Reconsider the problem of cooling of a rotating rod (shaft) by natural convection described in Example 8.6. Determine the shaft rotation at which the heat transfer contribution due to the rotation convection is about the same as that due to natural convection, and calculate the total heat transfer rate at this condition. Also, graph the variation of q, as well as its two components (qr and qnc) with shaft rpm ranging from 3 rpm to 15 rpm, and comment upon the results.
GIVEN
? Cooling of rotational shaft by natural convection
? Rod diameter (D) = 20 cm = 0.2 m
? Air temperature (T?) = 20°C
? Temperature of rotating rod (Tb) = 1000°C
FIND
? Shaft rotation at which heat transfer contribution due to rotational convection is same as that due
to natural convection.
? Total heat transfer rate at this condition.
? Graph of variation of q and qr and qnc with shaft rpm.
ASSUMPTIONS
? Radiation is negligible
? The shaft is horizontal
PROPERTIES AND CONSTANTS
The Nusselt number for this geometry is given by Equation (8.44)
The heat transfer contribution due to rotational convection becomes equal to heat transfer due to
natural convection when two RHS terms in equation (8.44) become equal. That is
Thus at 12.42 rpm heat transfer contribution due to rotational convection becomes equal to heat
transfer due to natural convection.
Heat transfer rate at this condition:
Thus the rate of heat transfer per unit length is
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