In the present work the partial oxidation of methanol to formaldehyde has been studied as an example of strongly exothermic reaction affected by internal diffusion in order to deep the topic of mass and heat transfer in packed-bed catalytic reactors both at particle level, introducing the calculation of the effectiveness factor for complex reactions network, and at reactor level, for what concerns long range gradients of composition and temperature. The aim of the work is to stress the impact of the use of rigorous numerical methods, today possible for the high performances reached by the computers, in the solution of a simultaneous set of many differential equations that are necessary to describe completely the mentioned system. A complete mathematical model of the particle and the reactor is presented and a solution strategy is reported for the chosen reaction by considering a reliable kinetic law and evaluating related parameters from experimental data reported by the literature. Calculation results are reported for both particle internal profiles and reactor simulation. The described approach can easily be extended to many other devices and reactors geometry such as, e.g., the ones used in the field of environmental catalysis.