In a single$-$effect evaporator, a colloidal solution is derived from $5\%$ to $50\%$ by weight. The solution has an elevated boiling point. The heat capacity of the feed is Cp$=4\mathrm{.}06$ kJ$/$kg$.$K and it enters the evaporator at $15\mathrm{.}6$ OC$.$ Saturated water vapor at $101\mathrm{.}32$ kPa is used for heating and the pressure in the steam section of the evaporator is $15\mathrm{.}3$ kPa. The total flow rate of the solution to be evaporated is $4536$ kg water$/$hour$.$ The entire heat dissipation is $1988$ W$/$m$2.$

a$)$Calculate the thermal break surface modifier. $($m$2)$

b$)$Take into account water vapor consumption