In a pipe-within-a-pipe heat exchanger, water flows in the annulus and an aniline-alcohol solution having the properties listed in Problem 6.20 flows in the central pipe. The inner pipe has a 0.527 -in.-ID and a 0.625 -in.-OD, and the ID of the outer pipe is $0.750 \mathrm{in}$. For a water bulk temperature of $80^{\circ} \mathrm{F}$ and an aniline bulk temperature of $140^{\circ} \mathrm{F}$, determine the overall heat transfer coefficient based on the outer diameter of the central pipe and the frictional pressure drop per unit length for water and the aniline for the following volumetric flow rates: (a) water rate $1 \mathrm{gpm}$, aniline rate $1 \mathrm{gpm}$; (b) water rate $10 \mathrm{gpm}$, aniline rate 1 gpm; (c) water rate $1 \mathrm{gpm}$, aniline rate $10 \mathrm{gpm}$; and (d) water rate $10 \mathrm{gpm}$, aniline rate $10 \mathrm{gpm} .(L / D=400$. $)$ Physical properties of aniline solution:
$$
\begin{array}{rcccc}
\hline \begin{array}{l}
\text { Temp- } \\
\text { erature } \\
\left({ }^{\circ} \mathrm{F}\right)
\end{array} & \begin{array}{c}
\text { Viscosity } \\
\text { (centipoise) }
\end{array} & \begin{array}{c}
\text { Thermal } \\
\text { Conductivity } \\
\left(\mathrm{Btu}^{\circ} \mathrm{htt}^{\circ} \mathrm{F}\right)
\end{array} & \begin{array}{c}
\text { Specific } \\
\text { Gravity }
\end{array} & \begin{array}{c}
\text { Specific } \\
\text { Heat } \\
\left(\mathrm{Bt}^{\prime} / \mathrm{Lb}^{\circ} \mathrm{F}\right)
\end{array} \\
\hline 68 & 5.1 & 0.100 & 1.03 & 0.50 \\
140 & 1.4 & 0.098 & 0.98 & 0.53 \\
212 & 0.6 & 0.095 & & 0.56 \\
\hline
\end{array}
$$