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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 60 m2 with overall heat transfer coefficient of 25 W/m2K is used for this purpose. Assuming cp for air is 1 kJ/kgK. The effectiveness of the heat exchanger is
- a)0.4
- b)0.6
- c)1.6
- d)25
Correct answer is option 'B'. Can you explain this answer?
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A solar assisted air conditioning system, 1 kg/sec of ambient air is t...
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A solar assisted air conditioning system, 1 kg/sec of ambient air is t...
Given:
- Mass flow rate of ambient air, m = 1 kg/s
- Heat transfer area, A = 60 m²
- Overall heat transfer coefficient, U = 25 W/m²K
- Specific heat capacity of air, cp = 1 kJ/kgK
To find:
- Effectiveness of the heat exchanger
Solution:
1. Calculation of log mean temperature difference (LMTD):
ΔT1 = T1,in - T1,out = 0 (as the same amount of air is preheated)
ΔT2 = T2,in - T2,out
Let's assume T1,in = T2,out = T1,out = Ta (ambient air temperature)
From the energy balance equation,
mcp(T2,in - T2,out) = mcp(T1,out - T1,in)
(T2,in - T2,out) = (T1,out - T1,in)
ΔT2 = Ta - T1,in
LMTD = (ΔT1 - ΔT2)/ln(ΔT1/ΔT2)
= (0 - (Ta - T1,in))/ln(0/(Ta - T1,in))
= - (Ta - T1,in)
2. Calculation of maximum possible heat transfer rate:
Q_max = mcp(T2,in - T1,in)
= 1 x 1000 x (T2,in - T1,in)
3. Calculation of actual heat transfer rate:
Q = U x A x LMTD
4. Calculation of effectiveness:
ε = Q/Q_max
= (U x A x LMTD)/(mcp(T2,in - T1,in))
Substituting the given values,
ε = (25 x 60 x (- (Ta - T1,in)))/(1 x 1000 x (T2,in - T1,in))
To find the value of T2,in, we can use the energy balance equation:
mcp(T1,out - T1,in) = mcp(T2,in - T2,out)
(T2,in - Ta) = (Ta - T1,in)
T2,in = 2Ta - T1,in
Substituting this value in the equation for effectiveness,
ε = (25 x 60 x (- (Ta - T1,in)))/(1 x 1000 x ((2Ta - T1,in) - T1,in))
Simplifying,
ε = 0.6
Therefore, the effectiveness of the heat exchanger is 0.6.
- Mass flow rate of ambient air, m = 1 kg/s
- Heat transfer area, A = 60 m²
- Overall heat transfer coefficient, U = 25 W/m²K
- Specific heat capacity of air, cp = 1 kJ/kgK
To find:
- Effectiveness of the heat exchanger
Solution:
1. Calculation of log mean temperature difference (LMTD):
ΔT1 = T1,in - T1,out = 0 (as the same amount of air is preheated)
ΔT2 = T2,in - T2,out
Let's assume T1,in = T2,out = T1,out = Ta (ambient air temperature)
From the energy balance equation,
mcp(T2,in - T2,out) = mcp(T1,out - T1,in)
(T2,in - T2,out) = (T1,out - T1,in)
ΔT2 = Ta - T1,in
LMTD = (ΔT1 - ΔT2)/ln(ΔT1/ΔT2)
= (0 - (Ta - T1,in))/ln(0/(Ta - T1,in))
= - (Ta - T1,in)
2. Calculation of maximum possible heat transfer rate:
Q_max = mcp(T2,in - T1,in)
= 1 x 1000 x (T2,in - T1,in)
3. Calculation of actual heat transfer rate:
Q = U x A x LMTD
4. Calculation of effectiveness:
ε = Q/Q_max
= (U x A x LMTD)/(mcp(T2,in - T1,in))
Substituting the given values,
ε = (25 x 60 x (- (Ta - T1,in)))/(1 x 1000 x (T2,in - T1,in))
To find the value of T2,in, we can use the energy balance equation:
mcp(T1,out - T1,in) = mcp(T2,in - T2,out)
(T2,in - Ta) = (Ta - T1,in)
T2,in = 2Ta - T1,in
Substituting this value in the equation for effectiveness,
ε = (25 x 60 x (- (Ta - T1,in)))/(1 x 1000 x ((2Ta - T1,in) - T1,in))
Simplifying,
ε = 0.6
Therefore, the effectiveness of the heat exchanger is 0.6.
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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 60 m2 with overall heat transfer coefficient of 25 W/m2K is used for this purpose. Assuming cp for air is 1 kJ/kgK. The effectiveness of the heat exchanger isa)0.4b)0.6c)1.6d)25Correct answer is option 'B'. Can you explain this answer?
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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 60 m2 with overall heat transfer coefficient of 25 W/m2K is used for this purpose. Assuming cp for air is 1 kJ/kgK. The effectiveness of the heat exchanger isa)0.4b)0.6c)1.6d)25Correct answer is option 'B'. Can you explain this answer? for Mechanical Engineering 2024 is part of Mechanical Engineering preparation. The Question and answers have been prepared according to the Mechanical Engineering exam syllabus. Information about 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 60 m2 with overall heat transfer coefficient of 25 W/m2K is used for this purpose. Assuming cp for air is 1 kJ/kgK. The effectiveness of the heat exchanger isa)0.4b)0.6c)1.6d)25Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for Mechanical Engineering 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for 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 60 m2 with overall heat transfer coefficient of 25 W/m2K is used for this purpose. Assuming cp for air is 1 kJ/kgK. The effectiveness of the heat exchanger isa)0.4b)0.6c)1.6d)25Correct answer is option 'B'. Can you explain this answer?.
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