In many industrial applications, liquid is heated or cooled in a closed vessel and agitated to speed up the heat transfer. The agitation maintains the inside temperature to be fairly uniform, somewhat analogous to the lumped parameter solution described by Eqn. 5.5. In this case, the mass average temperature T a? of the liquid will replace the temperature T of the solid in Eqn. 5.5. Also, the heat transfer coefficient will now be the inside heat transfer coefficient between the vessel wall and liquid. 1) Calculate how the mass average temperature (T a? ) of the liquid would change with time during agitated heating of a containerized liquid where the inside heat transfer coefficient is 120W/m2·K. The container wall temperature is at 121°C and the initial temperature of the fluid is 30°C. The container has a height of 10.67 cm and a radius of 4.19 cm. The density and specific heat of the liquid are 950 kg/m3 and 4100 J/kg, respectively. 2) How long does it take for the average temperature to reach 95% of the maximum possible temperature?