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Grashof number

Grashof number

Grashof number is a dimensionless number representing the ratio of buoyancy to viscosity.

It is expressed with the following equation:


Gr : Grashof number
: Gravitational acceleration [m/s2]
β : Coefficient of thermal expansion [1/K]
: Characteristic temperature difference [K]
: Characteristic length [m]
: Kinematic viscosity coefficient [m2/s]

Difference between a solid surface temperature and free-stream temperature, for example, is used as the characteristic temperature difference.

Grashof number of natural convection corresponds to the Reynolds number of forced convection, and indicates whether the flow caused by natural convection becomes laminar or turbulent.

The critical Grashof number of natural convection transitioning from laminar to turbulent flows is approximately 108 to 109, although it depends on types of fluids and conditions of flows.

Grashof number is said to be named after a German engineer Franz Grashof.