Rayleigh number

In fluid mechanics, the Rayleigh number (Ra, after Lord Rayleigh[1]) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection.[2][3][4] It characterises the fluid's flow regime:[5] a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108.

The Rayleigh number is defined as the product of the Grashof number (Gr), which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number (Pr), which describes the relationship between momentum diffusivity and thermal diffusivity: Ra = Gr × Pr.[4][3] Hence it may also be viewed as the ratio of buoyancy and viscosity forces multiplied by the ratio of momentum and thermal diffusivities: Ra = B/μ × ν/α. It is closely related to the Nusselt number (Nu).[5]

  1. ^ Chandrasekhar, S. (1961). Hydrodynamic and Hydromagnetic Stability. London: Oxford University Press. p. 10. ISBN 978-0-19-851237-0.
  2. ^ Baron Rayleigh (1916). "On convection currents in a horizontal layer of fluid, when the higher temperature is on the under side". London Edinburgh Dublin Phil. Mag. J. Sci. 32 (192): 529–546. doi:10.1080/14786441608635602.
  3. ^ a b Çengel, Yunus; Turner, Robert; Cimbala, John (2017). Fundamentals of thermal-fluid sciences (Fifth ed.). New York, NY. ISBN 9780078027680. OCLC 929985323.{{cite book}}: CS1 maint: location missing publisher (link)
  4. ^ a b Cite error: The named reference :1 was invoked but never defined (see the help page).
  5. ^ a b Çengel, Yunus A. (2002). Heat and Mass Transfer (Second ed.). McGraw-Hill. p. 466.