Consider the packed bed of aluminum spheres described in Problem 5.12 under conditions for which the bed is charged by hot air with an inlet velocity of V = 1 m/s and temperature of T_g,i = 300°C, but for which the convection coefficient is not prescribed. If the porosity of the bed is £ = 0.40 and the initial temperature of the spheres is T_i = 25°C, how long does it take a sphere near the inlet of the bed to accumulate 90% of its maximum possible energy?