Deriving the Schwarzschild solution

There are two different Bejan numbers (Be) named after Duke University professor Adrian Bejan which are used in the scientific domains of thermodynamics and fluid mechanics.

Thermodynamics

In the context of thermodynamics, the Bejan number is the ratio of heat transfer irreversibility to total irreversibility due to heat transfer and fluid friction:

$\mathrm {Be} ={\frac {{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}}{{\dot {S}}'_{\mathrm {gen} ,\,\Delta T}+{\dot {S}}'_{\mathrm {gen} ,\,\Delta p}}}$

where

${\dot {S}}'_{\mathrm {gen} ,\,\Delta T}$ is the entropy generation contributed by heat transfer

${\dot {S}}'_{\mathrm {gen} ,\,\Delta p}$ is the entropy generation contributed by fluid friction.

Fluid mechanics, heat transfer and mass transfer

In the context of fluid mechanics. the Bejan number is the dimensionless pressure drop along a channel of length $L$:

$\mathrm {Be} ={\frac {\Delta PL^{2}}{\mu \nu }}$

where

$\mu$ is the dynamic viscosity

$\nu$ is the momentum diffusivity

In the context of heat transfer. the Bejan number is the dimensionless pressure drop along a channel of length $L$:

$\mathrm {Be} ={\frac {\Delta PL^{2}}{\mu \alpha }}$

where

$\mu$ is the dynamic viscosity

$\alpha$ is the thermal diffusivity

The Be number plays in forced convection the same role that the Rayleigh number plays in natural convection.

In the context of mass transfer. the Bejan number is the dimensionless pressure drop along a channel of length $L$:

$\mathrm {Be} ={\frac {\Delta PL^{2}}{\mu D}}$

where

$\mu$ is the dynamic viscosity

$D$ is the mass diffusivity

For the case of Reynolds analogy (Le = Pr = Sc = 1), it is clear that all three definitions of Bejan number are the same.

Also, Awad and Lage: obtained a modified form of the Bejan number, originally proposed by Bhattacharjee and Grosshandler for momentum processes, by replacing the dynamic viscosity appearing in the original proposition with the equivalent product of the fluid density and the momentum diffusivity of the fluid. This modified form is not only more akin to the physics it represents but it also has the advantage of being dependent on only one viscosity coefficient. Moreover, this simple modification allows for a much simpler extension of Bejan number to other diffusion processes, such as a heat or a species transfer process, by simply replacing the diffusivity coefficient. Consequently, a general Bejan number representation for any process involving pressure-drop and diffusion becomes possible. It is shown that this general representation yields analogous results for any process satisfying the Reynolds analogy (i. e., when Pr = Sc = 1), in which case the momentum, energy, and species concentration representations of Bejan number turn out to be the same.

Therefore, it would be more natural and broad to define Be in general, simply as:

$\mathrm {Be} ={\frac {\Delta PL^{2}}{\rho \delta ^{2}}}$

where

$\rho$ is the fluid density

$\delta$ is the corresponding diffusivity of the process in consideration

In addition, Awad: presented Hagen number vs. Bejan number. Although their physical meaning is not the same because the former represents the dimensionless pressure gradient while the latter represents the dimensionless pressure drop, it will be shown that Hagen number coincides with Bejan number in cases where the characteristic length (l) is equal to the flow length (L). Also, a new expression of Bejan number in the Hagen-Poiseuille flow will be introduced. This expression is

$\mathrm {Be} ={{32ReL^{3}} \over {d^{3}}}$

where

$Re$ is the Reynolds number

$L$ is the flow length

$d$ is the pipe diameter

The above expression shows that the Bejan number in the Hagen-Poiseuille flow is indeed a dimensionless group, not recognized previously.

See also

• Adrian Bejan
• Entropy
• Exergy
• Thermodynamics
• Constructal theory

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.

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  In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang
  
  Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules
  
  Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.
  
  A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running
  
  The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more
  
  There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang