Water at 180°C enters a bare, 15-m-long, 2.5-cm wrought iron pipe at 3 m/s. If air at 10°C flows perpendicular to the pipe at 12 m/s, determine the outlet temperature of the water. (Note that the temperature difference between the air and the water varies along the pipe.)

Question

GIVEN

• Wrought-iron pipe with water flow inside and perpendicular air flow outside

• Water entrance temperature (TW,in) = 180°C

• Water velocity (VW) = 3 m/s

• Pipe length (L) = 15 m

• Pipe diameter (D) = 2.5 cm = 0.025 m

• Air temperature (Ta) = 10°C

• Air velocity (Va) = 12 m/s FIND

• Outlet temperature of the water (TW,out) ASSUMPTIONS

• Steady state

• Air flow approaching pipe is negligible

• Thermal resistance of the pipe is negligible

• The pipe thickness can be neglected

SKETCH

Answer 1

Air Side:

The Reynolds number on the air side is



The Nusselt number is given by



where C = 0.26, m = 0.6, and n = 0.37.

Note that the Prandtl number of air does not change appreciably between the air and water

temperatures. Therefore, Pr/Prs = 1.



Water Side:

The Reynolds number based on the inlet properties is



Applying



The overall heat transfer coefficient is



Let’s assume that the water temperature changes little from the pipe inlet to outlet. Since the air

temperature is constant and uniform, the heat transfer from the water is then analogous to the uniform

surface temperature analysis of may be applied



Solving for the water outlet temperature



Therefore, the assumption that the water changes little from pipe inlet to outlet is valid.

COMMENTS

The average water temperature is 178.5°C. This is not different enough from the inlet temperature to

justify another iteration using the water properties at the average water temperature.

Note that the convective thermal resistance of the air is 99.6% of the total thermal resistance.