Mini-project 2: Oil Pipeline Oil flowing through a $12 \mathrm{XS}$ schedule pipe crosses through a river that is $10 \mathrm{~m}$ wide. This pipe has a 11.75 inch inner diameter, and 12.75 inch outer diameter, and is made of steel. Assuming the steel has a conductivity of $40 \mathrm{~W} / \mathrm{m}-\mathrm{K}$. 1. What is the thermal resistance of heat transfer radially through the pipe? Please report your answer in $\mathrm{K} / \mathrm{W}$. The oil is heated to reduce viscosity and related pumping losses, and may be assumed to be $30^{\circ} \mathrm{C}$ as the pipe enters the river. OI properties may be approximated from Table A-13 in the textbook. The oil flows at an average velocity of $1.5 \mathrm{~m} / \mathrm{s}$ through the pipe. 2. What is the temperature at which you evaluated the oil properties for use in the heat transfer correlations? 3. What is the flow Reynolds number, and is the flow turbulent? 4. What is the Nusselt number and convective heat transfer coefficient for the oil? Please include which Nusselt number correlation you used and why it is appropriate/why you chose it. 5. What is the convective thermal resistance in the oil? Please report your answer in $\mathrm{K} / \mathrm{W}$. During late Winter/early Spring as the Spring melt is just starting, this section of river can be quite icy and the average temperature is very close to $0^{\circ} \mathrm{C}$. The river water itself is flowing at $2 \mathrm{~m} / \mathrm{s}$ over the pipeline. Assume the pipe goes through the center of the river such that any effects of the riverbed or water surface may be neglected. 6. What is the temperature at which you evaluated the water properties for use in the heat transfer correlations? 7. What is the Reynolds number of the water over the pipe, and is the flow turbulent? 8. What is the Nusselt number and convective heat transfer coefficient for the water? Please include which Nusselt number correlation you used and why it is appropriate/why you chose it. 9. What is the convective thermal resistance in the water? Please report your answer in $\mathrm{K} / \mathrm{W}$. For the overall system 10. What is the approximate total heat transfer from the oil to the water? Please report your answer in W. 11. What are the temperatures of the inner and outer surfaces of the pipe? 12. What is the temperature change of the oil as it erosses through the icy river? You may find it necessary to assume some temperatures initially, then iterate your solution to find the actual temperatures. When iterating. please make sure the temperatures used to evaluate fluid properties are converged to at least 3 significant figures (i.e., if a temperature at one iteration is 21.91 and 21.94 at the next iteration, you may simply use your results from calculations using 21.91 and don't need to repeat for 21.94). For all other intermediate calculations, however, you should be using full precision in your answers.