GATE 2016 ME (ME1) – Question 52
A steel ball of 10 mm diameter at 1000 K is required to be cooled to 350 K by immersing it in a water environment at 300 K. The convective heat transfer coefficient is 1000 W/m2-K. Thermal conductivity of steel is 40 W/m-K. The time constant for the cooling process is 16 s. The time required (in s) to reach the final temperature is __________
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Correct answer: 42.0 to 42.5
Explanation
The lumped-temperature ratio obeys(T−T∞)/(Ti−T∞)=exp(−t/τ). Here the ratio is(350−300)/(1000−300)=1/14. Thus t=16ln14=**42.225s**. The lumped criterion is consistent: Bi=h(D/6)/k≈0.0417<0.1.