Subtopic: Thermodynamic principles of I.C. engines
Question Statement:
In a counter-current flow double pipe heat exchanger (DPHE), temperature difference between the hot and cold liquids at all positions is held constant at C. If the effectiveness of the heat exchanger is 0.65 and heat capacity ratio of hot and cold liquids is 1, the number of transfer units (NTU) is _____.
Official Answer Key:
1.85 to 1.90
Step-by-Step Solution & Explanation
For a counter-flow heat exchanger with heat capacity ratio C_r = 1 (the condition under which ΔT stays constant along the exchanger length, as stated), effectiveness relates to NTU as: ε = NTU/(1+NTU).
0.65 = NTU/(1+NTU) ⇒ 0.65(1+NTU) = NTU ⇒ 0.65 = NTU(1−0.65) = 0.35×NTU
NTU = 0.65/0.35 = 1.857. This lies within the accepted range 1.85–1.90.
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