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GATE2020-ME-1: 34

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A small metal bead $(\text{radius}\: 0.5\: mm)$, initially at $100^{\circ}C$ , when placed in a stream of fluid at $20^{\circ}C$ , attains a temperature of $28^{\circ}C$ in $4.35$ seconds. The density and specific heat of the metal are $8500\:kg/m^{3}\:and\:400\:J/kg.K$, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient $(in\:W/m^{2}.K)$ between the metal bead and the fluid stream is 

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