A dimensionless number, Gr. It is used in the study of natural convection and represents the ratio of buoyancy forces to viscous forces:

where ρ is the density, g is the local acceleration due to gravity, β is the volume coefficient of expansion, l is the characteristic length, ΔT is the temperature difference, and μ is the viscosity. The product of the Grashof number and the Prandtl number characterizes the convective heat transfer. It can be applied to laminar and turbulent regimes and for vertical and horizontal planes and cylinders, such as pipes. An analogous form of the Grashof number used in the study of mass transfer by natural convection is:

where g is the acceleration due to gravity, Δρ is the density difference between two points, L is the characteristic length, and v is the kinematic viscosity of the fluid. It is named after German engineer Franz Grashof (1826–93).