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.

Question

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 FIND

• The overall heat transfer coefficient (U)

ASSUMPTIONS

• Steady state

• The variation of the Prandtl number of air with temperature is negligible

• The aluminum is pure

SKETCH



PROPERTIES AND CONSTANTS

thermal conductivity of aluminum (kal) = 238 W/(m K) at 75°C

for water at 30°C

Density (?w) = 996 kg/m3 Thermal conductivity (kw) = 0.615 W/(m K)

Absolute viscosity (?w) = 792 × 10–6 (Ns)/m2

Prandtl number (Prw) = 5.4

for dry air at 120°C

Thermal conductivity (ka) = 0.0320 W/(m K)

Kinematic viscosity (?) = 26.0 × 10–6 m2/s

Prandtl number (Pr) = 0.71

Answer 1

The Reynolds number on the water side is



The Nusselt number on the water side is



The Reynolds number on the air side is



Applying but neglecting the Prandtl number variation



The overall heat transfer coefficient based on the outer tube diameter is



COMMENTS

The air side thermal resistance accounts for 99% of the total resistance. The water side convective resistance and the conductive resistance of the tube are of the same order of magnitude.