**Related Resources: heat transfer**

### Grashof Number (GR)

Heat Transfer Engineering and Design

Grashof Number (GR)

The Grashof number is used to determine the heat transfer coefficient under free convection conditions. It is basically a ratio between the buoyancy forces and viscous forces.

Eq. 1

* Gr = g ( T _{w} - T_{air} ) ρ^{2} / ( T_{abs} µ^{2})*

*Alternatively*

* Eq 2
Gr = g β L ^{3} ( T_{w} - T_{air} ) ρ^{2} / v^{2}*

*Alternatively*

*Eq 3 *

Gr = (g L^{3} ξ ΔT ) / *v ^{2}*

Heat transfer requires circulation, therefore, the Grashof number (and heat transfer coefficient) will rise as the buoyancy forces increase and the viscous forces decrease.

Where:

*Gr =
g *= Gravitational constant

*= kinematic viscosity of the fluid*

ν

ν

*= Wall temperature*

T

T

_{w}*= Ambient air temperature*

T

T

_{air}*Density*

T

ρ =

T

_{abs}=ρ =

*= Absolute temperature*

T

T

_{abs}*= Viscosity*

µ

µ

ξ = coefficient of expansion of the fluid

ΔT = temperature difference between the surface and the bulk of the fluid

Related:

- Horizontal Heated Plate Facing Up Equation and Calculator
- Horizontal Plate Natural Convection Equations and Calculator
- Convective Heat Transfer Coefficient Equation Review
- Isothermal Vertical Plate Natural Convection Equation and Calculator
- Convective Heat Transfer Coefficient Equation Review
- Heat Transfer Practical Approach

Reference:

Rules of Thumb for Mechanical Engineers

J. Edward Pope, Editor