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GATE 2024 MT – Question 38

Transport Phenomena and Rate Processes · Heat transfer · 2 marks · Multiple choice

A slender cylindrical rod of conductivity $k$, length $L$, and diameter $d\ll L$ contacts an infinite liquid heat sink at its right end, as shown. At steady state, the right end is at $T_2$ and the heat sink at $T_0$. Their convection coefficient is $h$. With no other heat loss, the left-end temperature $T_1$ is

Diagram for GATE 2024 MT question 38
  1. $T_1=T_2+(T_2-T_0)hL/k$
  2. $T_1=T_2-(T_2-T_0)hL/k$
  3. $T_1=T_2-(T_2-T_0)k/(hL)$
  4. $T_1=T_2+(T_2-T_0)k/(hL)$

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Show answer and explanation

Correct answer: (A) $T_1=T_2+(T_2-T_0)hL/k$

Explanation

At steady state the same heat crosses the rod and its end interface: kA(T1−T2)/L=hA(T2−T0).

Cancel A and solve to obtain **T1=T2+(hL/k)(T2−T0), A**.