An exothermic process occurs uniformly throughout a 10-cm-diameter sphere (k = 300 W/.K, cp = 400 J/kg K. p 7500 kg/m3), and it generates heat at a constant rate of 1.2 MW/m3. The sphere initially is at a uniform temperature of 20o, and the exothermic process is commenced at time t = 0. To keep the sphere temperature under control, it is submerged in a liquid both maintained at 20oC. The heat transfer coefficient at the sphere surface is 250W/m2.K.
a. Derive the equation for variation of sphere temperature T with time t in the form of dT/dt.
b. Predict the steady state temperature of the sphere.
c. Calculate the time needed for the sphere temperature to reach the average of its initial and steady temperature.