Grashof Number
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 Reynold's number. It's believed to be named after Franz Grashof. Though this grouping of terms had already been in use, it wasn't named until around 1921, 28 years after Franz Grashof's death. It's not very clear why the grouping was named after him.
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:
where:
The L and D subscripts indicate the length scale basis for the Grashof Number.
The transition to turbulent flow occurs in the range 108 < GrL < 109 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.
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.
where:
and:
The Rayleigh number, shown below, is a dimensionless number that characterizes convection problems in heat transfer. A critical value exists for the Rayleigh number, above which fluid motion occurs.
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