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An exothermic process occurs uniformly throughout a 10-cm-diameter sphere (k = 300 W/m.K, cp = 400 J/kg.K, ? = 7500 kg/m3), and it generates heat at a constant rate of1.2 MW/m3. The sphere initially is at a uniform temperature of 20oC, and the exothermic process is commenced at time t = 0. To keep the sphere temperature undercontrol, it is submerged in a liquid bath maintained at 20oC. The heat transfer coefficient at the sphere surface is 250 W/m2.K. (a) Derive the equation for variationof 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 spheretemperature to reach the average of its initial and steady temperatures.
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