A long, half-round cylinder is placed in an air stream with its flat face down-stream. An electrical resistance heater inside the cylinder maintains the cylinder surface temperature at 50°C. The cylinder diameter is 5 cm, the air velocity is 31.8 m/s, and the air temperature is 20°C. Determine the power input of the heater per unit length of cylinder. Neglect radiation heat transfer.

Question

GIVEN

• A long, half-round cylinder in an air stream with its flat surface downstream

• Cylinder surface temperature (Ts) = 50°C

• Cylinder diameter (D) = 5 cm = 0.05 m

• Air velocity (U?) = 31.8 m/s

• Air temperature (T?) = 20°C FIND

• Power input to the heater ( Q G/L)

ASSUMPTIONS

• Steady state

• Radiative heat transfer is negligible

• Flow separates at the cylinder edges as shown below

SKETCH

Answer 1

The Reynolds number based on the film temperature is



This is within the range of the correlation, for the downstream surface



For the half-round upstream face, the average Nusselt number can be estimated by numerically

integrating the curve for ReD = 101,300



Performing the integration by the trapezoidal rule



The power input to the heater must equal the rate of convective heat loss



COMMENT

The use of rather than to estimate the upstream heat transfer

coefficient leads to a transfer coefficient 11% lower and a final result 6% lower than those presented

above.