An entry-flow problem for a non-isothermal catalytic-wall reactor

A reacting gas flows into a metal, thin-walled, tube which has a catalytic coating on its inner surface. A strong, temperature-dependent, exothermic reaction occurs giving a local hos spot. It is assumed that the surface temperature is controlled by heat conduction through the metal wall, heat transfer into the gas being negligible. A standard approximate technique is used to derive an integral equation which relates the mass transfer at the wall in the Blasius boundary layer to the wall temperature. A second integral equation is derived from the heat-conduction problem for the metal wall, and the coupled equations are solved numerically. The maximum temperature rise at the wall is found to be significantly higher than that obtained when a fully developed flow passes over a catalytic coating.