An annular chemical reactor consists of a packed bed of catalyst between two coaxial cylinders. The inner and outer cylinders have radii of ro and ri, respectively. It is reasonable to assume that...

P1

Extracted text: An annular chemical reactor consists of a packed bed of catalyst between two coaxial cylinders. The inner and outer cylinders have radii of ro and ri, respectively. It is reasonable to assume that there is no heat transfer through the surface of the inner cylinder, which is at a constant temperature To. The catalytic reaction releases heat at a uniform volumetric rate, S, throughout the reactor, whose effective thermal conductivity k may be considered constant. Neglect the temperature gradients in the axial direction. a) Derive a second-order differential equation to describe the radial temperature distribution in the annular reactor starting with a shell thermal energy balance.