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)
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