GATE 2022 ME (ME1) – Question 60
Consider a one-dimensional steady heat conduction process through a solid slab of thickness 0.1 m. The higher temperature side A has a surface temperature of 80 °C, and the heat transfer rate per unit area to low temperature side B is 4.5 kW/m$^2$. The thermal conductivity of the slab is 15 W/m.K. The rate of entropy generation per unit area during the heat transfer process is ________ W/m$^2$.K (round off to 2 decimal places).
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Correct answer: 1.17 to 1.19
Explanation
The temperature drop across the slab is $\Delta T = \frac{qL}{k} = \frac{4500 \times 0.1}{15} = 30$ K, so $T_B = 80 - 30 = 50$ °C. The entropy generation rate per unit area is $\dot{s}_{gen} = q\left(\frac{1}{T_B} - \frac{1}{T_A}\right) = 4500\left(\frac{1}{323.15} - \frac{1}{353.15}\right) = 1.18$ W/m² K.