Use of boundary‐layer theory to predict the effect of heat transfer on the laminar‐flow field in a vertical tube with a constant‐temperature wall

Rosen, Edward M.; Hanratty, Thomas J.

doi:10.1002/aic.690070126

Cited by 29 publications

(8 citation statements)

References 9 publications

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“…The results obtained by Rosen and Hanratty [4] are also drawn in this figure, and the two sets of curves are seen to be in reasonable good agreement, approaching the asymptotic value Uc = 2 in the downstream region of the pipe. In order to detect velocity inversions in the mixed flow, Rosen and Hanratty [4] carried out a set of experiments with water (Pr ~ 6) covering a range of 50 < Gr/Re < 1500. Their data points are plotted in Fig.…”

Section: Parabolic Velocity Profilesupporting

confidence: 54%

“…Results furnished by a computer code are compared with test computations in order to assess its performance. When applicable, the present results are also compared qualitatively with the experimental findings of Rosen and Hanratty [4] for water and Zeldin and Schmidt [7] for air, respectively.…”

Section: Introductionmentioning

confidence: 63%

“…In addition of Ref. [4], Marner and McMillan [6], as well as Collins [8] examined numerically the relative effect of natural and forced convection for Pr = 1 and Gr/Re = 60. Accordingly, Fig.…”

Section: Parabolic Velocity Profilementioning

confidence: 98%

“…The solution procedure was similar to that employed in [1] for variable density only, and the results for constant viscosity are essentially the same. Subsequent numerical studies were performed by Rosen and Hanratty [4], who presented an approximate solution of the equations of motion and energy involving uniform and variable viscosity. These authors included experimental evidence for water flow also.…”

Section: Introductionmentioning

confidence: 99%

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Numerical prediction of combined laminar convection in isothermal vertical tubes via the method of lines

Campo

1988

Wärme- und Stoffübertragung

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Abstract. Simultaneous hydrodynamic and thermal development of h a laminar flow due to superimposed natural and forced convection k in an isothermal vertical pipe is investigated numerically. The 1 distinct feature of the computational procedure is that it uses the L method of lines, wherein the Navier-Stokes equations accounting rh for buoyancy and constant properties are reduced to a system of first Nu order ordinary differential equations. The latter is readily solved by n a standard fourth-order Runge-Kutta technique. The paper includes p a detailed discussion of the proposed methodology, and in addition P to this, it provides the distributions of velocities, pressure and ternPe perature. All calculations are based on a coarse grid with ten lines Pr uniformly distributed in the cross-stream direction of the pipe when QT the velocity profile at the entrance is assumed parabolic. Computed r results accounting for both upflow and downflow situations are in R good agreement with other more elaborate numerical investigations Re and also with available experimental data employing air and water as working fluids. Numerische Berechnung yon kombinierter laminarer Konvektion in isothermen senkrechten Rohren nach der Method of linesZusammenfassung. Die simultane hydrodynamische und thermische Entwicklung einer laminaren Str6mung infolge der Uberlagerung von freier und erzwungener Konvektion in einem isothermen senkrechten Rohr wird numerisch untersucht. Die besondere Eigenschaft der rechnerischen Prozedur ist, dab diese die ,,Method of lines" benutzt, worin die Navier-Stokes-Gleichungen fiir Antrieb bei konstanten Stoffwerten zu einem System einfacher Differentialgleichungen erster Ordnung reduziert werden. Das letztere ist ohne weiteres mit der Runge-Kutta-Technik 4. Ordnung zu 16sen. Die Untersuchung beinhaltet eine detaillierte Diskussion der vorgeschlagenen Methodik und in Anffigung an diese liefert es die Verteilung von Geschwindigkeiten, Druck und Temperatur. Alle Kalkulationen basieren auf einem groben Gitter mit 10 Linien, die einheitlich in der Querstromrichtung des Rohres verteilt sind, wenn das Geschwindigkeitsprofil am Eingang des Rohres parabolisch angenommen wird. Die errechneten Ergebnisse, die sowohl fiir Aufw/irts-als auch Abwfirtsstr6mungen gelten, stimmen gut mit anderen aufwendigen Untersuchungen und ebenso mit verfiigbaren experimentellen Daten, die Luft und Wasser als Arbeitsfluide gebrauchen, fiberein.

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Section: Parabolic Velocity Profilesupporting

confidence: 54%

Section: Introductionmentioning

confidence: 63%

Section: Parabolic Velocity Profilementioning

confidence: 98%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Numerical prediction of combined laminar convection in isothermal vertical tubes via the method of lines

Campo

1988

Wärme- und Stoffübertragung

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“…Most of the earlier investigations were concerned with the theoretical analysis of laminar mixed convection in circular tubes [1,2,3,4,5]. Flow in heated channels has been analysed by Ostrach [6,7], Lu [8] and Nan [9].…”

Section: Introductionmentioning

confidence: 99%

Experimental study of combined free and forced laminar convection in an asymmetrically heated two-dimensional aiding flow

Rao

Barrow

1972

Wärme- und Stoffübertragung

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Experimental study of laminar flow heat transfer with prescribed wall heat flux

Akins

Dranoff

1963

AIChE Journal

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The data for 0 < p < 1 are inconclusive but seem to indicate that the rotation of the outer cylinder stabilizes the flow against the formation of wavy vortices.Observations of the flow patterns between the first and second critical points (for p = 0) were also made, and the appearance of a transition region between steady square Taylor vortices and wavy vortices was noticed.Laminar-flow heat transfer in a cylindrical tube was studied experimentally in order to test a recent analytical method of predicting temperature profiles (1 ). The experimental equipment was designed to measure wall temperatures to better than 0 . 1 O C . and to utilize small radial heat fluxes so as to minimize effects of natural convection. A series of experiments was carried out on five different types of prescribed wall heat flux with water flowing in a vertical tube. The measured wall temperatures in these experiments compared well with those predicted by the theoretical solution. Small deviations which did exist were explained in terms of experimental errors. The agreement found indicates that the analytical method may be safely used in the study of experimental data in such heat transfer and analogous mass transfer problems. Ever since the classical work of Graetz in 1883 (2) there has been considerable interest in the problem of laminar-flow heat transfer. Many analytical solutions are available for the prediction of temperature in laminar-flow fields for various geometries and boundary conditions and with certain simplifying assumptions regarding fluid properties. Recently solutions have appeared for the case in which the flowing fluid is heated in a tube in which the wall heat flux vayies in the direction of flow. Solutions of this type are useful not only in the heat transfer con-R. G. Akins i.the temperatures measured during the experiment were very steady, both at the walls of the tube and in the mixing cup, thus indicating the absence of any turbulence. On the contrary, when several preliminary runs were made at

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Use of boundary‐layer theory to predict the effect of heat transfer on the laminar‐flow field in a vertical tube with a constant‐temperature wall

Cited by 29 publications

References 9 publications

Numerical prediction of combined laminar convection in isothermal vertical tubes via the method of lines

Numerical prediction of combined laminar convection in isothermal vertical tubes via the method of lines

Experimental study of combined free and forced laminar convection in an asymmetrically heated two-dimensional aiding flow

Experimental study of laminar flow heat transfer with prescribed wall heat flux

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