GATE 2016 ME (ME2) – Question 53
Two cylindrical shafts A and B, initially at the same temperature, are put into a furnace simultaneously. Their surfaces immediately remain at the furnace gas temperature; axial temperature variation is negligible. A: diameter 0.4 m, thermal conductivity 40 W/m K, volumetric heat capacity 2×10⁶ J/m³ K. B: diameter 0.1 m, conductivity 20 W/m K, volumetric heat capacity 2×10⁷ J/m³ K. Shaft A reaches 400°C at its centreline in 2 hours. The time for shaft B to reach 400°C at its centreline is ______ hours.
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Correct answer: 2.4 to 2.6
Explanation
With prescribed surface temperature and the same initial and target temperatures, corresponding centre temperatures require equal Fourier number αt/R². Diffusivities are40/(2e6)=2e−5 and20/(2e7)=1e−6m²/s. Therefore tB/tA=(0.1/0.4)²·(2e−5/1e−6)=1.25. Hence **tB=2.5hours**.