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In a solar assisted air conditioning system, 1 kg/sec of ambient air is to be preheated by the same amount of air leaving the system. A counter-flow heat exchanger having an area of 60m2 with overall heat transfer coefficient of 25 W/m2 - K is used for this purpose. Assuming for air is 1kJ/kg K. The effectiveness of the heat exchanger is
  • a)
    0.
  • b)
    0.6
  • c)
    1.6
  • d)
    25
Correct answer is option 'B'. Can you explain this answer?
Verified Answer
In a solar assisted air conditioning system, 1 kg/sec of ambient air ...
This is the case of a balanced counter flow heat exchanger.
∴ ε = NTU/1+NTU
Where NTU = UA/(mcp)min
For balanced heat exchanger,
(mcp)h = (mcp)c
∴ NTU = 60 x 25 / 1000 = 1.5
∴ ε = 1.5/1+1.5 = 0.6
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Most Upvoted Answer
In a solar assisted air conditioning system, 1 kg/sec of ambient air ...

Calculation of Effectiveness of Heat Exchanger:

- Given data:
- Mass flow rate of air (m) = 1 kg/s
- Heat transfer area (A) = 60 m2
- Overall heat transfer coefficient (U) = 25 W/m2-K
- Specific heat of air (Cp) = 1 kJ/kg-K

- The formula for effectiveness of a counter-flow heat exchanger is given by:
ε = (1 - e^(-NTU(1 - Cmin))) / (1 + Cmin)

- Calculate NTU:
NTU = U * A / m * Cp

- Calculate Cmin:
Cmin = min(C1, C2)
where C1 = m * Cp = 1 kJ/s-K

- Substitute the values in the formula:
NTU = (25 * 60) / (1 * 1) = 150
Cmin = 1
ε = (1 - e^(-150(1 - 1))) / (1 + 1) = (1 - e^0) / 2 = (1 - 1) / 2 = 0

Therefore, the effectiveness of the heat exchanger is 0. This indicates that the heat exchanger is not able to transfer all the available heat between the two air streams.
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In a solar assisted air conditioning system, 1 kg/sec of ambient air is to be preheated by the same amount of air leaving the system. A counter-flow heat exchanger having an area of 60m2 with overall heat transfer coefficient of 25 W/m2 - K is used for this purpose. Assuming for air is 1kJ/kg K. The effectiveness of the heat exchanger isa) 0.b) 0.6c) 1.6d) 25Correct answer is option 'B'. Can you explain this answer?
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