While flowing at the rate of 1.25 kg/s in a simple counterflow heat exchanger, dry air is cooled from 65 to 38°C by means of cold air which enters at 15°C and flows at a rate of 1.6 kg/s. It is planned to lengthen the heat exchanger so that 1.25 kg/s. of air can be cooled from 65 to 26°C with a counterflow current of air at 1.6 kg/s entering at 15°C. Assuming that the specific heat of the air is constant, calculate the ratio of the length of the new heat exchanger to the length of the original.
GIVEN
A simple adiabatic air-to-air counter flow heat exchanger:
Case 1
? Warm air temperatures
? Th,in = 65°C
? Th,out = 38°C
? Air flow rates
? mh = 1.25 kg/s
? mc = 1.6 kg/s
? Cold air inlet temperature (Tc,in) = 15°C
After lengthening heat exchanger:
Case 2
? Warm air temperatures
? Th,in = 65°C
? Th,out = 26°C
? Air flow rates
? mh = 1.25 kg/s
? mc = 1.6 kg/s
? Cold air inlet temperature (Tc,in) = 15°C
FIND
? The ratio of the length of the new heat exchanger to the length of the original
ASSUMPTIONS
? The specific heat of air is constant
? The overall heat transfer coefficient (U) is the same in both cases
SKETCH
For both cases
The effectiveness, from Equation (10.22a), is
Since the area is directly proportional to the length.
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