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GATE 2017 ME (ME2) – Question 57

Heat Transfer · Unsteady conduction and lumped parameter systems · 2 marks · Multiple choice

A 60 mm metal ball initially at 220°C is cooled by an air jet at 20°C with h = 200 W/m² K. Its specific heat, conductivity and density are 400 J/kg K, 400 W/m K and 9000 kg/m³. Temperature after 90 s is approximately ______ °C.

  1. 141
  2. 163
  3. 189
  4. 210

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Correct answer: (A) 141

Explanation

For a sphere, characteristic length V/A=d/6=0.01m and Biot number is200·0.01/400=0.005, justifying lumped capacitance. The thermal time constant isρc(V/A)/h=9000·400·0.01/200=180s. Thus T=20+(220−20)exp(−90/180)=141.31°C, approximately **141°C, A**.