In fluid mechanics (especially fluid thermodynamics), the Grashof number (, after Franz Grashof) is a dimensionless number which approximates the ratio of the buoyancy to viscous forces acting on a fluid. It frequently arises in the study of situations involving natural convection and is analogous to the Reynolds number ().
Definition
Heat transfer
Free convection is caused by a change in density of a fluid due to a temperature change or gradient. Usually the density decreases due to an increase in temperature and causes the fluid to rise. This motion is caused by the buoyancy force. The major force that resists the motion is the viscous force. The Grashof number is a way to quantify the opposing forces.
The Grashof number is:
:<math> \mathrm{Gr}_L = \frac{g \beta (T_s - T_\infty ) L^3}{\nu ^2}\, </math> for vertical flat plates
:<math> \mathrm{Gr}_D = \frac{g \beta (T_s - T_\infty ) D^3}{\nu ^2}\, </math> for pipes and bluff bodies
where:
- is gravitational acceleration due to Earth
- is the coefficient of volume expansion (equal to approximately for ideal gases)
- is the surface temperature
- is the bulk temperature
- is the vertical length
- is the diameter
- is the kinematic viscosity.
The and subscripts indicate the length scale basis for the Grashof number.
The transition to turbulent flow occurs in the range for natural convection from vertical flat plates. At higher Grashof numbers, the boundary layer is turbulent; at lower Grashof numbers, the boundary layer is laminar, that is, in the range .
Mass transfer
There is an analogous form of the Grashof number used in cases of natural convection mass transfer problems. In the case of mass transfer, natural convection is caused by concentration gradients rather than temperature gradients. Using slope of the linear regression line through data points, it is concluded that increase in the value of Grashof number or any buoyancy related parameter implies an increase in the wall temperature and this makes the bond(s) between the fluid to become weaker, strength of the internal friction to decrease, the gravity to becomes stronger enough (i.e. makes the specific weight appreciably different between the immediate fluid layers adjacent to the wall). The effects of buoyancy parameter are highly significant in the laminar flow within the boundary layer formed on a vertically moving cylinder. This is only achievable when the prescribed surface temperature (PST) and prescribed wall heat flux (WHF) are considered. It can be concluded that buoyancy parameter has a negligible positive effect on the local Nusselt number. This is only true when the magnitude of Prandtl number is small or prescribed wall heat flux (WHF) is considered. Sherwood number, Bejan Number, Entropy generation, Stanton Number and pressure gradient are increasing properties of buoyancy related parameter while concentration profiles, frictional force, and motile microorganism are decreasing properties.