Grashof number

From Wikipedia, the free encyclopedia

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

<math> Gr = \frac{g \beta (T_s - T_\infty ) L^3}{\nu ^2}\, </math>

where

g = acceleration due to Earth's 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.

<math> Gr_c = \frac{g \beta^* (C_{a,s} - C_{a,a} ) L^3}{\nu^2}</math>

where

<math> \beta^* = -\frac{1}{\rho} \left ( \frac{\partial \rho}{\partial C_a} \right )_{T,p}</math>

and

g = acceleration due to Earth's gravity

C_a,s = concentration of species a at surface

C_a,a = concentration of species a in ambient medium

L = characteristic length

ν = kinematic viscosity

ρ = fluid density

C_a = concentration of species a

T = constant temperature

p = constant pressure

[edit] See also

v • d • e Dimensionless numbers in fluid dynamics

Archimedes • Bagnold • Biot • Bond • Brinkman • Capillary • Damköhler • Dean • Deborah • Eckert • Ekman • Eötvös • Euler • Froude • Galilei • Grashof • Hagen • Knudsen • Laplace • Lewis • Mach • Magnetic Reynolds • Marangoni • Morton • Nusselt • Ohnesorge • Péclet • Prandtl • Rayleigh • Reynolds • Richardson • Roshko • Rossby• Ruark • Schmidt • Sherwood • Stanton • Stokes • Strouhal • Suratman • Taylor • Weber • Weissenberg • Womersley

[edit] References

ca:Nombre de Grashof

de:Grashof-Zahl es:Número de Grashof fr:Nombre de Grashof ko:그라스호프 수 it:Numero di Grashof nl:Getal van Grashof ja:グラスホフ数 pl:Liczba Grashofa fi:Grashofin luku