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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 ) ρ² / ( T_abs µ²)

Alternatively

Eq 2
Gr = g β L³ ( T_w - T_air ) ρ² / v²

Alternatively

Eq 3
Gr = (g L³ ξ ΔT ) / v²

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
ν = kinematic viscosity of the fluid
T_w = Wall temperature
T_air = Ambient air temperature
T_abs =
ρ = Density
T_abs = Absolute temperature
µ = Viscosity
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