In a concentric tube counter-flow heat exchanger, hot oil enters at 102^{\circ} {C} and leaves at 65^{\circ} {C}. Cold water enters at 25^{\circ} {C} and leaves at 42^{\circ} {C}. The log mean temperature difference (LMTD) is ______________{ }^{\circ} {C} (round off to one decimal place).

GATE Mechanical Engineering (ME) 2020 Shift 1 Solved Paper

Question : 23 of 65

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In a concentric tube counter-flow heat exchanger, hot oil enters at

102^{∘} {C}

and leaves at

65^{∘} {C}

. Cold water enters at

25^{∘} {C}

and leaves at

42^{∘} {C}

. The log mean temperature difference (LMTD) is ______________

{ }^{∘} {C}

(round off to one decimal place).

Solution:

\;\text " LMTD "\;=\;{∆ T_{1}-∆ T_{2}}/{\ln (\;{∆ T_{1}}/{∆ T_{2}})}

∆ T_{1}=T_{h i}-T_{c o}=60^{∘}

∆ T_{2}=T_{h 0}-T_{c i}=40^{∘}

\;\text " LMTD "\;=\;{60-40}/{ℓ n(\;{60}/{40})}=49.33^{∘} {C}

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