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GATE 2019 ME (ME1) – Question 57

Heat Transfer · Modes of heat transfer, one-dimensional conduction, resistance concept · 2 marks · Numerical answer

Three slabs are joined as shown without contact resistance. Each is 1 m thick and has conductivity 5 W/(m·K). The centre slab has nonuniform heat generation averaging 10000 W/m³; outer slabs have none. Both extreme faces convect to fluid at 30°C with h = 100 W/(m²·K). Flow is one-dimensional and steady with constant properties. Left extreme temperature T1 is 100°C. Find right extreme temperature T2 (°C).

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Correct answer: 60 to 60

Explanation

Heat generated per unit area is $10000(1)=10000$ W/m². Left convection removes $100(100-30)=7000$ W/m², leaving 3000 W/m² through the right face. Thus $100(T_2-30)=3000$ and **$T_2=60^\circ\mathrm C$**. Overall energy balance suffices despite nonuniform generation.