A shell$-$and$-$tube heat exchanger is to be required to decrease the temperature of $190,000I\frac{b_m}{h}$ nitrobenzene from $180F$ to $110F.$ Cooling water available at $27C$ is decided to be used for this purpose where the outlet temperature of the cooling water is needed to limit to $120F.$ You are asked to calculate the design overall heat transfer coefficient of the shell$-$and$-$tube heat exchanger desired for this duty. Assume that the nitrobenzene stream is flowing on the shell side and there is no fouling offered by the nitrobenzene stream. Do single trial only.

Other data:

Use simplified Delaware method

Use fixed tubesheet heat exchanger $($TEMA $L$ as rear end$)$ for your design

Use $24ft$ tube length, $1$ in OD tube $(16$ BWG$),$ and $1\mathrm{.}25$ in triangular pitch

Use $U_{\text{r}\text{e}\text{q}}$ to start $=110Bt\frac{u}{h}*f{t}^2*F$ and ignore viscosity correction factors

Thermal conductivity of wall:

$35Bt\frac{u}{h}*ftF$

Specific gravity of water:

$1\mathrm{.}0$

Specific gravity of nitrobenzene:

$0\mathrm{.}84$

Average thermal conductivity of water:

$0\mathrm{.}36Bt\frac{u}{h}*ft*F$

Average thermal conductivity of nitrobenzene: $0\mathrm{.}08Bt\frac{u}{h}*ft*F$