please solve the following heat transfer problem A singleeff

please solve the following heat transfer problem

A single-effect evaporator is used to concentrate 1500 lb/hr of 10% NaOH solution with the feed temperature 150 degree F. The temperature and mass flow rate of the saturated steam is 300 degree F and 1000 lb/hr, respectively. The vapor pressure inside the evaporator is 2 psia and the specific heat of the vapor is 0.45 Btu/(lb degree F). The overall heat transfer coefficient is 30 Btu/ft^2 .hr. degree F). Find: what is the concentration of the concentrated NaOH solution? what is the heat transfer area? the economy the capacity (Trial and error is required)

Solution

Flow rate of NaOH= 1500 lb/hr.

Feed temperature T_f= 150°F.

Flow rate of steam = 1000 lb/hr

Temperature of steam = 300°F

The vapour pressure is given , hence see steam table to know the temperature at that point .

Then use the formula :

Q = mc_pT . T is the temperature difference .

Use LMTD formula to get mean temperature difference

LMTD = (T₁-T₂₎/ln(T₁/T₂)

T₁= T_Hot_In - T_cold_out

T₂= T_Hot_Out - T_Cold_In

Remember cold fluid is NaoH & hot is steam.

Then use the equation :

Q = UA (LMTD).

Where U is the overall heat transfer coefficient while A is the area of heat transfer.

U is given , so you will get value of A