(Solution) - Water flowing in a long aluminum tube is to be -(2025 Original AI-Free Solution)

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Water flowing in a long aluminum tube is to be heated by air flowing perpendicular to the exterior of the tube. The ID of the tube is 1.85 cm and its OD is 2.3 cm. The mass flow rate of the water through the tube is 0.65 kg/s and the temperature of the water in the tube averages 30°C. The free stream velocity and ambient temperature of the air are 10 m/s and 120°C, respectively. Estimate the overall heat transfer coefficient for the heat exchanger using appropriate correlations from previous chapters. State all your assumptions.
GIVEN
Air flowing perpendicular to the exterior of an aluminum tube with water flowing within the tube
Tube diameters
Inside (Di) = 1.85 cm = 0.0185 m
Outside (Do) = 2.3 cm = 0.023 m
Mass flow rate of water (mw) = 0.65 kg/s
Average temperature of the water (Tw) = 30°C
Air free stream velocity (Va) = 10 m/s
Air temperature (Ta) = 120°C
ASSUMPTIONS
Steady state
The variation of the Prandtl number of air with temperature is negligible
The aluminum ispure