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In fluid mechanics, the Rayleigh number (Ra) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free convection or natural convection. When the Rayleigh number is below a critical value for that fluid, heat transfer is primarily 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. Hence the Rayleigh number itself may also be viewed as the ratio of buoyancy and viscosity forces multiplied by the ratio of momentum and thermal diffusivities. ==Classical Definition== For free convection near a vertical wall, the Rayleigh number is defined as: : where: :''x'' is the characteristic length :Ra''x'' is the Rayleigh number for characteristic length ''x'' :Gr''x'' is the Grashof number for characteristic length ''x'' :Pr is the Prandtl number :''g'' is acceleration due to gravity :''Ts'' is the surface temperature :''T∞'' is the quiescent temperature (fluid temperature far from the surface of the object) :''ν'' is the kinematic viscosity :''α'' is the thermal diffusivity :''β'' is the thermal expansion coefficient (equals to 1/''T'', for ideal gases, where ''T'' is absolute temperature). In the above, the fluid properties Pr, ''ν'', ''α'' and ''β'' are evaluated at the film temperature, which is defined as: : For a uniform wall heating flux, the modified Rayleigh number is defined as: : where: :''q"o'' is the uniform surface heat flux :''k'' is the thermal conductivity.〔M. Favre-Marinet and S. Tardu, Convective Heat Transfer, ISTE, Ltd, London, 2009 〕 For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Rayleigh number」の詳細全文を読む スポンサード リンク
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