In a lead-shot tower, spherical 0.95-cm-diameter BB shots are formed by drops of molten lead which solidify as they descend in cooler air. At the terminal velocity, i.e., when the drag equals the gravitational force, estimate the total heat transfer coefficient if the lead surface is at 171°C, the surface of the lead has an emissivity of 0.63, and the air temperature is 16°C. Assume CD = 0.75 for the first trial calculation.
GIVEN
• Spherical lead-shot falling through the air at terminal velocity
• Shot diameter (D) = 0.95 cm = 0.0095 m
• Lead surface temperature (Ts) = 171°C = 494 K
• Lead surface emissivity (?) = 0.63
• Air temperature (T?) = 16°C 289 K
• Assume CD = 0.75 for the first trial calculation FIND
• The total average heat transfer coefficient (htotal). ASSUMPTIONS
• The surroundings act as a black body enclosure at T?
SKETCH
The weight of the lead shot is
Terminal velocity occurs when the weight is balanced by the drag force which is given
Solving for the terminal velocity
Using the recommended drag coefficient for the first iteration
Repeating this procedure for further iterations
The Nusselt number is given by
The total rate of heat transfer can be used to calculate the total heat transfer coefficient as follows
COMMENTS
97% of the heat transfer is due to convection.
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