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GATE 2024 MT – Question 15

Transport Phenomena and Rate Processes · Heat transfer · 1 mark · Multiple choice

Two different-metal rods, each of length $L/2$ and diameter $d\ll L$, have constant conductivities $k_1>k_2$ and perfect contact (zero interface thermal resistance), as shown. Their outer ends are maintained at $T_1>T_2$, and the rods are otherwise insulated. Which graph gives the steady temperature profile? The thickest line is temperature; the horizontal axis is distance from the left end to the right end.

Diagram for GATE 2024 MT question 15
  1. Graph A
  2. Graph B
  3. Graph C
  4. Graph D

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Show answer and explanation

Correct answer: (B) Graph B

Explanation

Steady one-dimensional heat flux is continuous and equals −k dT/dx.

Each constant-conductivity segment has a linear profile, and the larger k1 gives a smaller slope magnitude than k2.

Perfect contact keeps interface temperature continuous.

These features identify **B**.