Hi! I think the formula for Gr is missing a squared term for density in the numerator. Alternatively, the viscosity term in the denominator should be the kinematic viscosity.
Thank you for your comment. In Grashoff No. there is no density term if the kinematic viscosity is used which shouldn't be represented by Mu thank you for spotting this, in this particular version it should be upsilon for the kinematic viscosity. Much appreciated for your feedback!
These values are arbitrary constants which are determined experimentally. They are dependent upon several factors which involve the thermodynamic and physical properties of the fluid/material. Typically, you find criteria within published literature for a given Reynolds and Prandtl range. I hope this helps.
Thank you for your interest, the reference texts we use is "Heat Transfer, 9th Edition" by J.P. Holman, and "Foundation of Heat Transfer, 6th Edition" by Frank P. Incropera
