Chapter 3, Problem 3.47P

To maximize production and minimize pumping costs,crude oil is heated to reduce its viscosity during transportationfrom a production field.

1. Consider a pipe-in-pipe configuration consisting ofconcentric steel tubes with an intervening insulatingmaterial. The innertube is used to transport warmcrude oil through cold ocean water. The inner steelpipe $\left(k_s=35\text{W/m}\cdot \text{K}\right)$ has an inside diameterof $D_{i,1}=150\text{mm}$ and wall thickness $t_i=10\text{mm}$ whilethe outer steel pipe has an inside diameter of $D_{i,2}=250\text{mm}$ and wallthickness $t_o=t_i.$ Determinethe maximum allowable crude oil temperature toensure the polyurethane foam insulation $\left(k_p=0.075\text{W/m}\cdot \text{K}\right)$ between the two pipes does notexceed its maximum service temperature of $T_{\text{p,max}}=70°\text{C}\text{.}$ The ocean wateris at $T_{\infty ,o}=-5°\text{C}$ and providesan external convection heat transfer coefficient of $h_o=500{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ The convection coefficient associatedwith the flowing crude oil is $h_i=450{\text{W/m}}^{\text{2}}\cdot \text{K}\text{.}$ It is proposed to enhance the performance of thepipe-in-pipe device by replacing a thin $\left(t_a=5\text{mm}\right)$ section of polyurethane located at the outside of theinner pipe with an aerogel insulation material $\left(k_a=0.012\text{W/m}\cdot \text{K}\right).$ Determine the maximumallowable crude oil temperature to ensure maximumpolyurethane temperatures are below $T_{\text{p,max}}=70°\text{C}\text{.}$