A two-dimensional model of a single channel of a monolith reactor is used to evaluate the values of the Nusselt and Sherwood numbers under reaction conditions. The circular channel is assumed to have axisymmetry with a first-order reaction occurring at the wall. The values of the Nusselt and Sherwood numbers do not correlate uniquely with the Graetz number but rather depend on the reaction rate at the wall. Hence they depend on such variables as gas velocity, inlet temperature and reactant concentration.