The fixed bed reactor is packed with catalyst pellets with cylindrical shape. The radius is 3mm and the height is 6mm. The reactor is designed to operate isothermally at 800K, in the startup phase, inert gas with 1000K will be injected into the reactor to heat up the pellets before the reactant. The physical properties of the catalyst are as below: Thermal conductivity = 97.5 W/mK Density = 8.90 g/cm3 Heat capacity = 0.46 kJ/(kg K) a) Calculate the time required to heat up the center of the catalyst pellet to 800K from 300K as requested. b) If we replace the pellets with spherical particles of equivalent volume. Calculate the time required to heat up the center of the sphere to 800K (also from 300K)