Chapter 3, Problem 3.132P

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 $\left(\rho =2700kg/m^3,c=950J/kg\cdot K,k=240W/m\cdot K\right)$ and a charging process for which gas enters the storage unit at a temperature of $T_{g,i}=300°C$. If the initial temperature of the spheres is $T_i=25°C$ and the convection coefficient is $h=75W/m^2\cdot K$, 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?