(Solved): 2.4-10. Surface Area and Steam Consumption of an Evaporator. A single-effect evaporator is concentr ...

2.4-10. Surface Area and Steam Consumption of an Evaporator. A single-effect evaporator is concentrating a feed solution of organic colloids from 5 to $50\mathrm{wt}\%$. The solution has a negligible boilingpoint elevation. The heat capacity of the feed is $c_p=4.06\mathrm{kJ}/\mathrm{kg}\cdot \mathrm{K}$ $\left(0.97\mathrm{btu}/{\mathrm{lb}}_{\mathrm{m}}\cdot {}^{\circ }\mathrm{F}\right)$ and the feed enters at $15.6^{\circ }\mathrm{C}\left(60^{\circ }\mathrm{F}\right)$. Saturated steam at $101.32\mathrm{kPa}$ is available for heating, and the pressure in the vapor space of the evaporator is $15.3\mathrm{kPa}$. A total of $4536\mathrm{kg}/\mathrm{h}(10$ $000{\mathrm{lb}}_{\mathrm{m}}/\mathrm{h}$ ) of water is to be evaporated. The overall heat-transfer coefficient is $1988\mathrm{W}/{\mathrm{m}}^2\cdot \mathrm{K}\left(350\mathrm{btu}/\mathrm{h}\cdot {}^{\circ }\mathrm{F}\right)$. What is the required surface area in ${\mathrm{m}}^2$ and the steam consumption?