Bound on vertical heat transport at large Prandtl number

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• 作者：Xiaoming Wang
• 关键词：Rayleigh– ; Bé ; nard convection ; Boussinesq equations ; Prandtl number ; Rayleigh number ; Nusselt number
• 刊名：Physica D
• 出版年：2008
• 出版时间：15 May 2008
• 年：2008
• 卷：237
• 期：6
• 页码：854-858
• 全文大小：278 K

文摘

We prove a new upper bound on the vertical heat transport in Rayleigh–Bénard convection of the form class=""inlMMLBox"">cience?_ob=MathURL&_method=retrieve&_udi=B6TVK-4R3351R-2&_mathId=mml2&_user=1067359&_cdi=5537&_rdoc=11&_acct=C000058823&_version=1&_userid=2795313&md5=02c911fc2fea9d43ebcf3ba117680fb7"">c=""http://www.sciencedirect.com/cache/MiamiImageURL/B6TVK-4R3351R-2-4P/0?wchp=dGLbVzb-zSkWb"" alt=""View the MathML source"" title=""View the MathML source"" align=""absbottom"" border=""0"" height=19 width=""79""/> under the assumption that the ratio of Prandtl number over Rayleigh number satisfies class=""inlMMLBox"">cience?_ob=MathURL&_method=retrieve&_udi=B6TVK-4R3351R-2&_mathId=mml3&_user=1067359&_cdi=5537&_rdoc=11&_acct=C000058823&_version=1&_userid=2795313&md5=9e10ec998522072e5dc4ef6b5e9b610b"">c=""http://www.sciencedirect.com/cache/MiamiImageURL/B6TVK-4R3351R-2-2J/0?wchp=dGLbVzb-zSkWb"" alt=""View the MathML source"" title=""View the MathML source"" align=""absbottom"" border=""0"" height=17 width=""44""/> where the non-dimensional constant coration:none; color:black"" href=""/science?_ob=MathURL&_method=retrieve&_udi=B6TVK-4R3351R-2&_mathId=mml4&_user=1067359&_cdi=5537&_rdoc=11&_acct=C000058823&_version=1&_userid=2795313&md5=5aff636c74f027ddc0f01b7b47b74ee6"" title=""Click to view the MathML source"" alt=""Click to view the MathML source"">c₀ depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) class=""inlMMLBox"">cience?_ob=MathURL&_method=retrieve&_udi=B6TVK-4R3351R-2&_mathId=mml5&_user=1067359&_cdi=5537&_rdoc=11&_acct=C000058823&_version=1&_userid=2795313&md5=ab6690ee0b098dd2562a0ed947b586f1"">c=""http://www.sciencedirect.com/cache/MiamiImageURL/B6TVK-4R3351R-2-4N/0?wchp=dGLbVzb-zSkWb"" alt=""View the MathML source"" title=""View the MathML source"" align=""absbottom"" border=""0"" height=17 width=""24""/> bound (modulo logarithmic correction) on vertical heat transport for the infinite Prandtl number model for convection due to Constantin and Doering [P. Constantin, C.R. Doering, Infinite Prandtl number convection, J. Stat. Phys. 94 (1) (1999) 159–172] and Doering, Otto and Reznikoff [C.R. Doering, F. Otto, M.G. Reznikoff, Bounds on vertical heat transport for infinite Prandtl number Rayleigh–Bénard convection, J. Fluid Mech. 560 (2006) 229–241]. It also improves a uniform (in Prandtl number) class=""inlMMLBox"">cience?_ob=MathURL&_method=retrieve&_udi=B6TVK-4R3351R-2&_mathId=mml6&_user=1067359&_cdi=5537&_rdoc=11&_acct=C000058823&_version=1&_userid=2795313&md5=374c2d2d51a448c5998643ba353df15a"">c=""http://www.sciencedirect.com/cache/MiamiImageURL/B6TVK-4R3351R-2-4/0?wchp=dGLbVzb-zSkWb"" alt=""View the MathML source"" title=""View the MathML source"" align=""absbottom"" border=""0"" height=17 width=""24""/> bound for the Nusselt number [P. Constantin, C.R. Doering, Heat transfer in convective turbulence, Nonlinearity 9 (1996) 1049–1060] in the case of large Prandtl number.