Example $8\mathrm{.}4-3$: Evaporation of an NaOH Solution.

An evaporator is used to concentrate $4536k\frac{g}{h}$ of a $20\%$ solution of NaOH in water entering at $60C$ to a product of $50\%$ solid. The pressure of the saturated steam used is $172\mathrm{.}4$kPa and the pressure in the vapor space of the evaporator is $11\mathrm{.}7$kPa. The overall heat$-$transfer coefficient is $1560\frac{W}{m^2}.K.$

Calculate the steam used, the steam economy in $(kg$ vaporized$/$kg steam$)$ used, and the heating surface area in $m^2.$