Grashof number
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The Grashof number Gr is a dimensionless number in fluid dynamics and Heat Transfer which approximates the ratio of the buoyancy to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection. It is named after the German engineer Franz Grashof.
for vertical flat plates
for pipes- for bluff bodies
where the L and D subscripts indicates the length scale basis for the Grashof Number.
- g = acceleration due to Earth's gravity
- β = volumetric thermal expansion coefficient (equal to approximately 1/T, for ideal fluids, where T is absolute temperature)
- Ts = source temperature
- T∞ = film temperature
- L = length
- D = diameter
- ν = kinematic viscosity
The transition to turbulent flow occurs in the range 108 < GrL < 109 for natural convection from vertical flat plates. At higher Grashof numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is laminar.
The product of the Grashof number and the Prandtl number gives the Rayleigh number, a dimensionless number that characterizes convection problems in heat transfer.
There is an analogous form of the Grashof number used in cases of natural convection mass transfer problems.
where
and
- g = acceleration due to Earth's gravity
- Ca,s = concentration of species a at surface
- Ca,a = concentration of species a in ambient medium
- L = characteristic length
- ν = kinematic viscosity
- ρ = fluid density
- Ca = concentration of species a
- T = constant temperature
- p = constant pressure
[edit] See also
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T(infinite) is not film temperature. This is ambient temperature.
[edit] References
- Jaluria, Yogesh. Natural Convection Heat and Mass Transfer (New York: Pergamon Press, 1980).
