A mercury-in-glass thermometer at 40°C (OD = 1 cm) is inserted through duct wall into a 3 m/s air stream at 66°C. This can be modelled as cylinder in cross-flow, as shown in figure. Estimate the heat transfer coefficient between the air and the thermometer.
GIVEN
• Thermometer in an air stream
• Thermometer temperature (Ts) = 40°C
• Thermometer outside diameter (D) = 1 cm = 0.01 m
• Air velocity (V) = 3 m/s
• Air temperature (Tb) = 66°C
FIND
• The heat transfer coefficient ch
ASSUMPTIONS
• Steady state
• Turbulence in the free stream approaching the thermometer is low
• Effect of the duct walls in negligible
SKETCH
PROPERTIES AND CONSTANTS
From Appendix 2, Table 28, for dry air at the bulk temperature of 66°C
Thermal conductivity (k) = 0.0282 W/(m K) Kinematic viscosity (?) = 20*10-6 m2/s Prandtl number (Pr) = 0.71 At the thermometer surface temperature of 40°C, the Prandtl number (Prs) = 0.71
The Reynolds number for this case is
The Nusselt number is given by
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