English Русский 中文 Português Español Français Deutsch 概要 編集委員会 連絡先 アクセス Begell House
View in A-Z Index

Grashof number, Gr, is a nondimensional parameter used in the correlation of heat and mass transfer due to thermally induced natural convection at a solid surface immersed in a fluid. It is defined as



  • g = acceleration due to gravity, m s−2

  • l = representative dimension, m

  • ξ = coefficient of expansion of the fluid, K−1

  • ΔT = temperature difference between the surface and the bulk of the fluid, K

  • ν = kinematic viscosity of the fluid, m2s−1 .

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.

The form of the Grashof number can be derived by considering the forces on a small element of fluid of volume l3.

The buoyancy force, Fb, on this element has the magnitude gl3Δρ, where Δρ is the difference in density between the element and the surrounding fluid. The order of magnitude of the viscous force, Fv, on the element is ηul, where η is the fluid viscosity, and u the velocity of the element relative to the surrounding fluid. Hence,


The order of magnitude of the velocity u may be obtained by equating viscous and momentum forces, i.e.,




Substituting this value into the ratio of buoyancy to viscous forces


and using the relationship




Since Reynolds number, Re, represents the ratio of momentum to viscous forces (see Reynolds Number) the relative magnitudes of Gr and Re are an indication of the relative importance of natural and forced convection in determining heat transfer. Forced convection effects are usually insignificant when Gr/Re2 >> 1 and conversely natural convection effects may be neglected when Gr/Re2 << 1. When the ratio is of the order of one, combined effects of natural and forced convection have to be taken into account.


Hewitt G. F, Shires, G. L. and Bott T. R. (1994) Process Heat Transfer, CRC Press, Boca Raton, FL, USA.


  1. Hewitt G. F, Shires, G. L. and Bott T. R. (1994) Process Heat Transfer, CRC Press, Boca Raton, FL, USA.
表示回数: 97534 記事追加日: 2 February 2011 記事最終修正日: 14 February 2011 ©著作権 2010-3921 トップへ戻る
A-Z索引 著者/編集者 意味マップ ビジュアルギャラリー 寄稿 Guest