Magneto-hydrodynamic channel flow as influenced by wall conductance

Zusammenfassung Die Theorie vonHartmann undLazarus, Shercliff undChang sowieLundgren der magneto-hydrodynamischen Kanalströmung wird erweitert, indem der elektrische Leitungswiderstand von gegenüberliegenden Wänden als verschieden gross angenommen wird. Es zeigt sich merkwürdigerweise, dass die Geschwindigkeits- und Stromdichteverteilung nach wie vor symmetrisch bleibt. Beide Verteilungen hängen nur von der Summe der Wandleitungsfähigkeiten ab und von der Hartmann-Zahl.     

High-Reynolds-number effects on turbulent scalings in compressible channel flow

The effect of the Reynolds number in a supersonic isothermal channel flow is studied using a direct numerical simulation (DNS). The bulk Mach number based on the wall temperature is 1.5, and the bulk Reynolds number is increased up to Re_τ ≈︁ 1000. The use of van Driest velocity transformation in the presence of heated walls has been questioned due to the poor accuracy at low Reynolds number. For this reason alternative transformations of the velocity profile and turbulence statistics have been proposed, as, for instance, semi-local scalings. We show that the van Driest transformation recovers its accuracy as the Reynolds number is increased. The Reynolds stresses collapse on the incompressible ones, when properly scaled with density, and very good agreement with the incompressible stresses is found in the outer layer. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Numerical investigation of transient heat transfer to hydromagnetic channel flow with radiative heat and convective cooling

This present study consists of a numerical investigation of transient heat transfer in channel flow of an electrically conducting variable viscosity Boussinesq fluid in the presence of a magnetic field and thermal radiation. The temperature dependent nature of viscosity is assumed to follow an exponentially model and the system exchanges heat with the ambient following Newton’s law of cooling. The governing nonlinear equations of momentum and energy transport are solved numerically using a semi-implicit finite difference method. Solutions are presented in graphical form and given in terms of fluid velocity, fluid temperature, skin friction and heat transfer rate for various parametric values. Our results reveal that combined effect of thermal radiation, magnetic field, viscosity variation and convective cooling have significant impact in controlling the rate of heat transfer in the boundary layer region.     

A study of effects of wall-normal rotation on the turbulent channel flow

The effects of the wall–normal rotation on the turbulence channel flow have been studied. A series of direct numerical simulations have been performed with various rotation rates for Reynolds number 180 based on the friction velocity in the non–rotating case. All remarkable changes are discussed. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Slip effects on MHD flow of third order fluid in a planar channel

In this paper, the peristaltic flow of magnetohydrodynamic (MHD) third order fluid in a planar channel with slip condition is investigated. The solutions are derived under long wavelength and low Reynolds number approximations. Explicit expressions of stream function, longitudinal pressure gradient, longitudinal velocity, temperature and coefficient of heat transfer are given. The pumping and trapping phenomena are analyzed in the presence of MHD and slip effects. The effects of parameters on temperature distribution and heat transfer coefficient are discussed. A comparison is provided with the different existing cases.     

Combined free and forced convection effects on the magnetohydrodynamic flow through a channel

Zusammenfassung Die freie Konvektion einer elektrisch leitenden Flüssigkeit in einer horizontalen Kanalströmung in Anwesenheit eines homogenen vertikalen Magnetfeldes wird analysiert. Für die Erwärmung der oberen Wand ergibt sich eine Neigung der Strömung zur Instabilität. Der starke Einfluss des Magnetfeldes auf die Strömung wird diskutiert.     

Flow limitation in convective dominated open capillary channel flows

In this work the flow rate limitation of convective dominated flows in open capillary channels is investigated experimentally. Since irreversible flow losses are small in this type of flow, the flow variables are approximately symmetrical with respect to the middle of the channel. Therefore a very precise proof of the origin of the limitation is possible. A new technique for the determination of the key property, the speed index, is presented. The speed index confirms that also in convective dominated flows the flow limitation occurs due to a choking-effect. (© 2006 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

A theoretical consideration of a free convective boundary layer on an isothermal horizontal conic

Approximate analytical solution of simplified Navier–Stokes and Fourier–Kirchhoff equations describing free convective heat transfer from isothermal surface of horizontal conic of the base angle α has been presented. The solution is based on the typical for natural convection assumption that the normal to the surface component of velocity is negligibly small in comparison with the tangential one. The results obtained for boundary cases of conic under considerations are in good agreement with known solutions for a horizontal cylinder α=π/2 and a vertical round plate α=0.     

Magneto-gasdynamic channel flow

Zusammenfassung Die Gleichungen für die ?quasi-eindimensionale? Str?mung eines elektrisch leitenden Gases werden im Falle eines Stromfadens mit ver?nderlichem Querschnitt hergeleitet, wobei die Str?mung unter dem Einfluss eines elektrischen und magnetischen Feldes steht. Obwohl kein allgemeines Integral angegeben werden konnte, ergeben sich interessante Folgerungen für die Beschleunigung der Str?mung und für die ?nderung der Mach-Zahl. Zum Beispiel kann in gewissen Geschwindigkeitsbereichen eine überschallstr?mung ?magneto-gasdynamisch? auch bei konstantem Str?mungsquerschnitt beschleunigt werden. Bei variablem Querschnitt sind die Gleichungen für einen besonderen Fall integriert worden; das Ergebnis dieser Integration kann als weiteres Beispiel für die Veranschaulichung der Wirkung einer elektromagnetischen Energiezufuhr dienen. Die auch bei konstantem Querschnitt bestehenden mannigfaltigen M?glichkeiten werden für verschiedene Anfangsbedingungen diskutiert, wobei F?lle sich zeigen, bei denen Beschleunigungen und Verz?gerungen mit Durchg?ngen durch die Schallgeschwindigkeit auftreten sowie auch neue F?lle von ?Blockierungen? sich offenbaren.      

Combined free and forced convection effects on the magnetohydrodynamic flow through a porous channel

The combined effect of free and forced convection on the flow of an electrically conducting liquid between two horizontal parallel porous walls has been studied. There is a transverse magnetic field at the walls. The equations of motion and energy have been solved by a small perturbation method. The flow phenomenon has been characterized by the non-dimensional numbers like R (cross-flow Reynolds number), K (Brinkman number), G (Grashof number), M (magnetic number) and the effects of these numbers on the velocity and temperature fields, induced magnetic field, electric field and shearing stress at the walls have been studied.     

Combined effects of free and forced convection on magnetohydrodynamic flow in a rotating channel

The steady flow in a channel rotating with an angular velocity \(\vec \Omega \) and subjected to a constant transverse magnetic field is analysed. An exact solution of the governing equations is obtained. The solution in the dimensionless form contains three parameters: the Grash of number,G, the Hartmann number,M ² and the rotation parameter,K ². The effects of these parameters on the velocity and magnetic field distributions are studied. For large values ofK ² andM ², there arise thin boundary layers on the walls of the channel which may be identified as the Ekman-Hartmann layers.     

Simultaneous effects of partial slip and thermal-diffusion and diffusion-thermo on steady MHD convective flow due to a rotating disk

The purpose of present research is to derive analytical expressions for the solution of steady MHD convective and slip flow due to a rotating disk. Viscous dissipation and Ohmic heating are taken into account. The nonlinear partial differential equations for MHD laminar flow of the homogeneous fluid are reduced to a system of five coupled ordinary differential equations by using similarity transformation. The derived solution is expressed in series of exponentially-decaying functions using homotopy analysis method (HAM). The convergence of the obtained series solutions is examined. Finally some figures are sketched to show the accuracy of the applied method and assessment of various slip parameter γ, magnetic field parameter M, Eckert Ec, Schmidt Sc and Soret Sr numbers on the profiles of the dimensionless velocity, temperature and concentration distributions. Validity of the obtained results are verified by the numerical results.     

Compressible magnetogasdynamic channel flow

Zusammenfassung Die stationäre Strömung eines kompressiblen, elektrisch leitenden Mediums in einem Kanal wird in einfachster Weise als eindimensionales Problem behandelt,wobei die elektrische Leitfähigkeit als skalare Funktion eingeführt ist. Felder und Querschnittsverlauf sind als nicht konstant angenommen. Die Lösung wird zweckmässig dargestellt und interpretiert anhand eines Diagrammes, dessen Koordinaten Geschwindigkeit und Machzahl sind. Ein einfaches Zahlenbeispiel wird behandelt, bei dem Querschnitt und Magnetfeld längs des Kanals so variieren, dass eine konstante elektrische Stromdichte entsteht.

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This work was supported by the Air Force Office of Scientific Research under Contract AF 49(638)758 with the California Institute of Technology.     

Effect of contraction on turbulent channel flow

Summary Measurements in an effectively two-dimensional channel indicate that flow acceleration at constant Reynolds Number can have appreciable effects on the turbulence structure. As in wakes, the structure approaches equilibrium exponentially after the acceleration. The effect of acceleration appears to be (at least qualitatively) of the same kind as is observed when turbulence is subjected to rapid distortion.

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Zusammenfassung Messungen in einem effektiv zwei-dimensionalen Kanal zeigen, daß eine Strömungsbeschleunigung bei konstanter Reynolds-Zahl einen wesentlichen Einfluß auf die Turbulenz-Struktur haben kann. Nach der Beschleunigung findet man eine exponentielle Annäherung an das Gleichgewicht, wie bei Dellen. Der Beschleunigungs-Effekt auf die Turbulenz erscheint, wenigstens qualitativ, von der gleichen Art zu sein wie der Einfluß von raschen Verformungen.

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Symbols c _f skin-friction coefficient = - D half-width of the channel - L length of contraction=12 inches - dp/dx pressure gradient - V mean velocity in thex-direction,U=U ₀ aty=D - U mean velocity - average of the mean velocity - U ^* friction velocity = (₀/)^± - root mean square value of the turbulent velocity fluctuations inx, y andz directions - X coordinate in the direction of the flow;X=0 at the end of contraction - Y coordinate perpendicular to the surface of the wall on which measurements are madey=0 at the wall andy=D at the centre of the channel - ₀ Wall shear stress - density of the fluid - viscosity of the fluid - kinematic viscosity of the fluid=/     

Lie symmetry group analysis of magnetic field effects on free convective flow of a nanofluid over a semi-infinite stretching sheet

We investigate the steady two-dimensional flow of an incompressible water based nanofluid over a linearly semi-infinite stretching sheet in the presence of magnetic field numerically. The basic boundary layer equations for momentum and heat transfer are non-linear partial differential equations. Lie symmetry group transformations are used to convert the boundary layer equations into non-linear ordinary differential equations. The dimensionless governing equations for this investigation are solved numerically using Nachtsheim–Swigert shooting iteration technique together with fourth order Runge–Kutta integration scheme. Effects of the nanoparticle volume fraction ϕ, magnetic parameter M, Prandtl number Pr on the velocity and the temperature profiles are presented graphically and examined for different metallic and non-metallic nanoparticles. The skin friction coefficient and the local Nusselt number are also discussed for different nanoparticles.     

Vertical free convective boundary-layer flow in a porous medium using a thermal nonequilibrium model: Elliptical effects

In this paper we study the effect of adopting a two-temperature model of microscopic heat transfer on the classical Cheng &; Minkowycz [1] vertical free convection boundary-layer flow in a porous medium. Such a model, which allows the solid and fluid phases not to be in local thermal equilibrium, is found to modify substantially the behaviour of the flow relatively close to the leading edge. A companion paper deals with the (parabolic) boundary-layer theory, but the present work investigates in detail how elliptical effects are manifested. This is undertaken by solving the full equations of motion, rather than the boundary-layer approximation. In general, it is found that at any point in the flow, the temperature of the solid phase is higher than that of the fluid phase, and therefore that the thermal field of the solid phase is of greater extent than that of the fluid phase. The microscopic inter-phase heat transfer is characterised by the coefficient, H,and it is shown that these thermal non-equilibrium effects are strongest when H is small.     

A note on the universal stability of convective flow with variable viscosity

The stability of convective motion of a fluid driven by volumetric heat sources and applied pressure gradient is investigated. The viscosity of the fluid is assumed to depend linearly on temperature. The sufficient conditions for the existence of such a flow are obtained based on the energy inequalities. Copyright © 2007 John Wiley & Sons, Ltd.     

MHD free convective flow past semi-infinite vertical permeable wall

In this paper,the basic equations governing the flow and heat transfer of an incompressible viscous and electrically conducting fluid past a semi-infinite vertical permeable plate in the form of partia...     

Similarity solutions for magneto-forced-unsteady free convective laminar boundary-layer flow

The group theoretic method is applied for solving problem of a unsteady free-convective laminar boundary-layer flow on a non-isothermal vertical plate under the effect of an external velocity and a magnetic field normal to the plate. The application of two-parameter transformation group reduces the number of independent variables, by two, and consequently the system of governing partial differential equations with the boundary and initial conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. The Runge–Kutta shooting method used to find the numerical solution of the velocity field, shear stress, heat transfer and heat flux has been obtained. The effect of the magnetic field on the velocity field and the Prandtl number on the heat transfer and heat flux has been discussed.     

Study of free convective boundary layer of isothermal lateral surface of axisymmetrical horizontal body

Approximate analytical solution of simplified Navier–Stokes and Fourier–Kirchhoff equations describing free convective heat transfer from isothermal surface has been presented. It is supposed that the surface has the horizontal axis of symmetry and its axial cross-section lateral boundary is a concave function. The equation for the boundary layer thickness is derived for typical for natural convection assumptions. The most important are that the convective fluid flow is stationary and the normal to the surface component of velocity is negligibly small in comparison with the tangential one. The theoretical results are verified by two characteristic cases of the revolution surfaces namely for horizontal conic and vertical round plate. Both limits of presented solution coincide with known formulas.