Grashof Number Calculator

Calculate the buoyancy-to-viscosity ratio used to screen a natural-convection heat-transfer problem.

Grashof number (Gr)3.1591E8Dimensionless · Gr = gβ|ΔT|L³/ν²
Expansion coefficient used0.0033 1/KIdeal-gas estimate

Scope: Grashof number screens buoyancy versus viscous effects in a natural-convection problem. It does not itself predict heat-transfer coefficient or flow pattern; use a geometry- and range-appropriate correlation after checking Gr, Pr and Rayleigh number.

Method and variables

This page calculates Gr = gβ|ΔT|L3/ν2. β is volumetric thermal expansion coefficient, ΔT is surface-to-fluid temperature difference, L is the characteristic length and ν is kinematic viscosity.

Worked example

For air approximated at a 303.15 K film temperature, β ≈ 1/303.15 K−1. With |ΔT| = 20 K, L = 0.5 m, ν = 1.6 × 10−5 m²/s and standard gravity, Gr is about 3.2 × 109.

Important limits

For fluid properties, use a consistent reference state—often a film temperature for external natural convection. The ideal-gas β = 1/T option is only an approximation. Gr alone cannot select a heat-transfer correlation or account for orientation, enclosure effects, radiation, turbulence, phase change, property variation or forced flow.

Reference

Related tools

Prandtl Number Calculator · Dimensionless Numbers Calculators

Frequently asked questions

What does Grashof number compare?
Grashof number compares buoyancy effects created by a temperature-driven density difference with viscous effects in a natural-convection problem.

Why use the absolute temperature difference?
This calculator reports the magnitude used in the conventional dimensionless group. Whether a surface is warmer or cooler than the surrounding fluid still matters when selecting a geometry-specific natural-convection correlation.

Can Grashof number give me a heat-transfer coefficient?
No. It is an input to a suitable natural-convection correlation, usually together with Prandtl or Rayleigh number, geometry and boundary conditions.