Effect of Heat Transfer on Flow Field at Low Reynolds Numbers in Vertical Tubes

Hanratty, Thomas J.; Rosen, Edward M.; Kabel, Robert L.

doi:10.1021/ie50581a041

Cited by 85 publications

(31 citation statements)

References 1 publication

(1 reference statement)

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“…In the limit as the wave number (Y of the disturbance approaches 0, Equation (8) reduces to (4) predicts NRe,c = 0 when Equation (9) is satisfied and is thus consistent with a special case of hydrodynamic stability theory for small disturbance flows. The inviscid instability of these flows will be considered more fully in a future paper.…”

Section: Upflaw Heatingsupporting

confidence: 71%

“…For constant flux heating of water flowing through a vertical pipe, experimental investigations have shown that natural convection effects can significantly distort the laminar flow field (8). This system is a good one for evaluating the stability criteria, because analytical solutions for the fully developed distorted laminar velocity and temperature profiles for Newtonian liquids have been obtained by several investigators (3, 8, 9).…”

Section: Constant Heat Flux Velocity Fieldsmentioning

confidence: 99%

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Laminar‐Turbulent transition for nonisothermal pipe flow

Scheele

Greene

1966

AIChE Journal

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Finite disturbance pipe flow stability criteria are evaluated for constant flux heating of liquids flowing through vertical pipes under small disturbance conditions where velocity profile distortion due to natural convection is significant. For Newtonian flow in long heated pipes the analysis of Hanks correctly predicts the transition to turbulence observed for upflow heating and is qualitatively consistent with the transition to asymmetric flow which occurs in downflow heating, whereas the criterion of Ryan and Johnson predicts stability for experimentally unstable flows. In the practically more important case of short pipe lengths experimental data obtained over the viscosity range from 1 to 21 centipoises show that noturol convection induced transition will occur a t low Reynolds numbers for both Newtonian and non-Newtonian liquids for conditions consistent with predictions of Hanks' analysis.No completely general theoretical predictions exist for determining whether flow in a straight, smooth, circular cross section pipe will be laminar or turbulent because of difficulties associated with characterizing the nature of the disturbances. This paper investigates the validity of proposed stability criteria for large disturbance flows by comparing predicted and experimental values of the transition Reynolds number N R~,~ for nonisothermal pipe flows in which the interaction of the temperature and velocity fields is significant. which is a function of the ratio of input energy to energy dissipation for an. element of fluid, hypothesizing that when Zj reaches a maximum value of 808 at some point in a laminar flow field the flow will be sufficiently unstable to become turbulent. The value of 808 was chosen because it leads to a critical Reynolds number (defined with the use of the pipe radius as the length parameter) of 1,050 for an isothermal Newtonian fluid. Ryan and Johnson experimentally verified the stability criterion for isothermal flow of pseudoplastic fluids. Hanks and Christiansen (7) extended the criterion to include the heated flow of pseudoplastic liquids, and Hanks (6) has applied the criterion to pipe flow of fluids with yield stresses.Since Zj is geometry dependent, Hanks ( 5 ) suggested a more general stability parameter which for steady state rectilinear pipe flows reduces toand postulated that when-A reaches a critical value of 808 at some point in the flow field, transition will occur. A = Zj only for fully developed, isothermal Newtonian pipe flows. Equations (1) and (2) are not identical for nonisothermal flows because of fluid property variations with temperature.Equations (1)

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Section: Upflaw Heatingsupporting

confidence: 71%

Section: Constant Heat Flux Velocity Fieldsmentioning

confidence: 99%

Laminar‐Turbulent transition for nonisothermal pipe flow

Scheele

Greene

1966

AIChE Journal

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“…A following brief review is emphasised on the flow reversal phenomenon and the flow instability in a vertical tube. For such configuration, the pioneers works by Hanratty and colleagues in the early sixties [3,4] have clearly shown that the non-isothermal flow appears to be highly unstable and may undergo its transition from a steady laminar state to an unstable one at rather low Reynolds number. The unstable flow structure, which was not turbulent, has shown, in fact, the 'new equilibrium' state that consisted of large scale, regular and periodic fluid motions.…”

Section: Introductionmentioning

confidence: 99%

Numerical investigation of flow reversal and instability in mixed laminar vertical tube flow

Nguyen

Maı̈ga

Landry

et al. 2004

International Journal of Thermal Sciences

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“…There have been a variety of experimental, analytical, and numerical investigations of opposing mixed convection in vertical pipes [5][6][7][8][9]. Flow reversals were predicted and were observed experimentally.…”

Section: Introductionmentioning

confidence: 99%

Analysis of fully developed opposing mixed convection between inclined parallel plates

Lavine

1988

Wärme- und Stoffübertragung

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Abstract. An exact solution is presented of fully developed, laminar flow between inclined parallel plates with a uniform wall heat flux boundary condition. The flow is downward and the heat flux is into the channel, so that natural convection opposes the forced flow. The solution depends on the two parameters P1 = Gr sin O/Re and P2 = Gr cos O/Re 2 Pr. Four different flow reversal regimes are observed: 1) no reversal, 2) top reversal, 3) bottom reversal, and 4) top and bottom reversal. Velocity profiles, temperature profiles, wall friction, and Nusselt numbers are presented. Despite the simplicity of the problem which has been analyzed, it does display some features which have been observed in real mixed convection flows, such as flow reversal and nonmonotonic dependence on tilt angle. Berechnung der roll entwickelten entgegengesetzt geriehteten Misch-Konvektion zwischeu geneigten parallelen PlattenZusammenfassung. Es wird eine exakte L6sung ftir voll entwickelte laminare Str6mung zwischen geneigten parallelen Platten mit einheitlichem Wand-Wfirmestrom als Randbedingung dargestellt. Die Str6mung ist abwfirts gerichtet und der Wfirmestrom fiihrt in den Kanal, so daB die freie Konvektion der erzwungenen entgegengesetzt gerichtet ist. Die L6sung hfingt yon den beiden Parametern P1 = Gr sin O/Re und P2 = Gr cos O/Re 2 Pr ab. Vier verschiedene Bereiche der Str6mungsumkehr wurden betrachtet: 1) keine Richtungsumkehr, 2) Umkehr an der Oberseite, 3) Umkehr an der Unterseite und 4) Umkehr an Ober-und Unterseite. Es wurden Geschwindigkeits-und Temperaturprofile, Wandreibung und Nusselt-Zahlen dargestellt. Trotz der Einfachheit des analysierten Problems werden einige Dinge dargestellt, welche in realer gemischter Konvektion untersucht wurden, so z. B. Str6mungsumkehr und die nicht-monotone Abhfingigkeit yore Schr/igungswinkel.

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Effect of Heat Transfer on Flow Field at Low Reynolds Numbers in Vertical Tubes

Cited by 85 publications

References 1 publication

Laminar‐Turbulent transition for nonisothermal pipe flow

Laminar‐Turbulent transition for nonisothermal pipe flow

Numerical investigation of flow reversal and instability in mixed laminar vertical tube flow

Analysis of fully developed opposing mixed convection between inclined parallel plates

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