Hilpert's empirical equation.

from [Journal of Applied Physiology]

"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

1. Hilpert, R. Wärmeabgabe von geheizten Drähten ond Rohren in Luftstrom. Forsch. Geb. Ingenieurwes. 4: 215-224, 1933.

Dang Brian, you beat me to it. But I think I can add some more.

My old copy of Holman's Heat Transfer, 4th ed says that Hilpert found these coefficients using gases (Pr = 0.7) and didn't apply a Prandtl number correction. So:

Nu = 0.193 * Re^0.62 * (0.7)^.33, or Nu = 0.171 * Re^0.62

which is Hilpert's equation.

Also, these coefficients are dependent on Re. So if we write:

Nu = C * Re^n * Pr^0.33

then:

|Re | C | n | |0.4-4 | 0.989 | 0.33 | |4-40 | 0.911 | 0.385| |40-4000 | 0.683 | 0.466| |4E3-4E4 | 0.193 | 0.618| |4E4-4E5 | 0.0266| 0.815| (use the hash marks to line up the columns)

Lance

Brian Whatcott, > from

That all helps - Thanks.

(I'm actually looking at forced convection in a heat exchanger)

Thanks again - Simon.