Thermal energy storage systems commonly involve a packed bed of solid spheres, through which a hot gas flows if the system is being charged, or a cold gas if it is being discharged. in a charging process, heat transfer from the hot gas increases 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^3; 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 300 degrees c. the initial temperature of the spheres is ti = 25 degrees c and the convection heat transfer coefficient is h = 75 w/m^2*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?