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GATE 2025 CH – Question 38

Heat Transfer · Conduction: steady and unsteady, equation of energy · 2 marks · Multiple choice

A hot plate is placed in contact with a cold plate of a different thermal conductivity as shown in the figure. The initial temperature (at time $t = 0$) of the hot plate and cold plate are $T_h$ and $T_c$, respectively. Assume perfect contact between the plates.

[Figure: a hot plate lying on top of a cold plate, with the contact surface marked as Surface S.]

Which one of the following is an appropriate boundary condition at the surface S for solving the unsteady state, one-dimensional heat conduction equations for the hot plate and cold plate for $t > 0$?

Diagram for GATE 2025 CH question 38
  1. Temperature at S is same for both the plates
  2. Gradient of temperature at S is same for both the plates
  3. Gradient of temperature vanishes at S
  4. Temperature at S is the average of $T_h$ and $T_c$

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Correct answer: (A) Temperature at S is same for both the plates

Explanation

Perfect contact means there is no temperature jump across the interface, so the two plates have the same temperature at S at all times. The heat flux is also continuous there, $-k_h\frac{\partial T_h}{\partial x} = -k_c\frac{\partial T_c}{\partial x}$, but because the thermal conductivities differ the gradients themselves are not equal. The surface temperature is also not the simple average of the initial values, unless the plates have equal thermal effusivity.