GATE 2016 ME (ME3) – Question 53
A cylindrical steel rod, 0.01 m in diameter and 0.2 m in length is first heated to 750 oC and then immersed in a water bath at 100 oC. The heat transfer coefficient is 250 W/m2-K. The density, specific heat and thermal conductivity of steel are ρ= 7801 kg/m3, c = 473 J/kg-K, and k = 43 W/m-K, respectively. The time required for the rod to reach 300 oC is ________ seconds.
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Correct answer: 42 to 45
Explanation
Using all exposed surfaces, L_c=V/A=DL/(4L+2D)=0.002439m and Bi=hL_c/k≈0.0142, supporting lumped cooling. The time constant isρcL_c/h≈36.00s. Then t=(ρcL_c/h)ln[(750−100)/(300−100)]≈**42.43s**. Neglecting the small end areas gives about43.49s, also within the official range.