The GATE Grind

GATE 2020 ME (ME1) – Question 44

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

A metal bead of radius 0.5 mm, initially at 100°C, attains 28°C in 4.35 s when placed in fluid at 20°C. Metal density is 8500 kg/m³ and specific heat 400 J/(kg·K). Treating the bead as a lumped system, find the convective heat-transfer coefficient (W/(m²·K)).

  1. 283.3
  2. 299.8
  3. 149.9
  4. 449.7

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (B) 299.8

Explanation

Lumped cooling gives $(T-T_\infty)/(T_i-T_\infty)=e^{-hAt/(\rho Vc_p)}$. For a sphere V/A=r/3. Thus $h=\rho c_pr\ln(80/8)/(3t)=299.95$ W/m²·K using the printed time, matching the rounded option **299.8, B**.