A $1-2$ shell and tube heat exchanger will be used to heat $4$ kg $/$ s of a liquid food $($ density $1020$ kg $/$ m$^3.$ Cp $-3850$ J $/$ kg$.$K $,$ p $=0\mathrm{.}5$x$10$ Pa$.$s $,$ k $=0\mathrm{.}68$ W $/$ m$.$K $)$ from $5\backslash$deg C to $75\backslash$deg C by $10$ kg $/$ s of liquid water at an inlet temperature of $95\backslash$deg C $.$ Heating medium flows through the shell $-$ side $.$ The fouling coeficient for the shell side is estimated as $0\mathrm{.}004$ m$2$ K $/$ W $.$ The heat transfer coefficient for the shell side will be assumed as $10000$ W $/$ mK The pipe has inner and outer diameter of $22\mathrm{.}1$ mm and $25\mathrm{.}4$ mm $,$ respectively $.$ Sr $=$ SL $=5$ cm $.$ Number of tubes is $86.$ a $)$ What type of heat transfer mechanism occurs in that system $,$ give your reasings by explaing the mechanism briefly and drawing the thermal resistance diagram $.(10$ point $)$ b $)$ Determine the heat transfer coefficient for the tube sides $(30$ point $)$ c $)$ If the proposed length of the STHE is $10$ m $,$ is this SHTE satisfactory for your requirement $?$ Your reply should be based on calculations $.$