An aluminum sphere having a diameter of 40mm was immersed in hot water with a temperature of 55C. The temperature at the center of the aluminum sphere then was recorded every 10s interval for 80s and the data are shown in Table 1. The properties of aluminum sphere are given as follows: =2707kg/m3k=204W/m.KCp=896J/kg.K=8.411105m2/s Table 1. Center temperature of the aluminum sphere (a) Evaluate the convective heat transfer coefficient (h) for the system by using Lumped System Analysis. (16 marks) (b) Predict the value of Biot (Bi) number for the above system using the value of h obtained in (a). (6 marks) (c) Using the value of h obtained in (a) and Heisler Chart, evaluate the time needed for the center of the sphere to reached 54.5C