A sphere 0.1-m-diameter is rotating at 20 rpm in a large container of CO2 at atmospheric pressure. If the sphere is at 60°C and the CO2 at 20°C, estimate the rate of heat transfer.
GIVEN
? A rotating sphere in carbon dioxide at atmospheric pressure
? Diameter (D) = 0.1 m
? Speed of rotation (?) = 20 rev/min
? Sphere temperature (Ts) = 60°C
? CO2 temperature (T?) = 20°C
FIND
? The rate of heat transfer
ASSUMPTIONS
? Steady state conditions
? The carbon dioxide is still
? Radiation is negligible
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 28, for CO2 at the mean temperature of 40°C
Converting the rotational speed to radians per second
The rotational Reynolds number for the sphere is
All requirements are met for the correlation presented in Equation (8.50)
The rate of heat transfer by natural convection is given by
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