A triple$-$effect forward$-$feed evaporator is used to concentrate a sugar solution from $40\%\frac{w}{w}$ to $70\%\frac{w}{w}$ sugar. The feed at a rate of $5\mathrm{.}0k\frac{g}{s}$ enters $1^{st}$ effect at $50C.$ The boiling point rise for all the solution is given by is the weight fraction of sugar in solution$).$ Saturated steam is supplied to the $1^{st}$ effect at $121C.$ The pressure in tshe vapour space of the last effect is $13\mathrm{.}4$kPa. The overall heat transfer coefficient in the $1^{st},2^{nd}$ and $3^{rd}$ effects is $3000,2200$ and $1500W{m}^{-2}{K}^{-1},$ respectively. Assume that the specific heat capacity has the same value of $4000JK{g}^{-1}{K}^{-1}$ for all solutions. Calculate:

The steam flow rate to the $1^{st}$ effect $(k\frac{g}{s})$

The heat transfer surface area $(A$ in $m^2)$

The steam economy

NOTE: i$)$ Calculate area for all $3$ effects, so report A$1,$ A$2,$ A$3$ in your solution

ii$)$ The boiling point of pure water at $13\mathrm{.}4$kPa is $51\mathrm{.}5C$