GATE 2022 MT – Question 62
Air enters a tube at 300 K and 1.5 kg/s. Tube inner diameter is 0.08 m, inner-wall temperature 700 K, and outlet-air temperature 600 K. For purely steady convection with $h=500$ W m$^{-2}$ K$^{-1}$, constant $c_p=1080$ J kg$^{-1}$ K$^{-1}$, and $\pi=3.14$, the tube length is ______ m (two decimal places).
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Correct answer: 16.55 to 18.55
Explanation
A differential energy balance gives $\dot m c_p\,dT/dx=h\pi D(T_w-T)$. Integration yields $L=\dot m c_p/(h\pi D)\ln[(T_w-T_{in})/(T_w-T_{out})]$. Substitute to obtain $L=1620/(500\times3.14\times0.08)\ln4=\boxed{17.88}$ m.