A triple effect forward feed evaporator is being used to evaporate a sugar solution containing 5 wt % solids to a concentrated solution of 80 %. The boiling point rise of the solutions (independent of pressure) can be estimated from BPR °C = 1.78x + 6.22x^2, where x is wt fraction of sugar in solution. Saturated steam at 205.5 kPa (121.1°C saturation temperature) is being used. The pressure in the vapor space of the third effect is 13.4 kPa. The feed rate is 10,000 kg/h at 26.7°C. The heat capacity of the liquid solutions is 4.19 - 3.52x, kJ/kg K. The heat of solution is considered to be negligible. The coefficients of heat transfer have been estimated as U1 = 3123, U2 = 1987, and U3 = 1136 W/m^2-K. if each effect has the same surface area, calculate the area, the steam rate used and the steam economy.

I really need help please don't reject. Please help me understand how to compute this in detail. especially on how to interpolate. thank you so much.

Note: When areas are not close, provide another trial. If areas are almost equal, therefore new assumptions are valid.

A triple effect forward feed evaporator is being used to evaporate a sugar solution containing 5 wt % solids to a concentrated solution of 80 %. The boiling point rise of the solutions (independent of pressure) can be estimated from BPR °C = 1.78x + 6.22x^2, where x is wt fraction of sugar in solution. Saturated steam at 205.5 kPa (121.1°C saturation temperature) is being used. The pressure in the vapor space of the third effect is 13.4 kPa. The feed rate is 10,000 kg/h at 26.7°C. The heat capacity of the liquid solutions is 4.19 - 3.52x, kJ/kg K. The heat of solution is considered to be negligible. The coefficients of heat transfer have been estimated as U1 = 3123, U2 = 1987, and U3 = 1136 W/m^2-K. if each effect has the same surface area, calculate the area, the steam rate used and the steam economy.