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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 ($x$, such that $x \geq 0$), are given by $$T_h(x)=80-3x \\ T_c(x)=20+2x$$ where $T_h$ and $T_c$ are in $^\circ C$, and $x$ is in meter.

The logarithmic mean temperature difference (in $^\circ C$) is

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