Question

A small metal bead (radius 0.5 mm), initially at 100°C, when placed in a stream of fluid at 20°C, attains a temperature of 28°C in 4.35 seconds. The density and specific heat of the metal are 8500 kg/m³ and 400 J/kgK, respectively. If the bead is considered as lumped system, the convective heat transfer coefficient (in W/m²K) between the metal bead and the fluid stream is

Options :

  1. 283.3

  2. 299.8

  3. 149.9

  4. 449.7

Show Answer

Answer :

299.8

Solution :

Given, Cp = 400 J/kgK, ρ = 8500 kg/m3, t = 4.35 sec, r = 0.5 mm

Ti = 100°C, T∞ = 20°C, T = 28°C

Using equation (1) and putting the given values :

ln ( 100 20 28 20 ) = ( h × 3 × 1000 0.5 × 8500 × 400 ) × 4.35

h = 2.302 × 0.5 × 8500 × 400 3000 × 4.35 = 299.87 W / m 2 K

∴ Heat transfer coefficient = 299.8 W/m2K

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