Project ForgeHeat Transfer
Convection
GATE 2019
Medium
A solid sphere (radius 1cm, initial 25°C, ρ=10^4 kg/m³, Cp=500 J/kg·K) is exposed to a gas stream at 100°C, h=50 W/m²·K, Biot<<1 (lumped system). The time (s) for the sphere to reach 95°C is (rounded off to nearest integer)
903 s(± 3 accepted)
Explanation
τ=ρCp(V/A)/h=ρCp(r/3)/h=10⁴×500×(0.01/3)/50=333.3s. θ/θ0=e^(−t/τ): (100−95)/(100−25)=5/75=1/15=e^(−t/τ). t=τ·ln15=333.3×2.708=903s.
Source: GATE CH 2019 (2019)
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