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| {{Incomplete|date=May 2009}}
| | Bonus: WP Twin and WP Twin Auto Backup: (link to ) While not a theme, I think this software is essential if you are maintaining your Wordpress blog or regularly create new blog sites. Thus, it is important to keep pace with this highly advanced age and have a regular interaction with your audience to keep a strong hold in the business market. This is a service where people write articles using a specific keyword you have given them. Donor oocytes and menopausal pregnancy: Oocyte donation to women of advanced reproductive age: pregnancy results and obstetrical outcomes in patients 45 years and older. Understanding how Word - Press works can be a challenge, but it is not too difficult when you learn more about it. <br><br>Thus, it is imperative that you must Hire Word - Press Developers who have the expertise and proficiency in delivering theme integration and customization services. If a newbie missed a certain part of the video then they could always rewind. This plugin is a must have for anyone who is serious about using Word - Press. You can up your site's rank with the search engines by simply taking a bit of time with your site. For a Wordpress website, you don't need a powerful web hosting account to host your site. <br><br>Just ensure that you hire experienced Word - Press CMS developer who is experienced enough to perform the task of Word - Press customization to get optimum benefits of Word - Press CMS. But if you are not willing to choose cost to the detriment of quality, originality and higher returns, then go for a self-hosted wordpress blog and increase the presence of your business in this new digital age. Setting Up Your Business Online Using Free Wordpress Websites. To turn the Word - Press Plugin on, click Activate on the far right side of the list. For any web design and development assignment, this is definitely one of the key concerns, specifically for online retail outlets as well as e-commerce websites. <br><br>Additionally Word - Press add a default theme named Twenty Fourteen. The SEOPressor Word - Press SEO Plugin works by analysing each page and post against your chosen keyword (or keyword phrase) and giving a score, with instructions on how to improve it. The templates are designed to be stand alone pages that have a different look and feel from the rest of your website. Giant business organizations can bank on enterprise solutions to incorporate latest web technologies such as content management system etc, yet some are looking for economical solutions. Wordpress template is loaded with lots of prototype that unite graphic features and content area. <br><br>He loves sharing information regarding wordpress, Majento, Drupal and Joomla development tips & tricks. Sanjeev Chuadhary is an expert writer who shares his knowledge about web development through their published articles and other resource. This allows updates to be sent anyone who wants them via an RSS reader or directly to their email. In the event you loved this information along with you would like to obtain details relating to [http://minecraftgameonlinefree.net/profile/277314/brclyne backup plugin] kindly pay a visit to our web-page. In addition, Word - Press design integration is also possible. Customers within a few seconds after visiting a site form their opinion about the site. |
| [[Image:Bénard cells convection.ogv|thumb|300px|Rayleigh-Bénard cells.]]
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| '''Natural convection''' is a mechanism, or type of [[heat exposure|heat transport]], in which the fluid motion is not generated by any external source (like a pump, fan, suction device, etc.) but only by density differences in the fluid occurring due to [[temperature gradient]]s. In natural convection, fluid surrounding a heat source receives heat, becomes less dense and rises. The surrounding, cooler fluid then moves to replace it. This cooler fluid is then heated and the process continues, forming a convection current; this process transfers heat energy from the bottom of the convection cell to top. The driving force for natural convection is buoyancy, a result of differences in fluid density. Because of this, the presence of a [[proper acceleration]] such as arises from resistance to gravity, or an [[equivalence principle|equivalent]] force (arising from [[acceleration]], [[centrifugal force]] or [[Coriolis effect]]), is essential for natural convection. For example, natural convection essentially does not operate in free-fall ([[inertial]]) environments, such as that of the orbiting International Space Station, where other heat transfer mechanisms are required to prevent electronic components from overheating.
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| Natural convection has attracted a great deal of attention from researchers because of its presence both in nature and engineering applications. In nature, convection cells formed from air raising above sunlight-warmed land or water are a major feature of all weather systems. Convection is also seen in the rising plume of hot air from [[fire]], oceanic currents, and sea-wind formation (where upward convection is also modified by [[Coriolis force]]s). In engineering applications, convection is commonly visualized in the formation of microstructures during the cooling of molten metals, and fluid flows around shrouded heat-dissipation fins, and solar ponds. A very common industrial application of natural convection is free air cooling without the aid of fans: this can happen on small scales (computer chips) to large scale process equipment.
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| ==Parameters==
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| ===Onset===
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| {{See also|Heat transfer}}
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| The onset of natural convection is determined by the [[Rayleigh number]] ('''Ra'''). This [[dimensionless number]] is given by
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| :<math>\textbf{Ra} = \frac{\Delta\rho g L^3}{D\mu}</math> | |
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| where
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| :<math>\Delta \rho</math> is the difference in density between the two parcels of material that are mixing
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| :<math>g</math> is the local [[gravitational acceleration]]
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| :<math>L</math> is the characteristic length-scale of convection: the depth of the boiling pot, for example
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| :<math>D</math> is the [[diffusivity]] of the characteristic that is causing the convection, and
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| :<math>\mu</math> is the [[dynamic viscosity]].
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| Natural convection will be more likely and/or more rapid with a greater variation in density between the two fluids, a larger acceleration due to gravity that drives the convection, and/or a larger distance through the convecting medium. Convection will be less likely and/or less rapid with more rapid diffusion (thereby diffusing away the gradient that is causing the convection) and/or a more viscous (sticky) fluid.
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| For thermal convection due to heating from below, as described in the boiling pot above, the equation is modified for thermal expansion and thermal diffusivity. Density variations due to thermal expansion are given by:
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| :<math>\Delta\rho=\rho_0 \beta \Delta T</math>
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| where
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| :<math>\rho_0</math> is the reference density, typically picked to be the average density of the medium,
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| :<math>\beta</math> is the [[coefficient of thermal expansion]], and
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| :<math>\Delta T</math> is the temperature difference across the medium.
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| The general diffusivity, <math>D</math>, is redefined as a [[thermal diffusivity]], <math>\alpha</math>.
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| :<math>D=\alpha</math>
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| Inserting these substitutions produces a Rayleigh number that can be used to predict thermal convection.<ref>{{cite book|isbn=978-0-521-66624-4|author=Donald L. Turcotte; Gerald Schubert.|year=2002|publisher=Cambridge University Press|location=Cambridge|title=Geodynamics}}</ref>
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| :<math>\textbf{Ra} = \frac{\rho_0 g \beta \Delta T L^3}{\alpha \mu}</math>
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| ===Turbulence===
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| The tendency of a particular naturally convective system towards turbulence relies on the [[Grashof number]] (Gr).<ref>{{cite book | author=Kays, William; Crawford, Michael; Weigand, Bernhard | title=Convective Heat and Mass Transfer, 4E | publisher=McGraw-Hill Professional | year=2004 | isbn=0072990732}}</ref>
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| :<math> Gr= \frac{g \beta \Delta T L^3}{\nu^2} </math>
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| In very sticky, viscous fluids (large ''ν''), fluid movement is restricted, and natural convection will be non-turbulent.
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| Following the treatment of the previous subsection, the typical fluid velocity is of the order of <math>g \Delta \rho L^2 / \mu</math>, up to a numerical factor depending on the geometry of the system. Therefore Grashof number can be thought of as [[Reynolds number]] with the velocity of natural convection replacing the velocity in Reynolds number's formula. However In practice, when referring to the Reynolds number, it is understood that one is considering forced convection, and the velocity is taken as the velocity dictated by external constraints (see below).
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| ===Behavior===
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| {{Incomplete|date=April 2010}}
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| The [[Grashof number]] can be formulated for natural convection occurring due to a [[concentration gradient]], sometimes termed thermo-solutal convection. In this case, a concentration of hot fluid diffuses into a cold fluid, in much the same way that ink poured into a container of water diffuses to dye the entire space. Then:
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| :<math> Gr= \frac{g \beta \Delta C L^3}{\nu^2} </math>
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| Natural convection is highly dependent on the geometry of the hot surface, various correlations exist in order to determine the heat transfer coefficient.
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| A general correlation that applies for a variety of geometries is
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| : <math>Nu = \left[Nu_0^\frac{1}{2} + Ra^ \frac{1}{6} \left(\frac {f_4\left(Pr\right)}{300}\right)^\frac{1}{6} \right]^2 </math>
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| The value of f<sub>4</sub>(Pr) is calculated using the following formula
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| : <math>f_4(Pr)= \left[1+ \left ( \frac {0.5}{Pr} \right )^\frac{9}{16} \right]^\frac{-16}{9}</math>
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| Nu is the [[Nusselt number]] and the values of Nu<sub>0</sub> and the characteristic length used to calculate Ra are listed below (see also Discussion):
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| {| class="wikitable"
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| |-
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| ! '''Geometry'''
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| ! '''Characteristic length'''
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| ! '''Nu<sub>0</sub>'''
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| |-
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| | Inclined plane
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| | x (Distance along plane)
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| | 0.68
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| |-
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| | Inclined disk
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| | 9D/11 (D = diameter)
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| | 0.56
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| |-
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| | Vertical cylinder
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| | x (height of cylinder)
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| | 0.68
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| |-
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| | Cone
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| | 4x/5 (x = distance along sloping surface)
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| | 0.54
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| |-
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| | Horizontal cylinder
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| | <math>\pi D/2</math> (D = diameter of cylinder)
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| | 0.36<math>\pi</math>
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| |}
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| '''Warning''': The values indicated for the '''Horizontal cylinder''' are '''wrong'''; see discussion.
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| ==Natural Convection from a Vertical Plate==
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| In this system heat is transferred from a vertical plate to a fluid moving parallel to it by natural convection. This will occur in any system wherein the density of the moving fluid varies with position. These phenomena will only be of significance when the moving fluid is minimally affected by forced convection.<ref name=unitop>{{cite book | author= W. McCabe J. Smith | title=Unit Operations of Chemical Engineering | publisher=McGraw-Hill | year=1956 | isbn= 0-07-044825-6}}</ref>
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| When considering the flow of fluid is a result of heating, the following correlations can be used, assuming the fluid is an ideal diatomic, has adjacent to a vertical plate at constant temperature and the flow of the fluid is completely laminar.<ref name=bennett>{{cite book | author=Bennett | title=Momentum, Heat and Mass Transfer | publisher=McGraw-Hill | year=1962 | isbn = 0-07-004667-0 }}</ref>
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| Nu<sub>m</sub> = 0.478(Gr<sup>0.25</sup>)<ref name=bennett />
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| [[Nusselt Number|Mean Nusselt Number]] = Nu<sub>m</sub> = h<sub>m</sub>L/k<ref name=bennett />
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| Where
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| h<sub>m</sub> = mean coefficient applicable between the lower edge of the plate and any point in a distance L (W/m<sup>2</sup>. K)
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| L = height of the vertical surface (m)
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| k = thermal conductivity (W/m. K)
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| [[Grashof Number]] = Gr = <math>[gL^3(t_s-t_\infty)]/v^2T</math> <ref name=unitop /><ref name=bennett />
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| Where
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| g = gravitational acceleration (m/s<sup>2</sup>)
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| L = distance above the lower edge (m)
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| t<sub>s</sub> = temperature of the wall (K)
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| t∞ = fluid temperature outside the thermal boundary layer (K)
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| v = kinematic viscosity of the fluid (m²/s)
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|
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| T = absolute temperature (K)
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| When the flow is turbulent different correlations involving the Rayleigh Number (a function of both the [[Grashof Number]] and the [[Prandtl Number]] must be used).<ref name=bennett />
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| ==Pattern formation==
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| [[Image:Convection1.gif|thumb|right|A fluid under [[Rayleigh-Bénard convection]]: the left picture represents the thermal field and the right picture its two-dimensional [[Fourier transform]].]]
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| Convection, especially Rayleigh-Bénard convection, where the convecting fluid is contained by two rigid horizontal plates, is a convenient example of a [[Pattern formation|pattern forming system]].
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| When heat is fed into the system from one direction (usually below), at small values it merely diffuses (''conducts'') from below upward, without causing fluid flow. As the heat flow is increased, above a critical value of the [[Rayleigh number]], the system undergoes a [[Bifurcation theory|bifurcation]] from the stable ''conducting'' state to the ''convecting'' state, where bulk motion of the fluid due to heat begins. If fluid parameters other than density do not depend significantly on temperature, the flow profile is [[Symmetry|symmetric]], with the same volume of fluid rising as falling. This is known as [[Boussinesq approximation (buoyancy)|Boussinesq]] convection.
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| As the temperature difference between the top and bottom of the fluid becomes higher, significant differences in fluid parameters other than density may develop in the fluid due to temperature. An example of such a parameter is [[viscosity]], which may begin to significantly vary horizontally across layers of fluid. This breaks the symmetry of the system, and generally changes the pattern of up- and down-moving fluid from stripes to hexagons, as seen at right. Such hexagons are one example of a [[convection cell]].
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| As the [[Rayleigh number]] is increased even further above the value where convection cells first appear, the system may undergo other bifurcations, and other more complex patterns, such as [[spiral]]s, may begin to appear.
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| ==Mantle convection==
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| {{Main|Mantle convection}}
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| Convection within [[Earth's mantle]] is the driving force for [[plate tectonics]]. Mantle convection is the result of a thermal gradient: the lower mantle is hotter than the upper mantle, and is therefore less dense. This sets up two primary types of instabilities. In the first type, plumes rise from the lower mantle, and corresponding unstable regions of [[lithosphere]] drip back into the mantle. In the second type, subducting oceanic plates (which largely constitute the upper thermal boundary layer of the mantle) plunge back into the mantle and move downwards towards the [[core-mantle boundary]]. Mantle convection occurs at rates of centimeters per year, and it takes on the order of hundreds of millions of years to complete a cycle of convection.
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| Neutrino flux measurements from the Earth's core (see [[kamLAND]]) show the source of about two-thirds of the heat in the inner core is the [[radioactive decay]] of [[potassium|<sup>40</sup>K]], uranium and thorium. This has allowed plate tectonics on Earth to continue far longer than it would have if it were simply driven by heat left over from Earth's formation; or with heat produced from gravitational [[potential energy]], as a result of physical rearrangement of denser portions of the Earth's interior toward the center of the planet (i.e., a type of prolonged falling and settling).
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| == See also ==
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| * [[Combined forced and natural convection]]
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| * [[Forced convection]]
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| * [[Convection]]
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| * [[Heat transfer]]
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| * [[Heat exchanger]]
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| == References ==
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| {{Reflist}}
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| [[Category:Heat transfer]]
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| [[Category:Fluid dynamics]]
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| [[Category:Convection]]
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