GATE AG 2011 • Q24 MCQ • 1 Mark

Section 7: Dairy and Food Engineering

Heat and Mass Transfer

Subtopic: Working principles of heat exchangers

Question Statement:

In a counter current concentric tube heat exchanger, the hot fluid enters at 360 K and leaves at 340 K. The cooling fluid enters at 300 K and leaves at 316 K. The logarithmic mean temperature difference in K is

Options:

  • (A) 17.9
  • (B) 39.2
  • (C) 41.9
  • (D) 57.3

Official Answer Key:

C

Step-by-Step Solution & Explanation

For counter-current flow, ΔT₁ = T_hot,in − T_cold,out = 360 − 316 = 44 K, ΔT₂ = T_hot,out − T_cold,in = 340 − 300 = 40 K. LMTD = (ΔT₁ − ΔT₂)/ln(ΔT₁/ΔT₂) = (44−40)/ln(44/40) = 4/ln(1.10) = 4/0.0953 = 41.97 ≈ 41.9 K, matching option (C).

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