Grashof number

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The Grashof number is a dimensionless number in fluid dynamics which approximates the ratio of the buoyancy force to the viscous force acting on a fluid. It is named after the German engineer Franz Grashof.

[ Gr = \frac]

where

g = acceleration due to gravity

β = volumetric thermal expansion coefficient

T_s = source temperature

T_∞ = quiescent temperature

L = characteristic length

ν = kinematic viscosity

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.

[ Gr_d = \frac\, ]

where

d = diameter of cylinder

ρ = fluid density

μ =(absolute) dynamic fluid viscosity

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