An engineer is designing a heating system that consists of multiple tubes placed in a duct carrying the air supply for a building. She decides to perform preliminary tests with a single copper tube, 2-cm-O.D., carrying condensing steam at 100°C. The air velocity in the duct is 5 m/s and its temperature is 20°C. The tube is placed normal to the flow, but it may be advantageous to place the tube at an angle to the air flow and thus increase the heat transfer surface area. It the duct width is 1 m, predict the outcome of the planned tests and estimate how the angle ? will affect the rate of heat transfer. Are there limits?

Question

GIVEN

• A copper tube carrying condensed steam in an air duct

• Tube outside diameter (D) = 2 cm = 0.02 m

• Steam temperature (Ts) = 100°C

• Air velocity (U?) = 5 m/s

• Air temperature (T?) = 20°C

• Duct width (w) = 1 m

FIND

• Is it more advantageous to have the tubes normal to the air flow or at some angle to the air flow?

ASSUMPTIONS

• Steady state

• Air velocity in the duct is uniform

• Thermal resistance due to steam condensing is negligible

• Thermal resistance of the tube wall is negligible

SKETCH



PROPERTIES AND CONSTANTS

Thermal conductivity (k) = 0.0251 W/(m K) Kinematic viscosity

(?) = 15.7 × 10–6 m2/s Prandtl number (Pr) = 0.71

Answer 1

The Reynolds number based on the tube diameter is



For the perpendicular position, the tube length (L) = w = 1 m and the Nusselt number can be calculated with ? = 90°



The rate of heat transfer is



For the angled position, the tube length (L) = w/sin?.



The rate of heat transfer is



The engineer will find that the rate of heat transfer will increase because the heat transfer coefficient decreases with (sin?)0.63 but the area increases with 1/sin?. Therefore, the rate of heat transfer increases with 1/(sin?)0.37.