Grashof Number

The Grashof number 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 = surface temperature
T = bulk temperature
L = length
D = diameter
ν = kinematic viscosity

The transition to turbulent flow occurs in the range 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

Read more about Grashof Number:  Derivation of Grashof Number

Other articles related to "grashof number, number":

Derivation of Grashof Number - Buckingham Pi Theorem
... of dimensional analysis that will result in the Grashof Number is known as the Buckingham Pi theorem ... From the two groups and the product forms the Grashof Number Taking and the preceding equation can be rendered as the same result from deriving the Grashof Number from the energy equation ... In forced convection the Reynolds Number governs the fluid flow ...

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