Glossary term
Grashof Number
A dimensionless number that compares buoyancy forces with viscous forces in natural-convection flow.
Definition
quantityThe Grashof number is a dimensionless measure of the ratio of buoyancy force to viscous force in natural convection.
In free or natural convection, fluid motion is driven by density differences caused by temperature variation rather than by a fan, pump, or imposed flow. The Grashof number indicates whether buoyancy is strong enough to overcome viscous resistance and generate significant motion. It plays a role in heat-transfer correlations, boundary-layer regime assessment, and comparison between natural-convection experiments and real systems.
The Grashof number is used in natural-convection analysis, where fluid motion arises because warmer or cooler fluid has a different density from its surroundings. Unlike forced convection, where the flow rate is imposed by a fan, pump, wind, or moving surface, natural convection depends on buoyancy. The Grashof number compares that buoyant driving force with viscous resistance.
For many engineering problems it is written as:
where g is gravitational acceleration, \beta is the volumetric thermal expansion coefficient, \Delta T is the temperature difference driving buoyancy, L is a characteristic length, and \nu is kinematic viscosity. The number is dimensionless.
Physical interpretation
Small Grashof number means viscosity dominates. Buoyancy may exist, but it is too weak to create substantial flow. Heat transfer is then close to conduction through a nearly stagnant fluid layer. Large Grashof number means buoyancy dominates enough to generate circulation, boundary layers, plumes, and potentially transition toward turbulence.
The characteristic length must match the geometry and correlation being used. For a vertical plate, it may be the plate height. For a horizontal cylinder, it may be diameter. For an enclosure, it may be cavity height or another geometry-specific scale. Using the wrong length can change Gr dramatically because length appears cubed.
Relation to heat transfer
The Grashof number usually appears in natural-convection correlations for the Nusselt number, which relates convective heat transfer to conduction. It is often combined with the Prandtl number into the Rayleigh number:
The Rayleigh number is widely used to determine natural-convection regime and estimate heat-transfer coefficients. In many correlations, Nu is expressed as a function of Ra or GrPr.
Engineering applications include heat loss from walls, cooling of electronic equipment without fans, solar collectors, heat exchangers operating under low-flow conditions, tank thermal stratification, furnace walls, building envelopes, and passive safety systems. In these systems, natural convection may be the primary heat-removal mechanism or an unwanted source of thermal loss.
Practical cautions
The Grashof number assumes that buoyancy is represented correctly by the temperature-dependent density difference. The Boussinesq approximation is often used when density variations are small enough to affect buoyancy but not the rest of the flow equations. Large temperature differences, compressible gases, phase change, radiation-dominated heat transfer, or strongly confined geometries can require more careful modelling.
A common mistake is to use a forced-convection mindset for natural convection. There may be no externally specified velocity, so Reynolds number is not an input in the same way. Another mistake is to copy a correlation without checking its geometry, surface orientation, thermal boundary condition, range of validity, and fluid-property evaluation temperature.