A horizontal disk 1 m in diameter rotates in air at 25°C. If the disk is at 100°C, estimate the number of revolutions per minute at which natural convection for a stationary disk becomes less than 10% of the heat transfer for a rotating disk.
GIVEN
? A rotating horizontal disk in air
? Diameter (D) = 1 m
? Air temperature (T?) = 25°C
? Disk temperature (Ts) = 100°C
FIND
? The rotational speed (w) at which natural convection becomes less than 10% of the thermal effects
of rotation
ASSUMPTIONS
? Steady state conditions
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 28, for dry air at the mean temperature of 62.5°C
The characteristic length for free convection from the stationary disk is
The Rayleigh number is
The Nusselt number for a static disk is given by Equation (8.16)
Assuming the rotational speed is high enough to product turbulent flow, the Nusselt number is given by Equation (8.47)
Since
we have
This can be written as
By trial and error: Re = 5.64 x 10(which is turbulent) and ?w = 111 rad/s = 1060 rpm.
Note that rc = 0.211 m.
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