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.