The GATE Grind

GATE 2021 CH – Question 17

Heat Transfer · Heat exchangers and evaporators: types and design · 1 mark · Multiple choice

In a double-pipe heat exchanger of 10 m length, a hot fluid flows in the annulus and a cold fluid flows in the inner pipe. The temperature profiles of the hot $(T_h)$ and cold $(T_c)$ fluids along the length of the heat exchanger $(x,\ x\ge0)$, are given by $T_h(x)=80-3x$ and $T_c(x)=20+2x$, where $T_h$ and $T_c$ are in °C, and $x$ is in meter. The logarithmic mean temperature difference (in °C) is

  1. 24.6
  2. 27.9
  3. 30.0
  4. 50.0

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Correct answer: (B) 27.9

Explanation

At $x=0$, the local temperature difference is $80-20=60$ °C. At $x=10$ m, the temperatures are 50 °C and 40 °C, so the difference is 10 °C.

Use the two **local endpoint differences**:
$$\Delta T_{lm}=\frac{60-10}{\ln(60/10)}=27.9055\ ^\circ\mathrm C.$$

Therefore the listed value is **27.9 °C (B)**. An arithmetic average of endpoint differences would not be the LMTD.