Laminar flow heat transfer from a flat plate with variable thermal conductivity

Zusammenfassung Es wird der Einfluss einer mit der Temperatur linear veränderlichen Leitfähigkeit auf die Wärmeübertragung an einer ebenen Platte untersucht.     

Stagnation point flow and heat transfer over a non-linearly moving flat plate in a parallel free stream with slip

An analysis is presented for the steady boundary layer flow and heat transfer of a viscous and incompressible fluid in the stagnation point towards a non-linearly moving flat plate in a parallel free stream with a partial slip velocity. The governing partial differential equations are converted into nonlinear ordinary differential equations by a similarity transformation, which are then solved numerically using the function bvp4c from Matlab for different values of the governing parameters. Dual (upper and lower branch) solutions are found to exist for certain parameters. Particular attention is given to deriving numerical results for the critical/turning points which determine the range of existence of the dual solutions. A stability analysis has been also performed to show that the upper branch solutions are stable and physically realizable, while the lower branch solutions are not stable and, therefore, not physically possible.     

Unsteady low prandtl number heat transfer for flow across a flat plate

Zusammenfassung Es wird eine Erklärung gegeben für das Problem der stationären laminaren Strömung über eine ebene Platte unter der Bedingung einer unstetigen Änderung der Oberflächentemperatur. Ergebnisse für die unstetige Wärmeübertragung werden gegeben, die sich auf Flüssigkeiten von niedriger Prandtlzahl beziehen. Abbildung 2 zeigt die Änderung des Verhältnisses der augenblicklichen Wärmeübertragung zum asymptotischen Grenzwert für eine Prandtlzahl von 0,01.

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This research was supported by the National Science Foundation through Grant G-1487 5.     

Group method analysis of magneto-elastico-viscous flow along a semi-infinite flat plate with heat transfer

The group theoretic method is applied for solving problem of the flow of an elastico-viscous liquid past an infinite flat plate in the presence of a magnetic field normal to the plate. The application of one-parameter transformation group reduces the number of independent variables, by one, and consequently the system of governing partial differential equations with boundary conditions reduces to a system of ordinary differential equations with appropriate corresponding conditions. Numerical solution of the velocity field and heat transfer have been obtained. The effect of the magnetic parameter M on velocity field, shear stress, temperature fields and heat transfer has been discussed.     

Combined forced and free convection heat transfer from a horizontal flat plate

The problem of combined forced and free convection heat transfer in boundary-layer flow past a heated or cooled, horizontal flat plate is studied in the limits of large and small Prandtl number using the technique of matched asymptotic expansions. It is found that the effects of natural convection are confined to small changes in the basic forced convection velocity and temperature fields providedGr/Re ^5/2 Pr ^2/3 1 forPr1, orGr/Re ^5/2 Pr ^1/2 1 forPr1. The governing similarity equations at the first two orders in these small parameters are solved and the results compared with the numerical solutions of Sparrow and Minkowycz (1962).

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Zusammenfassung Das Problem der kombinierten erzwungenen und freien Konvektion in der Grenzschichtströmung entlang einer geheizten oder gekühlten horizontalen ebenen Platte wurde untersucht im Grenzfall von kleinen und grossen Prandtl-Zahlen, mit Hilfe der angepassten asymptotischen Entwicklungen. Der Effekt der natürlichen Konvektion ergab sich als kleine Korrektur der Geschwindigkeits-und Temperatur-Felder, fallsGr/Re ^5/2 Pr ^2/3 1 fürPr1 oderGr/Re ^5/2 Pr ^1/2 1 fürPr1. Die Ähnlichkeitslösungen der beiden ersten Ordnungen in diesen Parametern wurden bestimmt, und die Resultate wurden mit der numerischen Lösung von Sparrow und Minkowycz (1962) verglichen.

     

Solutions of thermal boundary layer equations when temperature gradient at the moving flat plate in parabolic flow is prescribed

Solutions of steady as well as unsteady three-dimensional incompressible thermal boundary layer equations are studied when the temperature gradient at the moving flat plate in parabolic flow is prescribed. A general analysis is made and different cases are studied by giving values to β and Cx which determine the gradient and curvature of the outer flow steam lines. The components of velocity in boundary layer are discussed by Sarma and Gupta and those results are used to analyse the thermal boundary layer equations. The response of temperature of the plate are studied for large and small times and curves are drawn representing the variation of temperature with time for various cases. The limiting time is also calculated.     

Nonlinear convection at a porous flat plate with application to heat transfer from a dike

Solutions for a class of coupled nonlinear differential equations, arising in free convection flow at a vertical flat plate embedded in a saturated porous medium at high Reynolds numbers in the presence of heat sources (or sinks) and with nonlinear density temperature variation, are obtained. Further, using the Schauder theory and numerical results, existence and analyticity results are established.     

Convective flow and heat transfer of a viscous heat generating fluid in the presence of a moving,infinite, vertical,porous plate

The analysis of convective flow and heat transfer of a viscous heat generating fluid past a uniformly moving, infinite, vertical, porous plate has been made systematically with a view to throw adequate light on the effects of the plate-motion and the presence of heat generation/absorption on the flow and heat transfer characteristics. The equations of conservation of momentum and energy which govern the flow and heat transfer of the said problem have been solved numerically by the method of Runge-Kutta-Gill. The numerical results thus obtained for the flow and heat transfer characteristics have revealed many an interesting behaviour, of the skin friction and the rate of heat transfer coefficient at the plate.     

On the heat transfer from a finite plate in channel flow for vanishing Prandtl number

Summary The temperature field produced by a finite, hot plate at zero incidence in uniform channel flow is solved exactly for the limiting case of zero prandtl number by means of the Wiener-Hopf technique. The heat transfer on the plate is found to agree with the corresponding boundary layer result over most of the plate for Péclét numbers as low as ten. Extensions to similar Ossen-flow problems are indicated.     

Group solution for unsteady free-convection flow from a vertical moving plate subjected to constant heat flux

The problem of heat and mass transfer in an unsteady free-convection flow over a continuous moving vertical sheet in an ambient fluid is investigated for constant heat flux using the group theoretical method. The nonlinear coupled partial differential equation governing the flow and the boundary conditions are transformed to a system of ordinary differential equations with appropriate boundary conditions. The obtained ordinary differential equations are solved numerically using the shooting method. The effect of Prandlt number on the velocity and temperature of the boundary-layer is plotted in curves. A comparison with previous work is presented.     

Visco-elastic boundary layer flow past a stretching plate and heat transfer

In the present paper, we study the temperature profile in the case of a linear stretching plate for large Prandtl numberP by an asymptotic approach. Also, we evaluate the Nusselt number and the order of magnitude of Prandtl number for variable Nusselt numbers.     

A moving-wall boundary layer flow of a slightly rarefied gas free stream over a moving flat plate

In the current work, the boundary layer flow of a slightly rarefied gas free stream over a moving flat plate is presented and solved numerically. The first-order slip boundary condition is adopted in the derivation. The dimensionless velocity and shear stress profiles are plotted and discussed. A theoretical derivation of the estimated solution domain is developed, which will give a very close estimation to the exact solution domain obtained numerically. The influences of velocity slip at the wall on the velocity and shear stress are also addressed.     

The forces on a flat plate in a couette flow

A bounded shear flow proposed by Glauert is re-examined, to determine more precisely the disturbance caused by the boundary layer on the plate. Toomre and Rott's result, that the pressure gradient due to bounding overtakes the Li-Murray value for an unbounded flow within a surprisingly short distance of the leading edge, is thereby confirmed in a more realistic context. But both of these are found to be less important than that due to the induced circulation predicted by Glauert. While bounding produces a larger leading edge drag than the unbounded theory predicts, circulation gives more lift. The discussion of pressure on and ahead of the plate is given for general bounding. In particular, it shows that the present results are typical and that the anomaly found by Toomre and Rott always disappears when the limit of remote bounding is taken correctly.

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Zusammenfassung Eine seitlich begrenzte Scherströmung, wie sie von Glauert vorgeschlagen wurde, wird neu untersucht, um die Störung, welche durch die Grenzschicht an dieser Platte hervorgerufen wird, genauer zu bestimmen. Toomre und Rotts Resultat, welches besagt, daß der Druckgradient infolge der Begrenzung den von Li-Murray gefundenen Wert für unbegrenzte Strömung in bereits überraschend kurzem Abstand von der Vorderkante übersteigt, wird hierbei in einem etwas realistischeren Zusammenhang bestätigt. Hingegen sind beide Druckgradienten von geringerer Bedeutung als der Einfluß einer auf Glauert zurückgehenden induzierten Zirkulation. Während die begrenzte Strömung zu größerem Widerstand an der Vorderkante führt als eine unbegrenzte, wird durch die Zirkulation mehr Auftrieb erzeugt. Für beliebige Begrenzung wird der Druck an und vor der Platte diskutiert. Insbesondere wird gezeigt, daß die vorliegenden Resultate typisch sind und daß die auf Toomre und Rott zurückgehende Anomalie verschwindet, wenn nur der Grenzübergang für eine Begrenzung im Unendlichen Korrekt ausgeführt wird.

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This research was supported partly by the U.S. Army Research Office-Durham and partly by the National Science Foundation under Grants GP-8711 and 28483.     

Unsteady flow past a flat plate with suction

A solution is given for the transient response for laminar boundary layer flow past a flat plate to a step-function change in suction velocity. An arbitrary but constant suction velocity normal to the plate is allowed prior to step-change. Using the Laplace transform technique the solutions for the unsteady velocity profile and shear stress are obtained and are graphically sketched when the suction velocity doubles in the stepchange. The results show clear evidence of boundary-layer contraction when suction velocity is increased.     

Steady two-dimensional flow past a normal flat plate

A vorticity/stream function formulation is used to obtain a numerical simulation of steady two-dimensional flow of a viscous incompressible fluid past a normal flat plate for a range of Reynolds numbers. A method of Fornberg [J. Fluid Mech. 98, 819 (1980)] is used to determine upstream and downstream boundary conditions on the stream function. Special care is taken in the neighbourhood of the singularities in vorticity at the plate edges and this is very important because any errors introduced are swept downstream and severely affect such quantities as the length and width of the attached eddies. The computed results are compared with those of a laboratory experiment in which a plane strip is drawn through water and ethylene glycol for the range of Reynolds numbers for which the experimental flow is stable.     

Heat transfer to magnetohydrodynamic flow in a flat duct

Zusammenfassung Die Untersuchung befasst sich mit der Wärmeübertragung von den Wänden eines flachwandigen Kanals auf eine elektrisch leitende Flüssigkeit bei erzwungener Laminarströmung und in Gegenwart eines quergerichteten Magnetfeldes. Betrachtet wird der Fall konstanter Wandtemperatur mit variierender innerer Wärmeentwicklung durch viskose und elektrische Energiedissipation. Die massgebende Differentialgleichung wird durch eine Differenzengleichung ersetzt und mit der elektronischen Rechenmaschine gelöst. Als Resultat wird die Nusseltzahl angegeben, für die Prandtlzahl 1, die Hartmannzahlen 0, 4, 10 und die Graetzzahlen von 10 bis 10 000, wobei die Kennzahlen für Zähigkeit und elektrische Feldstärke als Parameter auftreten.     

Unsteady thermal stresses near a curvilinear hole in a plate with heat transfer under its warming by a heat flow

We describe an algorithm of determining quasistatic thermal stresses in multiply connected plates with heat transfer, induced by the disturbance of heat flow near holes. Our approach is based on the Laplace transformation and a modified relation of its numerical conversion. The boundary-value problems for the Helmholtz equation, from which the Laplace transform is determined, are solved using the method of boundary integral equations. We solve the integral equations by the method of mechanical quadratures. The results of calculation of nonstationary temperature fields and stresses induced by them in a strip with small holes of different shape are also presented. Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 51, No. 1, pp. 105–111, January–March, 2008.