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GATE 2023 CH – Question 22

Heat Transfer · Conduction: steady and unsteady, equation of energy · 1 mark · Multiple choice

A slab of thickness $L$, as shown in the figure below, has cross-sectional area $A$ and constant thermal conductivity $k$. $T_1$ and $T_2$ are the temperatures at $x = 0$ and $x = L$, respectively. Which one of the following options is the CORRECT expression of the thermal resistance for steady-state one-dimensional heat conduction?

a slab between $x = 0$ (temperature $T_1$) and $x = L$ (temperature $T_2$).
  1. $\frac{L}{kA}$
  2. $\frac{k}{LA}$
  3. $\frac{kA(T_1 - T_2)}{L}$
  4. $\frac{A}{Lk}$

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Show answer and explanation

Correct answer: (A) $\frac{L}{kA}$

Explanation

The heat flow is $Q = \frac{kA(T_1 - T_2)}{L}$, so the thermal resistance, the temperature difference divided by the heat flow, is $R = \frac{L}{kA}$.