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 and is analogous to the Reynolds number.
The significance of the Grashof number is that it represents the ratio between the buoyancy force due to spatial variation in fluid density (caused by temperature differences) to the restraining force due to the viscosisty of the fluid.
Formula:
Gr = (g Γ l3 Γ ΞΎ Γ ΞT ) Γ· v2
Where,g = acceleration due to gravity
l = representative dimension
ΞΎ = coefficient of expansion of the fluid
ΞT = temperature difference between the surface and the bulk of the fluid
Ξ½ = kinematic viscosity of the fluid