Compare the rate of heat transfer and the pressure drop for an in-line and a staggered arrangement of a tube bank consisting of 300 tubes, 1.8 m long and 2.5 cm OD. The tubes are to be arranged in 15 rows with longitudinal and transverse spacing of 5 cm. The tube surface temperature is 95°C and water at 35°C is flowing at a mass rate of 5400 kg/s over the tubes.

Question

GIVEN

Water flowing over an in-line and a staggered tube bank

Number of tubes (Nt) = 300

Length of tubes (L) = 1.8 m

Tube outside diameter (D) = 2.5 cm= 0.025 m

Number of rows (N) = 15

Normal and parallel spacing = 5 cm=0.05 m

Tube surface temperature (Tt) = 95°C

Water inlet temperature (Tw,in) = 35°C

Mass flow rate of water (m) = 5400 kg/s

FIND

(a) Compare the rate of heat transfer (q) and

(b) The pressure drop ( ?p) for the two configurations

ASSUMPTIONS

Steady state

Tube temperature is uniform

SKETCH



PROPERTIES AND CONSTANTS

for water at the inlet temperature of 35°C

Density (?) = 994.1 kg/m3

Thermal conductivity (k) = 0.624 W/(m K)

Prandtl number (Pr) = 4.8

Specific heat (c) = 4175 J/(kg K)

At the tube temperature of 95°C

Prs = 1.88

Answer 1

The water velocity can be calculated with the help of the sketch below.



W = 19(5 cm) + 5 cm = 100 cm = 1 m

Therefore, the water velocity is



Therefore, for the staggered configuration, the minimum free area is between adjacent tubes in a row,

and the maximum air velocity is



This is also the maximum velocity for the in-line case.

The Reynolds number for either case is



(a) The Nusselt number for the in-line case is given by



The Nusselt number for the staggered case is given by



These heat transfer coefficient differ by only 5%, therefore, the rate of heat transfer for the two tube

banks will be nearly equal.

(b) These pressure drop is given by





Staggered tube bank:



For nearly the same rate of heat transfer, the staggered bank has slightly lower pressure drop.

COMMENTS

These results are only true because the flow is turbulent. Greater difference would occur at lower

Reynolds numbers.