$($c$)$ Water flows in the inner tube of a double pipe heat exchanger and is eoeled with ethanol flowing in the jacket. The diameter of the inner pipe is $30mm$ and the pipe wall thickness is $7\mathrm{.}5mm.$ NOTE:

thermal conductivity of the inner tube is $45W{m}^{-1}{C}^{-1}$

Heat transfer film coefficient, water side: $h_o=1780W{m}^{-2}*C^{-1}$

Heat transfer film coefficient, ethanol side: $h_i=1050W{m}^{-2}*C^{-1}$

Inside fouling factor, $h_{di}=5680W{m}^{-2}.C^{-1}$ and

Outside fouling factor, $h_{do}=2440\frac{W}{m^2}.C$

$($i$)$ Determine the overall heat transfer coefficient, $U_0,$ based on the outside area of the inner pipe.

$($ii$)$ What is the significance of the term $\text{'}U\text{'}?$

How could one manage the equipment to get a more desirable value of $U$ and therefore increase the heat transfer efficiency within the equipment? Clearly justify support your suggestions.

$(3)$