Grash of number

Input(s)

g: Acceleration Due to Earth $\left(\mathrm{m} / \mathrm{s}^{2}\right)$

$\beta$: Volumetric Thermal Expansion Coefficient (1/K)

$\boldsymbol{T}_{\mathbf{1}}$: Surface Temperature (K)

$\boldsymbol{T}_{\boldsymbol{o}}$: Bulk Temperature (K)

$\boldsymbol{I}_{\boldsymbol{o}}$: Diameter $(\mathrm{m})$

$\mathrm{v}$: Kinematic Viscosity $\left(\mathrm{m}^{2} / \mathrm{s}\right)$

Output(s)

Gr: Grash of Number (dimensionless)

Formula(s)

$$ \mathrm{Gr}=\frac{\mathrm{g} * \beta *\left(\mathrm{~T}_{1}-\mathrm{T}_{\mathrm{o}}\right) * \mathrm{l}_{\mathrm{o}}^{3}}{\mathrm{v}^{2}} $$

Reference(s)

Bird, R.B., Stewart, W.E. and Lightfoot, E.N. (2002). Transport Phenomena (Second Ed.). John Wiley \& Sons, Chapter: 11, Page: 355.