Stability of a fluid in a rectangular region heated from below

Samuels, Michael R.; Churchill, Stuart W.

doi:10.1002/aic.690130115

Cited by 62 publications

(10 citation statements)

References 9 publications

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“…5 The presence of ice at the top or a moving fusion front has negligible effect on the critical Rayleigh numbers. 6 The presence of the maximum density region does not affect the critical values, provided the physical properties and the temperature difference are selected as described.…”

Section: Discussionmentioning

confidence: 99%

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Critical Rayleigh Numbers for Natural Convection of Water Confined in Square Cells With L/D From 0.5 to 8

Heitz

Westwater

1971

Journal of Heat Transfer

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An experimental study of heat, transfer modes in water heated from below was conducted using test cells of square cross section, 0.5 X 0.5 in., and heights of 1.25 to 4 in.Heat transfer was unidirectional and parallel to gravity.Tests both included and excluded the maximum density region of 4 deg C. Ice was present above the liquid during certain runs.The three modes of heat transfer, conduction and laminar and turbulent natural convection, were characterized by temperature profiles, fusion-front velocities and positions, and fluid flow patterns.Transitions between modes occur at well-defined critical Rayleigh numbers ivhich are distinct functions of the L/D of the liquid.The critical values are not affected by the presence of ice, motion of the fusion front, or the temperatures of the warm and cold boundaries, if the Rayleigh number is calculated as described.

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Section: Discussionmentioning

confidence: 99%

“…Finite-difference methods were used by Samuels and Churchill [5] to show that Ra cl = / (Pr, L/D), for 7» < L/D < 2, where D is the horizontal liquid dimension. Edwards and Catton [6] and Edwards [7] presented mathematical models to predict Ka cl with respect to L/D and cell-wall conductance.…”

Section: Introductionmentioning

confidence: 99%

Critical Rayleigh Numbers for Natural Convection of Water Confined in Square Cells With L/D From 0.5 to 8

Heitz

Westwater

1971

Journal of Heat Transfer

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“…All calculations were carried out for A X = A Y = 0.1 and AT = 0.001 except as noted to the contrary. The steady state temperature and velocity fields obtained by Samuels (1966) for a Newtonian fluid with Pr = 0.1 and Ra = 6000 were used as an initial condition for the first calculations. A step change to Pr = 1 and Ra = 6000 was made and the steady state obtained for this new Newtonian case.…”

Section: Ostwwold-de W a D E Model-solid Vertical Boundoriermentioning

confidence: 99%

Hydrodynamic stability and natural convection in Ostwald‐de Waele and Ellis fluids: The development of a numerical solution

1972

Self Cite

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An algorithm was developed for the finite-difference computation of hydrodynamic stability and natural convection in non-Newtonian fluids heated from below. Test calculations were carried out for fluids whose viscosity characteristics are described by the Ostwald-de Waele (power-law) and Ellis models and for roll-cells with both rigid and dragless vertical boundaries. The effects of time-step and grid-size were tested thoroughly. The results were found to be independent of the assumed initial state.The computed values of the Nusselt number and the critical Rayleigh number for Newtonian fluids agree well with prior experimental results. The computations for the Ostwald-de Waele model indicate that the approximate solution of Tien, Tsuei, and Sun may underestimate the critical Rayleigh Number. November, 1972

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“…This situation arises from the particular geometry and thermal boundary conditions involved in the actual problem. The origin of the secondary motion depicted in the present investigation appears more closely related to the multicellular flow arising from instabilities such as those studied by Samuel and Churchill [21]. Finally, it must be mentioned for completeness that the secondary flow pattern was found to remain identical in absence of symmetry line, that is, if the entire cavity is considered.…”

Section: Time Dependent Resultsmentioning

confidence: 79%

Natural convection in a rectangular cavity with wall temperature decreasing at a uniform rate

Vasseur

Robillard

1982

Wärme- und Stoffübertragung

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Abstract. The transient natural convection in a fluid contained in a rectangular enclosure, the wall of which is maintained at a uniform temperature which changes at a steady rate, is approached by a numerical method. Numerical solutions are obtained for Pr = 0.73, 7.3 and 73 and a range of Rayleigh numbers Ra = 102 ~ l0 s. At relatively low Rayleigh numbers the flow is characterized by the development of double cells with flow up the center and down the sidewalls. However it was found that an increase of the Rayleigh number leads to the development of strong secondary circulation on the axis of symmetry of the cavity near the top wall. Thus, as the Rayleigh number is increased the secondary cells grow in size. The effects of the secondary cells on the temperature field and heat transfer coefficients are discussed. Most results are obtained for the case of a square cavity (E ~-2) but the influence of the aspect ratio of the cavity is also studied for E = 1 and 4. Freie Konvektion in reehtwinkeligen Riiumen bei mit der Zeit linear fallenden WandtemperaturenZnsammenfassung. Mit einer numerischen Methode wird die nichtstationiire freie Konvektion im rechtwinkeligen Hohlraum angen~ihert, wenn die W[inde auf einheitlicher Temperatur sind, die sich linear mit der Zeit ~indert. Betrachtet wird der Bereich yon Pr = 0,73, 7,3 und 73 und Ra zwischen 102 und l0 s. Bei kleinen Ra-Werten bilden sich Doppelzellen, die im Zentrum aufw~irts und an den W~inden abw~rts str6men. Bei h6heren RaZahlen bildet sich eine ausgepr~igte Sekund~irzirkulation in der Symmetrieachse nahe der Deckelfliiche. Diese Sekund~irzellen wachsen mit steigender Ra-Zahl. Ihre Wirkungen auf Temperaturfeld und W~irmefibergang werden diskutiert. Die meisten Ergebnisse werden ftir den quadratischen Hohlraum (E = 2) erhalten, aber auch die Gr6Benverhiiltnisse E = 1 und 4 werden betrachtet (E ist Quotient aus H6he zu halber Breite).

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Stability of a fluid in a rectangular region heated from below

Cited by 62 publications

References 9 publications

Critical Rayleigh Numbers for Natural Convection of Water Confined in Square Cells With L/D From 0.5 to 8

Critical Rayleigh Numbers for Natural Convection of Water Confined in Square Cells With L/D From 0.5 to 8

Hydrodynamic stability and natural convection in Ostwald‐de Waele and Ellis fluids: The development of a numerical solution

Natural convection in a rectangular cavity with wall temperature decreasing at a uniform rate

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