GATE Mechanical 2022 Set 2 | Question: 55

Question

Consider a hydrodynamically and thermally fully-developed, steady fluid flow of $1$ $\text{kg/s}$ in a uniformly heated pipe with diameter of $0.1\: m$ and length of $40 \:m$. A constant heat flux of magnitude $15000\: W/m^{2}$ is imposed on the outer surface of the pipe. The bulk-mean temperature of the fluid at the entrance to the pipe is $200 ^{\circ}C$. 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 $0.08$ $W \cdot m^{-1} \cdot K^{-1}$ and $2600$ $J \cdot kg^{-1} \cdot K^{-1}$, respectively. The correlation $Nu = 0.023\: Re^{0.8}\: Pr^{0.4}$ is applicable, where the Nusselt Number $(Nu)$ is defined on the basis of the pipe diameter. The pipe surface temperature at the exit is _______________ $^{\circ}C$ (round off to the nearest integer).