{"id":20351,"date":"2018-11-19T18:57:41","date_gmt":"2018-11-19T18:57:41","guid":{"rendered":"http:\/\/sitepourvtc.com\/?page_id=20351"},"modified":"2023-02-14T13:15:49","modified_gmt":"2023-02-14T13:15:49","slug":"what-is-rayleigh-number","status":"publish","type":"page","link":"https:\/\/sitepourvtc.com\/nuclear-engineering\/heat-transfer\/introduction-to-heat-transfer\/characteristic-numbers\/what-is-rayleigh-number\/","title":{"rendered":"What is Rayleigh Number"},"content":{"rendered":"
The Rayleigh\u00a0number<\/strong>\u00a0is simply defined as the product of the Grashof number<\/a>, which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number<\/a>, which describes the relationship between momentum diffusivity and thermal diffusivity.<\/p>\n Rax<\/sub> = Grx<\/sub> . Pr<\/span><\/strong><\/p>\n The\u00a0Grashof number<\/strong> is defined as the ratio of the buoyant to a viscous force acting on a fluid in the velocity boundary layer. Its role in natural convection is much like that of the Reynolds number<\/a> in forced convection.\u00a0Natural convection\u00a0occurs if this motion and mixing are caused by density<\/a> variations resulting from temperature differences within the fluid. Usually, the density decreases due to increased temperature<\/a> and causes the fluid to rise. This motion is caused by the buoyant force. The major force that resists the motion is the viscous force. The Grashof number is a way to quantify the opposing forces.<\/p>\n The Rayleigh number<\/strong> is used to express heat transfer in natural convection. The magnitude of the Rayleigh number is a good indication of whether the natural convection boundary layer is laminar or turbulent. The simple empirical correlations for the average Nusselt number, Nu, in natural convection are of the form:<\/p>\n Nux<\/sub>\u00a0= C. Rax<\/sub>n<\/sup><\/span><\/strong><\/p>\n The values of the constants C<\/strong> and n<\/strong> depend on the geometry of the surface and the flow regime<\/a>, which is characterized by the range of the Rayleigh number<\/strong>. The value of n is usually n = 1\/4 for laminar flow and n = 1\/3 for turbulent flow.<\/p>\n The\u00a0Rayleigh\u00a0number<\/strong> is defined as:<\/p>\n <\/a><\/p>\n where:<\/p>\n g is the acceleration due to Earth’s gravity<\/p>\n \u03b2 is the coefficient of thermal expansion<\/p>\n Twall<\/sub> is the wall temperature<\/p>\n T\u221e<\/sub> is the bulk temperature<\/p>\n L is the vertical length<\/p>\n \u03b1 is the\u00a0thermal diffusivity<\/a><\/p>\n \u03bd is the kinematic viscosity.<\/p>\n For gases \u03b2 = 1\/T where the temperature is in K. For liquids, \u03b2 can be calculated if the variation of density with the temperature at constant pressure is known. For a vertical flat plate, the flow turns turbulent<\/a> for the value of:<\/p>\n Rax<\/sub>\u00a0= Grx<\/sub>\u00a0. Pr >\u00a0109<\/sup>\u00a0<\/span><\/strong><\/p>\n As in forced convection, the microscopic nature of flow and convection correlations are distinctly different in the laminar<\/a> and turbulent<\/a> regions.<\/p>\nExample:\u00a0Rayleigh Number <\/strong><\/h2>\n