A cylindrical vessel with an agitator is used to cool a liquid from an initial temperature of $90$ C$.$ The jacket of the vessel contains a $10$ C cooling medium. The inside diameter of the vessel is $1$ m and height of liquid in the vessel is $1\mathrm{.}5$ m$.$ The physical properties of the liquid are $=970$ kg$/$m$3,$ cp $=2\mathrm{.}75$ kJ$/$kg$$K$,$ k $=0\mathrm{.}4$ W$/$m$$K$.$ The overall heat transfer coefficient at the surface between cooling medium and product is $120$ W$/$m$2$K Estimate the time required to decrease the temperature of the liquid to $20$ C$.$ Assume the liquid in the vessel is well mixed.