Consider a packed bed of 75-mm-diameter aluminum spheres (rho = 2700 kg/m3 , c = 950 J/kg ⋅ K, k = 240 W/m ⋅ K) and a charging process for which gas enters the storage unit at a temperature of Tg, i = 300°C. If the initial temperature of the spheres is Ti = 25°C and the convection coeffcient is h = 75 W/m2 ⋅ K, how long does it take a 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 instead of aluminum?