Example $14\mathrm{.}2$A $($Forward$-$feed$)$

$4k\frac{g}{s}(14\mathrm{.}4$ tonne$/$hour$)$ of a liquor containing $10$ per cent solids is fed at $294K$ to the first effect of a triple$-$effect unit. Liquor with $50$ per cent solids is to be withdrawn from the third effect, which is at a pressure of $13k\frac{N}{m^2}(\frac{0\mathrm{.}13}{b}ar).$ The liquor may be assumed to have a specific heat of $4\mathrm{.}18k\frac{J}{k}gK$ and to have no boiling point rise. Saturated dry steam at $205k\frac{N}{m^2}$ is fed to the heating element of the first effect, and the condensate is removed at the steam temperature in each effect as shown in Figure $14\mathrm{.}5.$

If the three units are to have equal areas, estimate the area, the temperature differences and the steam consumption. Heat transfer coefficients of $3\mathrm{.}1,2\mathrm{.}0$ and $1\mathrm{.}1k\frac{W}{m^2}K$ for the first, second, and third effects respectively, may be assumed.