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Grashof number
 
 
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The Grashof number is a dimensionless number in fluid dynamics
Fluid dynamics

In physics, fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow — the natural science of fluids in motion....
 and Heat Transfer
Heat transfer

Heat transfer is the transition of thermal energy or simply heat from a hotter object to a cooler object . When an object or fluid is at a different temperature than its thermodynamic system or another object, transfer of thermal energy, also known as heat transfer, or heat exchange, occurs in such a way that the body and the surround...
 which approximates the ratio of the buoyancy
Buoyancy

In physics, buoyancy is the upward force that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body....
 to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection. It is named after the German engineer Franz Grashof
Franz Grashof

Franz Grashof was a Germany engineer. He was a professor of Applied Mechanics at the Technischen Hochschule Karlsruhe. He is one of the founding directors of Verein Deutscher Ingenieure in 1855....
.

for vertical flat plates

for pipes for bluff bodies

where the L and D subscripts indicates the length scale basis for the Grashof Number.

g = acceleration due to Earth's gravity
Standard gravity

Standard gravity, usually denoted by g0 or gn, is the nominal acceleration due to Earth's gravity at the Earth's surface at sea level....
β = volumetric thermal expansion coefficient
Coefficient of thermal expansion

When the temperature of a substance changes, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bonds....
 (equal to approximately 1/T, for ideal fluids, where T is absolute temperature)
Ts = source temperature
T8 = film temperature
L = length
D = diameter
ν = kinematic viscosity


The transition to turbulent flow occurs in the range for natural convection from vertical flat plates.






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The Grashof number is a dimensionless number in fluid dynamics
Fluid dynamics

In physics, fluid dynamics is the sub-discipline of fluid mechanics dealing with fluid flow — the natural science of fluids in motion....
 and Heat Transfer
Heat transfer

Heat transfer is the transition of thermal energy or simply heat from a hotter object to a cooler object . When an object or fluid is at a different temperature than its thermodynamic system or another object, transfer of thermal energy, also known as heat transfer, or heat exchange, occurs in such a way that the body and the surround...
 which approximates the ratio of the buoyancy
Buoyancy

In physics, buoyancy is the upward force that keeps things afloat. The net upward buoyancy force is equal to the magnitude of the weight of fluid displaced by the body....
 to viscous force acting on a fluid. It frequently arises in the study of situations involving natural convection. It is named after the German engineer Franz Grashof
Franz Grashof

Franz Grashof was a Germany engineer. He was a professor of Applied Mechanics at the Technischen Hochschule Karlsruhe. He is one of the founding directors of Verein Deutscher Ingenieure in 1855....
.

for vertical flat plates

for pipes for bluff bodies

where the L and D subscripts indicates the length scale basis for the Grashof Number.

g = acceleration due to Earth's gravity
Standard gravity

Standard gravity, usually denoted by g0 or gn, is the nominal acceleration due to Earth's gravity at the Earth's surface at sea level....
β = volumetric thermal expansion coefficient
Coefficient of thermal expansion

When the temperature of a substance changes, the energy that is stored in the intermolecular bonds between atoms changes. When the stored energy increases, so does the length of the molecular bonds....
 (equal to approximately 1/T, for ideal fluids, where T is absolute temperature)
Ts = source temperature
T8 = film temperature
L = length
D = diameter
ν = kinematic viscosity


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.

The product of the Grashof number and the Prandtl number
Prandtl number

The Prandtl number is a dimensionless number approximating the ratio of momentum diffusivity and thermal diffusivity. It is named after the German physicist Ludwig Prandtl....
 gives the Rayleigh number
Rayleigh number

In fluid mechanics, the Rayleigh number for a fluid is a dimensionless number associated with buoyancy driven flow . When the Rayleigh number is below the critical value for that fluid, heat transfer is primarily in the form of heat conduction; when it exceeds the critical value, heat transfer is primarily in the form of convection....
, a dimensionless number that characterizes convection problems in heat transfer.

There is an analogous form of the Grashof number used in cases of natural convection mass transfer
Mass transfer

Mass transfer is the transfer of mass from high concentration to low concentration. The phrase is commonly used in engineering for physical processes that involve molecule and convection transport of atoms and molecules within systems....
 problems.

where

and

g = acceleration due to Earth's gravity
Standard gravity

Standard gravity, usually denoted by g0 or gn, is the nominal acceleration due to Earth's gravity at the Earth's surface at sea level....
Ca,s = concentration of species a at surface
Ca,a = concentration of species a in ambient medium
L = characteristic length
ν = kinematic viscosity
ρ = fluid
Fluid

A fluid is defined as a substance that continually deforms under an applied shear stress. All liquids and all gases are fluids. Fluids are a subset of the Phase and include liquids, gas, Plasma physics and, to some extent, plasticity ....
 density
Density

The density of a material is defined as its mass per unit volume. The symbol of density is ....
Ca = concentration of species a
T = constant temperature
p = constant pressure
Q = Helmet Pleasure Ratio


See also