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# Topic: Rayleigh number

###### In the News (Wed 19 Jun 19)

 Rayleigh number - Wikipedia, the free encyclopedia In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with the heat transfer within the fluid. When the Rayleigh number is below the critical value for that fluid, heat transfer is primary in the form of conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection. In geophysics the Rayleigh number is of fundamental importance: it indicates the presence and strength of convection within a fluid body such as the Earth's mantle, which is a solid but which behaves as a fluid over geological time scales. en.wikipedia.org /wiki/Rayleigh_number   (217 words)

 Pseudo Random Number Generator.   (Site not responding. Last check: 2007-09-10) Basically the approach taken is to start with a number, called the seed, and to then apply a mathematical formulae which will produce another number in a relatively difficult to predict way. Methods whereby the random number produced on the basis of applying a formulae to a seed are used as the seed for the next number drawn, are most often used. The Weibull random number generator can also be used to generate numbers from the Rayleigh distribution (set alpha, the shape, at 2) and the exponential distribution (set alpha, the shape, at 1; and beta, the scale, at 1/lambda). home.clara.net /sisa/randhlp.htm   (1987 words)

 Ocean 540: Convective Heat Transfer Lord Rayleigh showed through linear perturbation analysis (for a general discussion see (13), section 7.1.2 or the derivation in (11), section 6-18), that for thermal instabilities to grow in a fluid, the Rayleigh number would have to exceed a critical value (the f This temperature distribution is reflected in the velocity field, with sluggish flow at the boundaries and in the interiors of the two cells, strong downwelling at the side boundaries, and strong upwelling in the middle of the domain: The Nusselt number is the ratio of heat transferred from a convecting system compared to that which would be transferred by conduction alone. www2.ocean.washington.edu /oc540/lec02-8   (554 words)

 Songlin Zhu: Research3 On the walls, all components of the velocity was zaro and the temperature was given by the measurements. Similar flow pattern was gotten at the selected Rayleigh number, but the magnitude of the velocity shown in the figure with a vector increased with the Rayleigh number. The average Nusselt numbers at different Rayleigh numbers are presented in table 1. www.unc.edu /~slzhu/research/CFD/lhre.html   (479 words)

 High Rayleigh number compressible convection in Venus’ atmosphere: Penetration, entrainment, and turbulence Cloud-level convection is characterized by cold, narrow downwellings that deeply penetrate the underlying stable layer and that entrain warmer air from the overlying stable layer. The convection layer depth, as determined from the horizontally averaged static stability, spans 9 km (47–56 km altitude) and 14 km (46–60 km altitude) for the moderate Rayleigh number and high Rayleigh number simulations, respectively. In the high Rayleigh number cases, convective penetration extends over a scale height from the bottom of the convection layer down to 38 km altitude. www.agu.org /pubs/crossref/1999/1998JE900029.shtml   (349 words)

 Clarkson U | TMFL | DJS Research | Buoyancy-induced flows within a two-dimensional, square enclosure. The numerical simulations reveal that the heat transport is approximately independent of the Prandtl number for the higher Rayleigh numbers considered, i.e., 10 As the Prandtl number is decreased, the lines of constant vorticity become coincident with the streamlines within the interior region of the enclosure. With an increase in the Rayleigh number, this oscillatory behavior results in a separation from the horizontal walls. www.clarkson.edu /fluidflow/djs/ms.html   (280 words)

 The Rayleigh problem   (Site not responding. Last check: 2007-09-10) Rayleigh's solution of the thermal convection problem is considered a major triumph of the linear stability theory. The concept of critical Rayleigh number finds application in such geophysical problems as solar convection, cloud formation in the atmosphere, and the motion of the earth's core. At this point it is useful to show that the Rayleigh number is the ratio of the buoyancy force to the viscous force. astron.berkeley.edu /~jrg/ay202/node133.html   (622 words)

 Rayleigh number For free convection near a vertical wall, this number is Ra Rayleigh number Gr Grashof number Pr Prandtl number g gravity T The Rayleigh number is named after Lord Rayleigh. www.ebroadcast.com.au /lookup/encyclopedia/ra/Rayleigh_number.html   (54 words)

 Session BI - Convection and Buoyancy Driven Flows II. This is a multi-parameter problem characterized by the mean Rayleigh number, the vertical stratification parameter, the Prandlt number, and the amplitude, \varepsilon, and frequency, ømega, of the jitter. For Prandtl number =0.9 and dimensionless driving frequency ømega=96, we find convection modulated at ømega and \fracømega2, as well as conduction in the phase diagram for a range of dimensionless amplitudes and Rayleigh numbers: 1 \times 10^-4 \le \Delta \le 5 \times 10^ -4 and 2000 \le Ra \le 8000. Measured critical Rayleigh numbers R_c(Ømega)/R_c(0), where R_c(0) is the Soret onset, agree with the linear stability analysis for the pure fluid. flux.aps.org /meetings/YR98/BAPSDFD98/abs/S2100.html   (1413 words)

 Solitary-wave Solution of Turbulence with Application to Benard Convection by Tsuge, Ishibasi and Nakagawa The mean temperature distribution is calculated, and thereby the Nusselt number is determined as a function of the Rayleigh number. Included are the temperature profiles at three different Rayleigh numbers and for the Prandtl number corresponding to the water. Fig.5: The Nusselt number against the Rayleigh number (Nu;the nondimensional heat transfer) calculated using (17) and plotted against the Rayleigh number (Ra;the nondimensional temperature difference between walls) on the original figure from ref.5. www.ca-homes.com /science/tsuge-1.htm   (1001 words)

 mit_convection   (Site not responding. Last check: 2007-09-10) The session organizers are soliciting the contribution of solutions to the 8:1 differentially-heated cavity problem for near-critical Rayleigh numbers, and hope to see finite difference, finite volume, finite element, and spectral methods applied to this seemingly-simple 2-D problem. In addition to the point and wall data, a number of relevant global quantities are required as delineated in Table 5. Number of processors used and the number of grid points per processor (degree-of-granularity) for parallel computations. www.me.unm.edu /~christon/mit_convection   (2923 words)

 MS Thesis   (Site not responding. Last check: 2007-09-10) The flow pattern is determined with the aid of a liquid crystal sheet at the lower heated surface of the apparatus, showing the temperature planform, and through the use of two types of fluid tracer particles seeded in the fluid and examined through the sidewalls of the apparatus. Initially, at low Rayleigh number (Ra*.lt.1x10^6), the convective planform shows two large cellular structures with fluid falling in the central region of the fluid layer and rising along two opposite sidewalls. As the Rayleigh number is increased, cold thermal plumes begin to form in the central region and occupy an increasingly larger percentage of the entire layer. www.me.umn.edu /~sjo/pubs/ms.html   (374 words)

 Free Convection and the Rayleigh Number at Nonoscience These requirement are expressed as a non-dimensional number, called the Rayleigh Number in honor of Lord Rayleigh who came up with the explanation for this convection behavior of an enclosed fluid subjected to a temperature differential. The Rayleigh number is the buoyant force divided by the product of the viscous drag and the rate of heat diffusion. Thus Rayleigh Number (a non-dimensional number, if you notice) is a quantitative measure/ representation of when the ’switch’ from conductive to convective transport happens for a given fluid plus geometry configuration. www.arunn.net /scienceblog/2006/08/03/free-convection-and-the-rayleigh-number   (1712 words)

 Highbeam Encyclopedia - Search Results for Rayleigh, Rayleigh, John William Strutt, 3d Baron, 1842-1919, English physicist. Find newspaper and magazine articles plus images and maps related to "Rayleigh," at HighBeam. Averaging correlation for fast GPS satellite signal acquisition in multipath Rayleigh fading channels.(Technical Feature)(Global Positioning System) www.encyclopedia.com /SearchResults.aspx?Q=Rayleigh,   (550 words)

 Rayleigh-Bénard convection   (Site not responding. Last check: 2007-09-10) The upper surface is unconstrained and is free to move and deform. Stimulated by these experiments, Rayleigh in 1916 derived the theoretical requirement for the development of convective motion in a layer of fluid with two free surfaces. is called the Rayleigh number, which represents the ratio of the destabilizing effect of buoyancy force to the stabilizing effect of viscous force. grus.berkeley.edu /~jrg/ay202/node132.html   (494 words)

 Homework.html Your solution should include: start with the equations, make them non-dimensional, define the Rayleigh number for this problem, prove exchange of stability (if it applies), either solve exactly or approximately (one term in velocity and temperature is sufficient) for the Rayleigh number, and determine the wave number at the critical Rayleigh number. Use the correlation given in class and insert the critical Rayleigh number, the critical Marangoni number, and derive an equation for the critical temperature difference when both mechanisms are important. Determine what the critical Rayleigh number is for instability, and the wave number at that critical condition. faculty.washington.edu /finlayso/che531/Homework.html   (1487 words)

 Textures in Binary Fluid Convection   (Site not responding. Last check: 2007-09-10) Near the traveling-wave transition the patterns are angular, consisting of geometric domains of straight rolls, whereas at higher Rayleigh number, the texture of the pattern is curved. In the mixture, the angular state forms as we lower the Rayleigh number and approach the traveling-wave state. In the pure fluid, there is not traveling-wave state, and the angular texture does not form as we lower the Rayleigh number and approach the onset value. physics.ucsd.edu /was-daedalus/convection/tx.html   (754 words)

 Rayleigh-Benard Convection   (Site not responding. Last check: 2007-09-10) This competition of forces is parameterized by the Rayleigh number, which is the temperature difference, but appropriately normalized to take into account the geometry of the convection cell and the physical properties of the fluid. If the Rayleigh number is greater than 1708, then convection occurs. Throughout this pave, we will use the reduced Rayleigh number, which is normalized to the onset value of 1708. physics.ucsd.edu /was-daedalus/convection/rb.html   (625 words)

 Russell J. Donnelly Early studies in our group showed that a wind tunnel using liquid helium as a test fluid could be used to test submarine models at full Reynolds number appropriate to a nuclear submarine at full throttle. Although helium I is a Navier-Stokes fluid, the possibility of generating ever higher Reynolds numbers carries with it ever decreasing Kolmogorov lengths. For example in a 10 cm pipe characteristic lengths at the highest Reynolds numbers could be less than 50 Angstroms. darkwing.uoregon.edu /~rjd/cyogenic.htm   (2250 words)

 Vic Castillo's HomePage   (Site not responding. Last check: 2007-09-10) This may shed light on the on the popular investigation of the scaling relation between the Nusselt and Rayleigh numbers. Since the relation between the Reynolds and Rayleigh number is known is known, this further supports the validity of the entropy-Rayleigh number relation. A Rayleigh number'' can be defined for this system and the system does make a transition from regular to chaotic motion. www-phys.llnl.gov /H_Div/Profiles/Castillo/vic.htm   (599 words)

 Session JK - Convection and Buoyancy Driven Flows IV. We present measurements of the Nusselt number \cal N as a function of the Rayleigh number R and the Prandtl number \sigma in cylindrical cells with aspect ratios \Gamma \equiv D/d = 3.0, 2.0,1.0, and 0.5 (D is the diameter and d the height). The combined range of Rayleigh number in the experiment spans from 2\times10^7 to 3\times10^10 and that of Pr from 30 and 1,350. The stability boundary is known to depend on the thermal Rayleigh number Ra_T, solute Rayleigh number Ra_S, Prandtl number Pr, and Lewis number Le. flux.aps.org /meetings/YR00/DFD00/abs/S1320.html   (1717 words)

 [No title] Mathematical theory : determination of the critical Rayleigh number The critical value of the Rayleigh number for apparition of Rayleigh-Benard instability is 1707. But if initial conditions are well chosen, if Rayleigh number increases, number of rolls inside the fluid increases too. www.enseeiht.fr /hmf/travaux/CD0001/travaux/optmfn/hi/01pa/hyb72/rb/rb.htm   (556 words)

 Rayleigh accommodation - hotels guest houses bed and breakfast self catering cottage accommodation in Rayleigh Essex UK The Rayleigh Clock is visible from most of Rayleigh High Street. Rayleigh is 4 miles west of Southend-on-Sea, 5 miles east of Basildon and 10 miles south of Chelmsford. To dial a Rayleigh number from outside the UK: dial the International Access Code of the country you are calling from - follow that by the Country Code for the country you are calling to (44 for the UK) - dial the local area code omitting the initial ‘0’ e.g. www.kayukay.co.uk /rayleigh.html   (227 words)

 Abstract of Charles Doering's Talk   (Site not responding. Last check: 2007-09-10) Thermal convection and fluid mechanics in a porous medium is relevant to a variety of phenomena ranging from groundwater flow and geothermal energy transport, to the effectiveness of fiberglass insulation, to the occurance of avalanches on snow covered mountainsides. In the research described here, the most basic model (the Darcy-Boussinesq equations at infinite Darcy-Prandtl number) is used to study convection and heat transport over a broad range of heating levels as measured by the nondimensional Rayleigh number Ra. Over an intermediate range of increasing Rayleigh numbers, the simulations display the `classical' (jargon to be explained) heat transport Nu ~ Ra scaling. www.faculty.iu-bremen.de /stoll/colloquium/abstract-2005-01-31.html   (305 words)

 Rayleigh Limit Calculator The calculator on the right uses these formulas to calculate the Rayleigh limit for a droplet of radius r or for a jet of length l and radius r. Checking the box Constant volume prevents the number of molecules from changing in case there is another parameter that can be changed instead. For a spherical system, a change in the Rayleigh limit will have effect on Radius and Number of molecules while for a cylindrical system, the Radius and the Length will be recalculated keeping the volume (Number of molecules) constant. phd.marginean.net /rayleigh.html   (375 words)

 EXERCISE 2 SC200, Spring 04. The critical Rayleigh number for which this transition occurs can be estimated from the Nusselt number, defined by is the critical Rayleigh number at the Rayleigh-Benard instability for a laterally infinite container. be the number of degrees of freedom in the x- and y- direction, respectively. www.ii.uib.no /~petter/SC200/oppgave2.html   (1061 words)

 Two stress-free surfaces   (Site not responding. Last check: 2007-09-10) The main interest in the problem, however, is that it allows a simple solution, which was first given by Rayleigh. The critical Rayleigh number is obtained by finding the minimum value of The regions above the curve correspond to instability, since a Rayleigh number lying there is higher than the Rayleigh number for marginal instability. grus.berkeley.edu /~jrg/ay202/node136.html   (327 words)

 Rayleigh - Wikipedia, the free encyclopedia John William Strutt, 3rd Baron Rayleigh, (aka Lord Rayleigh) a notable physicist and baron of Rayleigh; Robert John Strutt, 4th Baron Rayleigh, a notable physicist and baron of Rayleigh; The rayleigh (unit), a unit of luminous flux named after the second physicist; en.wikipedia.org /wiki/Rayleigh   (105 words)

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