"The airflow characteristics around a circular cylinder depend strongly on the Reynolds number (Re) [no dimensions (ND)], given by Re [the usual formulation] where v (m/s) is the airspeed, d (m) is the diameter of the cylinder, and v (m2/s) is the kinematic viscosity.
Hilpert (9) found that the average Nusselt number, Nu, for a cylinder could be written as Nu = hc* d / lambda = 0.193*Re^0.62 * Pr^0.33 (2)
where hc (W · m2 · K1) is the forced convection coefficient, lambda (W · m1 · K1) is the thermal conductivity of the surrounding medium, and Pr = v/alpha is the Prandtl number (ND), where alpha is the thermal diffusivity (m2/s).
Hilpert found that under atmospheric conditions this formula could also be used for noncircular cylinders, where d is then the widest part of the cylinder measured at right angles to the wind direction. " ~~~~~~~~~~~~~~~~~~~~~~
Notice that expression 2) agrees with your expression, for Prandtl numbers close to one.
Brian Whatcott Altus OK
Hilpert, R. Wärmeabgabe von geheizten Drähten ond Rohren in Luftstrom. Forsch. Geb. Ingenieurwes. 4: 215-224, 1933.