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Topic: Grashof number

Related Topics

Rayleigh number

Dimensionless number

Coefficient of thermal expansion

Froude number

Nusselt number

Reynolds number

Convection

Prandtl number

Thermal diffusivity

Buoyancy

Mach number

Celsius

	Single crystal manufacturing apparatus - Patent 4565671
		When the Grashof number N.sub.Gr generally exceeds the critical value determined by the geometrical size of the melting liquid 1 and thermal environmental conditions, a thermal convection 8 occurs in the melting liquid 8.
		in the equation of the above-described Grashof number increases.
		Thus, the Grashof number abruptly decreases, and the Grashof number can be reduced to be smaller than the critical value due to a certain intensity of the magnetic field.
	www.freepatentsonline.com /4565671.html (4475 words)

	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.
		The Rayleigh number is defined as the product of the Grashof number, which describes the relationship between buoyancy and inertia within a fluid, and the Prandtl number, which describes the relationship between the viscosity of a fluid and its temperature.
		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 (204 words)

	Dimensionless number - Wikipedia, the free encyclopedia
		In dimensional analysis, a dimensionless number (or more precisely, a number with the dimensions of 1) is a pure number without any physical units.
		Such a number is typically defined as a product or ratio of quantities which have units of identical dimension, in such a way that the corresponding units can be converted to identical units and then cancel.
		Dimensionless numbers are widely used in the fields of mathematics, physics, and engineering but also in everyday life.
	www.wikipedia.com /wiki/Dimensionless_Number (1040 words)

	Dimensionless number
		A dimensionless number is a quantity which describes a certain physical system and which is a pure number without any physical units.
		Such a number is typically defined as a product or ratio of quantities which do have units, in such a way that all units cancel.
		Dimensionless numbers are widely applied in the field of mechanical and chemical engineering.
	pedia.newsfilter.co.uk /wikipedia/d/di/dimensionless_number_1.html (470 words)

	[No title]
		Besides all, the Grashof number (Gr) is proportional to the characteristic temperature difference (difference of the temperatures at the vertical walls in this case).
		The task of the GAMM benchmark is to calculate the critical value of the Grashof number which corresponds to a bifurcation from steady to oscillatory state of the flow.
		The initial Grashof number should be close to the critical value such that iterations of the second step could converge, and converge rather quickly.
	www.spec.org /cpu/CFP2000/178.galgel/docs/README (1454 words)

	Department of Atmospheric Sciences: Feb 19, 2004
		For fluids with Pr < 12.5, the instability onset is in the steady convection mode and the critical Grashof number, 7900, is independent of Pr.
		For fluids with Pr > 12.5, however, the onset is in the oscillatory mode and the Grashof number decreases with increasing Pr,.
		However, the experimental and numerical prediction of the critical Grashof number is very different from the linear theory.
	www.atmo.arizona.edu /calendar/nc02192004.html (265 words)

	Spartanburg SC \| GoUpstate.com \| Spartanburg Herald-Journal (Site not responding. Last check: 2007-10-10)
		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.
		The Rayleigh number is named after Lord Rayleigh and is defined as the product of the Grashof number, which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number, which describes the relationship between momentum diffusivity and thermal diffusivity.
		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.
	www.goupstate.com /apps/pbcs.dll/section?category=NEWS&template=wiki&text=Rayleigh_number (215 words)

	Grashof Numbers : Background (Site not responding. Last check: 2007-10-10)
		The Grashof number is analogous to the Reynolds number in forced convection.
		Essentially, the Grashof number is a ratio of buoyant forces to viscous forces.
		Because the Grashof number is the characteristic dimensionless group of free convection, it arises in problems dealing with heat transfer coefficient correlations.
	www.owlnet.rice.edu /~ceng402/proj05/hoy/hoyroos/background/background.html (287 words)

	An experimental and three-dimensional numerical investigation of the Czochralski solidification of single silicon ...
		The length scale used to define the Grashof number was the melt height.
		At 1 and 4 rpm, the frequency of oscillation was found to be a function of the Grashof number.
		A Prandtl number of 0.0189 and a series of Grashof numbers between 9.3E + 4 and 5.8E + 6 was used.
	repository.upenn.edu /dissertations/AAI9727195 (410 words)

	Station Information - Dimensionless number
		For the purposes of the experimenter, different systems which share the same description by dimensionless numbers are equivalent.
		Rayleigh number: Buoyancy and viscous forces in free convection
		Reynolds number: Characterizing the flow behaviour (laminar or turbulent
	www.stationinformation.com /encyclopedia/d/di/dimensionless_number_1.html (398 words)

	Rayleigh number (Site not responding. Last check: 2007-10-10)
		The Rayleigh number is a dimensionlessnumber of fundamental importance in geophysics, where it is an indicator ofthe presence and strength of convection within a fluid body such as the Earth's liquid mantle.
		The Rayleigh number results from a comparison of buoyancy and viscosity, and its low value for the Earth's mantleindicates that convection occurs throughout the mantle as a whole, and not just within mantle layers.
		It is defined as theproduct of the Grashof number, which describes the relationship between buoyancy and inertia within a fluid,and the Prandtl number, which describes the relationship between the viscosity of a fluid and its temperature.
	www.therfcc.org /rayleigh-number-256568.html (137 words)

	grashof number Resources
		The Grashof number is a dimensionless number in fluid dynamics which approximates the ratio of the buoyancy force to the viscous...
		Besides all, the Grashof number.....governing parameter (Reynolds number, Grashof number, etc.) is found.....to calculate the critical value of the...
		Rayleigh.....may be characterized by the Grashof number of the flow and by the Prandtl.....over the vertical plate..
	www.techrectory.com /Physics/directory/grashof-number.html (215 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		At low Grashof number regime with weak magnetic field, a circulating flow is formed in the enclosure.
		Further, when the magnetic field is weak and the Grashof number is high, the convection is dominant and vertical temperature stratification is predominant in the core region.
		The average Nusselt number decreases with an increase of Hartmann number.
	www.elsevier.com /cdweb/journals/00207225/articles/33/8/002072259400120.abstract.en (214 words)

	Effect of Operating Conditions on the Mixed Convection in a Channel with Discrete Heat Sources and Partially Filled ... (Site not responding. Last check: 2007-10-10)
		The main object is to show the effect of Reynolds number, the heat flux, and Grashof number on the heat transfer characteristics.
		The results show that with the increase of Reynolds number, the surface and maximum temperature of the heat sources decrease, and both the local and average Nusselt number increase.
		With increasing the heat flux or Grashof number, the temperatures of the heat sources increase, the heat transfer coefficient increases, the maximum temperature increases linearly and the average Nusselt number increases exponentially.
	www.mans.eun.eg /faceng/FacMag/abstracts/elkady.htm (314 words)

	[No title] (Site not responding. Last check: 2007-10-10)
		On analysis, the rational modification was effected by the Grashof number Gr, which is a dimensionless number and shows the influence of the flotage on the speed field and the temperature field.
		As a result, it was found that the modified dimensionless Grashof number explains the erosion velocity of the gradient zone well.
		Moreover, the function of the correlation between the erosion velocity and the modified Grashof number was obtained by regression calculation and could estimate the erosion condition of the gradient zone quantitatively.
	www.elsevier.com /cdweb/journals/09601481/articles/23/2/S096014810000174.abstract.en (210 words)

	Grashof Number
		Grashof number (Gr) is a dimensionless number used in heat transfer studies involving free or natural convection.
		Even though the origin of Grashof number is in the area of heat transfer, it is also used in mass transfer where flow can occur due to concentration differences.
		The Grashof number is used to describe natural convection in laminar and turbulent flows in heat and mass transports.
	www.dekker.com /sdek/207383136-19165749/abstract~db=enc~content=a713499277 (590 words)

	Dimensionless Numbers in Heat Transfer (Site not responding. Last check: 2007-10-10)
		For flow over a flat plate, the critical Reynolds number is observed to vary between 1e+5 to 3e+6 depending on the turbulence level in the free stream and the roughness of the surface.
		The Grashof number is the ratio of buoyancy forces to the viscous forces.
		In natural convection the Grashof number plays the same role the is played by the Reynolds number in forced convection.
	www.coolingzone.com /Content/Library/Tutorials/Tutorial%201/DNHT.html (2128 words)

	Grashof Number and Rayleigh Number (Site not responding. Last check: 2007-10-10)
		Grashof number replaces the Reynolds number in the convection correlation equation.
		In free convection, buoyancy driven flow sometimes dominates the flow inertia, therefore, the Nusselt number is a function of the Grashof number and the Prandtle number alone.
		The most important use of the Rayleigh number is to characterize the laminar to turbulence transition of a free convection boundary layer flow.
	www.eng.fsu.edu /~shih/eml3016/lecture-notes/free%20convection/sld003.htm (136 words)

	Theory (Site not responding. Last check: 2007-10-10)
		This number is important, because at low Renold's numbers the flow is laminar, but at high numbers the flow becomes turbulent, which is a distinction needed for system analysis.
		For free convection, the Grashof number denotes the magnitude of the buoyant forces to the viscous forces.
		Comparing the Nusselt number to the Grashof number signifies the allowable heat that is leaving the body of the object to the buoyancy and viscous forces, or how fast the air is rising past the system.
	www.vu.union.edu /~dambruom/senior/4_theory.html (542 words)

	Single crystal pulling system - Patent 4592895
		In general, when the Grashof number exceeds a certain critical value determined by various factors, such as geometrical dimensions of the melt, thermal boundary conditions and so forth, thermal convections occur within the melt.
		However, as can be seen from the equation for the Grashof number, the greater the crucible radius, the greater the Grashof number, so that the thermal convections of the melt become more violent.
		in the aforementioned equation for the Grashof number to be increased, thereby causing the Grashof number thereof to be drastically decreased.
	www.freepatentsonline.com /4592895.html (4198 words)

	Mechanical and Aerospace Engineering \| Fuels Combustion Research
		The Spalding transfer number, B, is a non-dimensional thermodynamic parameter measuring the ratio of drive toward vaporization through the heat of combustion (along with the sensible enthalpy difference between the ambient environment and the droplet surface), divided by the resistance to vaporization through the heat of vaporization:
		As the Damköhler number increases due to increased droplet size or increased gas phase temperature, the burning rate slowly increases until a critical point is reached.
		Based on the above Grashof number argument, for droplet sizes on the order of 1 millimeter and larger should only be accurate when conducted in drop towers or aboard orbiting spacecraft.
	www.princeton.edu /~combust/research/mgc/sphere.html (2658 words)

	Dimensionless field equations (Site not responding. Last check: 2007-10-10)
		Sc, the Schmidt number, is the ratio of the diffusivities of momentum and species, a necessarily positive quantity.
		The interdiffusion Prandtl number occurs twice in the energy equation: in the interdiffusion term; and in the bulk advection term, where it is proportional to the variation in the mixture specific heat.
		As explained in §2.1.3, the variation of the mixture specific heat and the interdiffusion effect are two aspects of the same phenomenon.
	www.ae.su.oz.au /~mcbain/papers/thesis/node24.html (683 words)

	Dimensionless Number - Wikipedia
		According to the Pi-Theorem, the functional dependence between a certain number of variables (e.g.: n) can be reduced by the number of independent dimensions occuring in those variables (e.g.
		The dimensionless numbers can be derived by dimensional analysis.
		According to the Pi-Theorem, the n=5 variables can be reduced by the k=3 dimensions to form p=n-k=5-3=2 independent dimensionless numbers which are in case of the stirrer
	nostalgia.wikipedia.org /wiki/Dimensionless_Number (249 words)

	Dimensionless field equations
		Sc, the Schmidt number, is the ratio of the diffusivities of momentum and species, a necessarily positive quantity.
		The interdiffusion Prandtl number occurs twice in the energy equation: in the interdiffusion term; and in the bulk advection term, where it is proportional to the variation in the mixture specific heat.
		As explained in §2.1.3, the variation of the mixture specific heat and the interdiffusion effect are two aspects of the same phenomenon.
	www.eng.jcu.edu.au /mech/staff/geordie/papers/thesis/node24.html (683 words)

	Low-Dimensional Dynamical Models of Thermal Convection (Site not responding. Last check: 2007-10-10)
		Using the four most energetic empirical eigenfunctions for the velocity and temperature as basis functions and applying Galerkin's method, a reduced model consisting of eight nonlinear ordinary differential equations is obtained.
		In particular, the critical Grashof number at the onset of the first temporal flow instability (Hopf bifurcation) as well as the frequency and amplitude of oscillations at supercritical conditions are in excellent agreement with the predictions of the full model.
		Far from the "design" conditions, the LOM predicts the existence of multiple stable steady solutions at large values of Gr, and a unique stable steady solution at small values of Gr, and exhibits hysteretic behavior that is qualitatively similar to that observed in direct numerical simulations based on the full model.
	exploration.grc.nasa.gov /fcarchive/fluids/papers/Liakopoulos/Low-Dimensional.htm (243 words)

	178.galgel: SPEC CPU2000 Benchmark Description
		The GAMM benchmark considers fixed values of the Prandtl number and the aspect ratio (0.015 and 4 respectively), and varies the boundary conditions.
		A relatively small number of degrees of freedom makes it possible to study linear stability of steady solutions, requiring solution of an eigenvalue problem, which is usually impossible for an arbitrary CFD code.
		However, only the number of basis functions in horizontal and vertical directions is provided in the SPEC input, the other data taking default values.
	www.spec.org /osg/cpu2000/CFP2000/178.galgel/docs/178.galgel.html (788 words)

	Re: Grashof Number
		The Reynolds number can be defined using either the height or the width.
		Grashof Number - Adrian, Mon, 30 Apr 2001, 12:33 a.m.
		Re: Grashof Number - Roger Lucheta, Mon, 30 Apr 2001, 9:11 a.m.
	www.cfd-online.com /Forum/main_archive_2001.cgi/read/16435 (181 words)

	RMP Lecture Notes
		The Grashof Number is used to assess the impact of natural convection (MSH Eq.
		The fluid properties used to calculate the Grashof number should be evaluated at the film temperature, the arithmetic mean between the bulk and wall temperatures.
		When the Grashof Number is greater than 1000, heat transfer coefficients should be corrected to reflect the increase due to free circulation.
	www.cbu.edu /~rprice/lectures/htcoeff.html (697 words)

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