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.m¹K^-1 and 2600 J-kg¹K^-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 _______ °C (round off to the nearest integer).

Correct Answer: The pipe surface temperature at the exit of the pipe is 321.267 °C (which rounds to 321 °C as the nearest integer).

Analysis of the Given Data and Image:
Based on the schematic diagram and parameters shown in the provided image:

• Fluid mass flow rate: $\dot{m}=1\text{kg/s}$
• Pipe diameter: $D=0.1\text{m}$
• Pipe length: $L=40\text{m}$
• Uniform surface heat flux: