Q3. Thermal energy storage systems for a high temperature gas reactor would involve a packed bed of solid spheres. through which a hot gas flows if the system is being charged to store heat, or a cold gas if heat is being discharged. In a charging process, heat transfer from the hot gas increases the thermal energy stored within the colder spheres; during discharge, the stored energy decreases as heat is transferred from the warmer spheres to the cooler gas. Consider a packed bed of 75-mm-diameter aluminum spheres (p=2,700 kg/m,c,= 950 JkeK, k= 240 W/mK) and a charging process for which a hot gas enters the storage unit at a temperature of Ty=300C. If the initial temperature of the spheres is T, =25C and the convection heat transfer coefficient is h = 75 W/m?K, how long does it take the sphere near the inlet of the system to accumulate 90% of the maximum possible thermal energy? What is the corresponding temperature at the center of the sphere? Is there any advantage to using copper spheres instead of aluminum? e ; Aurinum sphere ; D =75 mm, T;= 25C S ; Tqi= 3009C g % p = 2700 kgim? 8= B c = 950 Mhg-K h =75 WimiH y K = 240 WineK _