linear boundary value problem. The effects of various parameters on the velocity and temperature profiles as well as the local skin-friction coefficient and the local Nusselt number are presented graphically and in the tabular form. The results show that application of Boussinesq approximations in a non-Newtonian fluid subjected to high temperature differences gives a significant error in the values of the skin-friction coefficient and the application of an external magnetic field reduces this error markedly in the case of shear-thickening fluid.     

An implicit-Chebyshev pseudospectral method for the effect of radiation on power-law fluid past a vertical plate immersed in a porous medium

An implicit-Chebyshev collocation spectral method is employed in this study. This method was used to compute the problem of unsteady free convection with heat transfer from an isothermal vertical flat plate to a non-Newtonian fluid saturated porous medium, which is modeled as a power-law fluid. Boundary layer and Boussinesq approximations have been incorporated. The Darcy–Brinkman–Forchheimer model is applied to describe the flow field, where the magnetic field and the radiation effects are taken into account. Because of the non-Newtonian rheology, these problems are non-linear and must be solved numerically. The domain of the problem is discretized according to the implicit-Chebyshev spectral collocation scheme. In this study, the spatial derivatives are computed with a differentiation matrix and the time derivatives are computed with Crank–Nicolson implicit finite-difference method. Numerical calculations are carried out for the various parameters entering into the problem. Velocity and temperature profiles are shown in tables and graphically. It is found that as time approaches infinity, the values of friction factor and heat transfer coefficients approach the steady state values.     

Application of parameter differentiation for flow of a third grade fluid past an infinite porous plate

This article investigates the analytic solution for the flow of a third grade fluid past an infinite porous plate. The method of parameter differentiation is used to linearized the governing flow equation. The solution of the obtained linear equation is developed by differential transform method in combination with the method of superposition. The obtained results are compared with existing results in the literature and an excellent agreement is found. This shows that the parameter differentiation is a powerful technique for solving nonlinear problems. © 2009 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2010     

An asymptotic method for free convection past a vertical plate

Zusammenfassung Das Problem der freien Strömung an einer ungleichmässig erhitzten Wand wird auf die Berechnung einer Reihe von Funktionen zurückgeführt, von denen jede einer linearen Differentialgleichung mit konstanten Koeffizienten genügt.

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Written under the sponsorship of the National Science Foundation, Contract NSF-G3050, New York University. Reproduction in whole or in part permitted for any purpose of the United States Government.     

Effects of mass transfer on free convective flow of a dissipative,incompressible fluid past an infinite vertical porous plate with suction

An analysis of the mass transfer effects on the free convective flow of an incompressible, dissipative, viscous fluid past an infinite, vertical porous plate with constant suction, has been carried out. Approximate solutions to coupled non-linear equations governing the flow are derived. The velocity and the temperature profiles are shown graphically for air (P=0·71). The effects of Gr (Grashof number), Gc (the modified Grashof number), Sc (Schmidt number), E (Eckert number) are discussed qualitatively during the course of discussion. It is observed that due to the addition of the foreign mass, there is a rise in the velocity and a fall in the temperature. But the skin-friction increases when Sc?1 and it decreases when Sc ～1. The rate of heat transfer increases for Sc<1 and decreases for Sc>1.     

Oscillatory free convection flow of a second order fluid from a vertical plate

This paper investigates the problem of free convection flow of a second order liquid in the boundary layer from a semi-infinite vertical plate in which the mean surface temperature varies as a function of the distance from the leading edge of the plate. Study of the oscillatory flow is restricted to small amplitudesε only. Several graphs have been drawn and tables have been presented to depict the effect of elasticity of the liquid and Prandtl number on the velocity and temperature distributions and Nusselt number.     

Flow of an electrically conducting fluid past a porous flat plate in the presence of a transverse magnetic field

Zusammenfassung Für die Strömung einer inkompressiblen, zähen, elektrisch leitenden Flüssigkeit über eine poröse Platte werden die Gleichungen vonNavier undStokes, vonMaxwell und die Wärmeübertragungsgleichung integriert. Dabei wird vorausgesetzt, dass Flüssigkeit aus der porösen Platte austritt oder durch sie abgesogen wird. Man findet, dass sowohl die Geschwindigkeiten als auch die Schubspannungen mit steigender magnetischer Druckzahl für Absaugen und Ausblasen anwachsen. Das induzierte Feld an der Plattenoberfläche wird kleiner, wenn die Ausblasegeschwindigkeit abnimmt. Für den Grenzfall unendlicher elektrischer Leitfähigkeit wächst der Wärmeübergang mit der magnetischen Druckzahl im Falle des Ausblasens.     

Free molecular flow past a flat plate in the presence of a nontrivial gas-surface interaction

Aerodynamic forces acting on a flat plate, placed in a uniform free molecular flow, are investigated by means of a non trivial gas-surface interaction model proposed by the authors. Drag and lift coefficients and lift to drag ratio are calculated for a large number of values of some meaningful parameters, such as the speed ratio, the gas-wall temperature ratio, the attack angle and two coefficients contained in the reemission model. Simple analytical expressions, different from the classical ones, are obtained for very high or very low speed ratio values.

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Riassunto Le forze aerodinamiche agenti su una lastra piana, posta in una corrente uniforme di gas in regime di molecole libere, sono studiate per mezzo di un modello non banale di interazione gas-superficie solida, già proposta dagli autori. I coefficienti di resistenza e di portanza e il rapporto tra queste due quantità sono calcolati per un notevole numero di valori assegnati ad alcuni parametri significativi, come il rapporto di velocità, il rapporto tra temperatura del gas e della parete, l'angolo di attacco e due coefficienti propri del modello di riemissione. Per velocità molto alte o molto piccole si forniscono delle espressioni analitiche esplicite, differenti da quelle ricavabili dalla teoria classica dei coefficienti di accomodamento.

     

Fluctuating flow of a Maxwell fluid past a porous plate with variable suction

The problem dealing with the two-dimensional flow of an incompressible viscoelastic Maxwell fluid past an infinite porous plate is investigated. It is assumed that the suction velocity is normal to the plate and oscillates about a mean value. The external free-stream velocity varies periodically in time. The resulting differential equation subject to the relevant boundary and initial conditions is numerically solved by means of a numerical technique, in which a coordinate transformation is employed to transform the semi-infinite physical space to a bounded computational domain. The effects of various values of the emerging parameters, e.g. the elasticity parameter, the oscillation amplitude and frequency of the external flow and the suction velocity, on the time series of velocity, especially on the boundary-layer structure near the plate, are discussed. The nature of the shear stress engendered due to the flow is also investigated.     

Hydromagnetic rotating flow of a fourth‐order fluid past a porous plate

The rotating flow in the presence of a magnetic field is a problem belonging to hydromagnetics and deserves to be more widely studied than it has been to date. In the non‐linear regime the literature is scarce. We develop the governing equations for the unsteady hydromagnetic rotating flow of a fourth‐order fluid past a porous plate. The steady flow is governed by a boundary value problem in which the order of differential equations is more than the number of available boundary conditions. It is shown that by augmenting the boundary conditions based on asymptotic structures at infinity it is possible to obtain numerical solutions of the nonlinear hydromagnetic equations. Effects of uniform suction or blowing past the porous plate, exerted magnetic field and rotation on the flow phenomena, especially on the boundary layer structure near the plate, are numerically analysed and discussed. The flow behaviours of the Newtonian fluid and second‐, third‐ and fourth‐order non‐Newtonian fluids are compared for the special flow problem, respectively. Copyright © 2004 John Wiley & Sons, Ltd.     

Effects of thermophoresis on hydromagnetic mixed convection and mass transfer flow past a vertical permeable plate with variable suction and thermal radiation

The present paper deals with the effect of surface mass transfer on MHD mixed convection flow past a heated vertical flat permeable surface in the presence of thermophoresis, radiative heat flux and heat source/sink. Usual similarity transformations are introduced to obtain similarity solution, using regular perturbation technique. To observe physical insight and interesting aspects of the problem in the presence of thermophoresis, the non-dimensional velocity, temperature and concentration field are numerically studied and displayed graphically for pertinent parameters. It is observed that the thermophoresis has dominant effect on mass transfer mechanism in particle deposition process. The model finds applications in studying particulate deposition on turbine blades, removing small particles from gas streams and determining chemical vapor deposition rate in chemical industries.     

Free convection flow of an elastico-viscous liquid through a vertical circular cylinder

The problem of free convection flow of an elastico-viscous liquid through a vertical circular cylinder at constant temperature including the effects of frictional heating and distributed heat sources or sinks has been considered. The equations of motion and energy have been solved by an iteration technique. The effects of the elasticity of the liquid, buoyancy forces and heat sources or sinks on the velocity and temperature fields, skin-friction and Nusselt number have been discussed.     

Free convection boundary layers on a vertical surface in a heat-generating porous medium

The natural convection boundary-layer flow on a solid verticalsurface with heat generated within the boundary layer at a rateproportional to (T – T)^p (p 1) is considered. The surfaceis held at the ambient temperature T except near the leadingedge where it is held at a temperature above ambient. The behaviourof the flow as it develops from the leading edge is examinedand is seen to become independent of the initial heat input;however, it does depend strongly on the exponent p. For 1 p 2, the local heating eventually dominates at large distancesand there is a convective flow driven by this mechanism. Forp 4, the local heating does not have a significant effect,the fluid temperature remains relatively small throughout andthe heat transfer dies out through a wall jet flow. For 2 <p < 4, the local heating has a significant effect at relativelysmall distances, with a thermal runaway developing at a finitedistance along the surface.