In solvent production plant, raw material stream heated from $20\backslash$deg C to $45\backslash$deg C by using $90\backslash$deg C hot

process stream. For this purpose, counter$-$current plate type heat exchanger used that has $12$ m$2$

heat transfer area. Raw material and process stream flow rates are given as $10$ kg$/$s and $21$ kg$/$s$,$

respectively. Assume there is no heat loss to environment, stream heat capacities are constant

and F$=1.($Cp$,$raw $=4\mathrm{.}2$ kJ$/$kg$.$K$,$ Cp$,$process $=2\mathrm{.}50$ kJ$/$kg$.$K$)$

a$)$ Calculate the process stream outlet temperature and overall heat transfer coefficient using

LMTD method.

b$)$ Sketch the temperature profile.