Calculate the overall heat transfer coefficient and the rate of heat flow from the hot gasses to the cold air in the cross flow tube-bank of heat exchanger shown in the accompanying illustration for the following operating conditions

Air flow rate = 0.4 kg/s.

Hot gas flow rate = 0.65 kg/s.

Temperature of hot gasses entering exchanger = 870°C.

Temperature of cold air entering exchanger = 40°C.

Both gases are approximately at atmospheric pressure.



GIVEN

? The crossflow tube bank heat exchanger shown above

? Air flow rate

( ma ) = 0.4 kg/s



? Gas flow rate

( mg) = 0.65 kg/s

? Entrance temperatures

? Air (Ta,in) = 40°C

? Gas (Tg,in) = 870°C

? Both gases are at 1 atm pressure

FIND

(a) The overall heat transfer coefficient

(b) The rate of heat transfer (q)

ASSUMPTIONS

? The hot gases have the same thermal properties as air

? No scaling

? Thermal resistance of the tube walls can be neglected

PROPERTIES AND CONSTANTS

From Appendix 2, Table 28, for dry air at the entering temperatures




(a) Heat transfer coefficient inside tubes hi

The Reynolds number in the tubes is



The Nusselt number for turbulent flow in a tube is given by Equation (6.61)



Heat transfer coefficient outside the tubes ho

The velocity of the air based on the minimum flow area is



From the sketch



The Reynolds number based on the minimum flow area is



Applying Equation (6.27)



The overall heat transfer coefficient, neglecting the thermal resistance of the tube wall, is



(b) The heat capacity rates are



The number of transfer units is





From Figure 10.22, e ? 0.25

The rate of heat transfer is given by Equation (10.23)

Physics & Space Science

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