Power law of horizontal convection at high Rayleigh numbers

Overall heat transfer and mean temperature distribution measurements have been made of turbulent thermal convection in horizontal water layers heated from below. The Nusselt number is found to be proportional to Ra0·278 in the range 2·76 × 105 < Ra < 1·05 × 108. Eight discrete heat flux transitions are found in this Rayleigh number range. An interferometric method is used to measure the mean temperature distribution for Rayleigh numbers between 3·11 × 105 and 1·86 × 107. Direct visual and photographic observations of the fluctuating interferogram patterns show that the main heat transfer mechanism is the release of thermals from the boundary layers. For relatively low Rayleigh numbers (up to 5 × 105) many of the thermals reach the opposite surface and coalesce to form large masses of relatively warm fluid near the cold surface and masses of cold fluid near the warm surface, resulting in a temperature-gradient reversal. With increasing Rayleigh numbers, fewer and fewer thermals reach the opposite bounding surface and the thermals show persistent horizontal movements near the bounding surfaces. The central region of the layer becomes an isothermal core. The mean temperature distributions for the high Rayleigh number range are found to follow a Z−2 power law over a considerable range, where Z is the distance from the bounding surface. A very limited agreement with the theoretically predicted Z−1 power law is also found.

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Flow Instabilities and Heat Transfer in Buoyancy Driven Flows of Inelastic Non-Newtonian Fluids in Inclined Rectangular Cavities

ASME 2010 3rd Joint US-European Fluids Engineering Summer Meeting: Volume 1, Symposia – Parts A, B, and C ◽

10.1115/fedsm-icnmm2010-30243 ◽

2010 ◽

Author(s):

Dennis Siginer ◽

Lyes Khezzar

Keyword(s):

Heat Transfer ◽

Prandtl Number ◽

Heat Transfer Rate ◽

Power Law ◽

Transfer Rate ◽

Newtonian Fluids ◽

Two Dimensional ◽

Aspect Ratios ◽

Flow Configurations ◽

Rayleigh Numbers

Steady two-dimensional natural convection in rectangular two dimensional cavities filled with non-Newtonian power law-Boussinesq fluids is numerically investigated. The conservation equations of mass, momentum and energy are solved using the finite volume method for varying inclination angles between 0° and 90° and two cavity height based Rayleigh numbers, Ra = 104 and 105, a Prandtl number of Pr = 102 and two cavity aspect ratios of 1, 4. For the vertical inclination of 90°, computations were performed for two Rayleigh numbers Ra = 104 and 105 and three Prandtl numbers of Pr = 102, 103 and 104. In all of the numerical experiments, the channel is heated from below and cooled from the top with insulated side-walls and the inclination angle is varied. A comprehensive comparison between the Newtonian and the non-Newtonian cases is presented based on the dependence of the average Nusselt number Nu on the angle of inclination together with the Rayleigh number, Prandtl number, power law index n and aspect ratio dependent flow configurations which undergo several exchange of stability as the angle of inclination O̸ is gradually increased from the horizontal resulting in a rather sudden drop in the heat transfer rate triggered by the last loss of stability and transition to a single cell configuration. Despite significant differences in the heat transfer rate and flow configurations both Newtonian and non-Newtonian fluids of the power law type exhibit qualitatively similar behavior.

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A Numerical Study of Local and Average Natural Convection Nusselt Numbers for Simultaneous Convection Above and Below a Uniformly Heated Horizontal Thin Plate

Journal of Heat Transfer ◽

10.1115/1.2824074 ◽

1997 ◽

Vol 119 (1) ◽

pp. 102-108 ◽

Cited By ~ 25

Author(s):

B. Chambers ◽

Tien-Yu T. Lee

Keyword(s):

Natural Convection ◽

Power Law ◽

Numerical Study ◽

Lower Surface ◽

Plate Edge ◽

Nusselt Numbers ◽

Plate Center ◽

Heated Plates ◽

Rayleigh Numbers ◽

Plate Width

Numerical simulations were conducted to determine local and average natural convection Nusselt numbers for uniformly heated horizontal plates with convection occurring simultaneously from upper and lower surfaces. Plate width and heating rate were used to vary the modified Rayleigh number over the range of 86 to 1.9 × 108. Upper surface Nusselt numbers were found to be smaller than corresponding lower surface Nusselt numbers. The local Nusselt number was largest at the plate edge and decreased towards the plate center for both surfaces. This variation followed approximately a minus 1/3-power law variation with the non-dimensionalized x coordinate on the upper surface for modified Rayleigh numbers greater than 104, and a minus 1/9-power law variation on the lower surface for all modified Rayleigh numbers. Comparative simulations were also performed for upward and downward facing uniformly heated plates (single sided convection). For these cases, Nusselt numbers on the upward facing plates were larger than for downward facing plates.

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Horizontal convection in shallow enclosures scales with height, not length, at low Rayleigh numbers

International Communications in Heat and Mass Transfer ◽

10.1016/j.icheatmasstransfer.2019.104308 ◽

2019 ◽

Vol 109 ◽

pp. 104308

Author(s):

Sajjad Hossain ◽

Tony Vo ◽

Gregory J. Sheard

Keyword(s):

Horizontal Convection ◽

Rayleigh Numbers

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Analysis of power law assumptions for short-period comets and Kuiper bodies

International Astronomical Union Colloquium ◽

10.1017/s0252921100031584 ◽

1999 ◽

Vol 173 ◽

pp. 289-293 ◽

Cited By ~ 1

Author(s):

J.R. Donnison ◽

L.I. Pettit

Keyword(s):

Power Law ◽

Pareto Distribution ◽

Limited Data ◽

Short Period ◽

Probability Plots ◽

Exponential Probability

AbstractA Pareto distribution was used to model the magnitude data for short-period comets up to 1988. It was found using exponential probability plots that the brightness did not vary with period and that the cut-off point previously adopted can be supported statistically. Examination of the diameters of Trans-Neptunian bodies showed that a power law does not adequately fit the limited data available.

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Hearing in Mice by GSR Audiometry: II. Magnitude of Unconditioned GSR as a Function of Intensity and Frequency Interactions

Journal of Speech and Hearing Research ◽

10.1044/jshr.1101.169 ◽

1968 ◽

Vol 11 (1) ◽

pp. 169-178 ◽

Cited By ~ 4

Author(s):

Alan Gill ◽

Charles I. Berlin

Keyword(s):

Power Law ◽

Response Magnitude ◽

Single Units ◽

Spectral Content ◽

Hearing Sensitivity ◽

Subjective Magnitude ◽

Orderly Fashion ◽

Viiith Nerve

The unconditioned GSR’s elicited by tones of 60, 70, 80, and 90 dB SPL were largest in the mouse in the ranges around 10,000 Hz. The growth of response magnitude with intensity followed a power law (10 .17 to 10 .22 , depending upon frequency) and suggested that the unconditioned GSR magnitude assessed overall subjective magnitude of tones to the mouse in an orderly fashion. It is suggested that hearing sensitivity as assessed by these means may be closely related to the spectral content of the mouse’s vocalization as well as to the number of critically sensitive single units in the mouse’s VIIIth nerve.

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510 Heart rate variability (power-law-regression) and age in patients with decompensated chronic heart failure

European Journal of Heart Failure Supplements ◽

10.1016/s1567-4215(04)90376-1 ◽

2004 ◽

Vol 3 (1) ◽

pp. 131

Author(s):

H SCHMIDT

Keyword(s):

Heart Failure ◽

Heart Rate ◽

Heart Rate Variability ◽

Chronic Heart Failure ◽

Power Law

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How Useful is the Power Law of Practice for Recognizing Practice in Concentration Tests?

European Journal of Psychological Assessment ◽

10.1027/1015-5759.23.3.157 ◽

2007 ◽

Vol 23 (3) ◽

pp. 157-165 ◽

Cited By ~ 4

Author(s):

Carmen Hagemeister

Keyword(s):

Logistic Regression ◽

Reaction Time ◽

Power Law ◽

Error Rate ◽

Reaction Times ◽

Practice Effect ◽

Practice Effects ◽

Rate Decrease ◽

Small Practice

Abstract. When concentration tests are completed repeatedly, reaction time and error rate decrease considerably, but the underlying ability does not improve. In order to overcome this validity problem this study aimed to test if the practice effect between tests and within tests can be useful in determining whether persons have already completed this test. The power law of practice postulates that practice effects are greater in unpracticed than in practiced persons. Two experiments were carried out in which the participants completed the same tests at the beginning and at the end of two test sessions set about 3 days apart. In both experiments, the logistic regression could indeed classify persons according to previous practice through the practice effect between the tests at the beginning and at the end of the session, and, less well but still significantly, through the practice effect within the first test of the session. Further analyses showed that the practice effects correlated more highly with the initial performance than was to be expected for mathematical reasons; typically persons with long reaction times have larger practice effects. Thus, small practice effects alone do not allow one to conclude that a person has worked on the test before.

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