GATE ME 2016 Set 2 — Question 52
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Heat Transfer → Heat Exchangers → LMTD Method
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Question
Consider a parallel-flow heat exchanger with area and a counter-flow heat exchanger with area . In both the heat exchangers, the hot stream flowing at 1 kg/s cools from 80 C to 50 C. For the cold stream in both the heat exchangers, the flow rate and the inlet temperature are 2 kg/s and 10 C, respectively. The hot and cold streams in both the heat exchangers are of the same fluid. Also, both the heat exchangers have the same overall heat transfer coefficient. The ratio is _________
Correct answer
0.91 to 0.95
Solution
First, find the exit temperature of the cold stream () using an energy balance. Since both streams are the same fluid, their specific heats cancel out:Next, calculate the Logarithmic Mean Temperature Difference (LMTD) for both cases:For parallel-flow ():
For counter-flow ():
The heat transfer rate is the same for both: . Given is the same, the ratio is:
For counter-flow ():
The heat transfer rate is the same for both: . Given is the same, the ratio is:
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