Question $1.$ A forward$-$feed double$-$effect evaporator is used to concentrate of $10\%$ caustic soda $($ NaOH $)$ solution to $50\%$ solid at $310$ K $.$ After the first effect, the solution is concentrated to $20\%$ solid. The overall heat transfer coefficients are $2\mathrm{.}8k\frac{W}{m^2}.K$ and $1\mathrm{.}7k\frac{W}{m^2}.K,$ respectively. Saturated steam is fed into the first effect at $360k\frac{N}{m^2}$ and at a rate of $4k\frac{g}{s}.$ The second effect is operated at $13\mathrm{.}5k\frac{N}{m^2}.$ Specific heat for all of solution and saturated steam can be taken as $4\mathrm{.}187k\frac{J}{k}g$ and $1\mathrm{.}84k\frac{J}{k}g,$ respectively. If the boilingpoint rise $($BPR$)$ is important, determine the feed flow rate $($F$),$ vapor production rate $($V$1,$V$2),$ and required heat transfer areas $($A$1,$A$2).$

$($Hint: There is no need to make any further correction for $T$ adjustment$)$