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An exothermic process occurs uniformly throughout a 10-cm-diameter sphere k 300 WmK cp 400 J kg K 7500 kg/m3 and it generates heat at a constant rate

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.

May 08 2020 View more View Less

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