A mathematical model for the temperature effect in a catalytic reactor with heat source/sink

The purpose of this study is to consider analytically the temperature effect in a catalytic reactor. We model the catalytic reactor as a long cylindrical porous pipe packed with tiny spheres with a coating of a catalytic material filled with a reagent (gas). At time t < 0, a steady motion of a chemically reacting dilute binary mixture of the reagent exists. At time t = 0, a constant pressure gradient is applied at one end of the tube. Expressions for transient flow variables are sought analytically. Our results, which are in agreement with earlier reports, show that the temperature across the cylinder is uniform and the time to achieve steady state for the axial velocity w is different from that for the concentration c.