A vessel with a paddle agitator and no baffles is used to heat liquid at a temperature of $37\backslash$deg C in the vessel. Jacket contains steam. The inner diameter of the vessel is $1\mathrm{.}5$ m and the agitator diameter is $0\mathrm{.}5$ m$,$ rotating at a speed of $175$ rpm$.$ Wall surface temperature $90\backslash$deg C$.$ The physical properties of the liquid are: $\backslash$rho $=977$ kg$/$m$3$; cp $=2\mathrm{.}72$ kJ$/$kg$.$K ; k $=0\mathrm{.}346$ W$/$m$.$K ; $=0\mathrm{.}12$ kg$/$m$.$s at $37\backslash$deg C and $7\mathrm{.}2$ x $10-3$ at $90\backslash$deg C$.$ Calculate the heat transfer coefficient to the walls of the jacket