Project ForgeHeat Transfer
Conduction
GATE 2020
Medium
An infinitely long rectangular fin is exposed to surrounding fluid at Ta=27°C. The steady-state balance gives d²θ/dx²=m²θ, θ=Tx−Ta, with m=0.04 cm⁻¹ and base temperature T0=227°C. The temperature (°C) at x=25cm is (round off to 1 decimal place)
100.6 °C(± 1 accepted)
Explanation
For an infinite fin, θ(x)=θ0·e^(−mx), with θ0=T0−Ta=200°C. θ(25)=200×e^(−0.04×25)=200×e^(−1)=200×0.3679=73.58°C. T(25)=73.58+27=100.6°C.
Source: GATE CH 2020 (2020)
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