Project ForgeHeat Transfer
Conduction
GATE 2016
Medium
A steel ball of 10 mm diameter at 1000 K is cooled to 350 K in a water environment at 300 K, with convective coefficient 1000 W/m²-K and steel thermal conductivity 40 W/m-K. The time constant for the cooling process τ is 16 s. The time required (in s) to reach the final temperature is __________.
42.25 s(± 0.25 accepted)
Explanation
Using the lumped-capacitance model, θ/θ0 = e^(-t/τ), with θ0=1000-300=700 K and θ=350-300=50 K. t = -τ·ln(θ/θ0) = -16·ln(50/700) = 16×2.639 ≈ 42.24 s.
Source: GATE ME 2016 Set-1 (2016)
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