Water at 80°C is flowing through a thin copper tube (15.2-cm-ID) at a velocity of 7.6 m/s. The duct is located in a room at 15°C and the heat transfer coefficient at the outer surface of the duct is 14.1 W/(m2 K). (a) Determine the heat transfer coefficient at the inner surface. (b) Estimate the length of duct in which the water temperature drops 1°C.

Question

GIVEN

• Water flowing through a thin copper tube in a room

• Water temperature (Tb) = 80°C

• Inside diameter of tube (D) = 15.2 cm = 0.152 cm

• Water velocity (V) = 7.6 m/s

• Room air temperature (T?) = 15°C

• Outer surface heat transfer coefficient ( h co ) = 14.1 W/(m2 K)

FIND

(a) The heat transfer coefficient at the inner surface ( h ci )

(b) Length of duct (L) for temperature drop of 1°C

ASSUMPTIONS

• Steady state

• Thermal resistance of the copper tube is negligible

• Fully developed flow

SKETCH



PROPERTIES AND CONSTANTS

for water at 80°C

Density (?) 971.6 kg/m3

Thermal conductivity (k) = 0.673 W/(m K)

Absolute viscosity (?) = 356.7 × 10–6 (Ns)/m2

Prandtl number (Pr) = 2.13

Specific heat (c) = 4194 J/(kg K)

Answer 1

The Reynolds number is



(a) Applying the Dittus-Boelter correlation of





(b) Since the pipe wall is thin, Ao = Ai and the overall heat transfer coefficient is



The length can be calculated using



Solving for the length



For these conditions, it would take over a kilometer for a 1°C temperature drop. This is largely the

result of the small natural convection heat transfer coefficient over the outer surface.