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Heat Transfer
Convection & Radiation
GATE 2022
Hard

Consider a hydrodynamically and thermally fully-developed, steady fluid flow of 1 kg/s in a uniformly heated pipe with diameter of 0.1 m and length of 40 m. A constant heat flux of magnitude 15000 W/m² is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is 200°C. The Reynolds number (Re) of the flow is 85000, and the Prandtl number (Pr) of the fluid is 5. The thermal conductivity and the specific heat of the fluid are 0.08 W·m⁻¹·K⁻¹ and 2600 J·kg⁻¹·K⁻¹, respectively. The correlation Nu=0.023Re^0.8·Pr^0.4 is applicable, where the Nusselt Number (Nu) is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is ________ °C (round off to the nearest integer).

321 °C(± 3 accepted)

Explanation

Bulk temperature rise (constant heat flux, energy balance): Q=q″·πDL=15000×π×0.1×40≈188,496 W. ΔTbulk=Q/(ṁcp)=188496/(1×2600)≈72.5 K, so Tbulk,exit=200+72.5=272.5°C. Convection coefficient from the correlation: Re^0.8≈8782, Pr^0.4≈1.904, Nu=0.023×8782×1.904≈384.6, h=Nu·k/D=384.6×0.08/0.1≈307.6 W/m².K. Surface temperature at exit: Ts=Tbulk+q″/h=272.5+15000/307.6≈321°C.

Source: GATE ME 2022 Session 2 (ME-2) (2022)

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