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Due to the endothermic nature of the steam methane reforming reaction, the process is often limited by the heat transfer behavior in the reactors. Poor thermal behavior sometimes leads to slow reaction kinetics, which is characterized by the presence of cold spots in the catalytic zones. Within this framework, the present work consists on a numerical investigation, in conjunction with an experimental one, on the one-dimensional heat transfer phenomenon during the heat supply of a catalytic-wall reactor, which is designed for hydrogen production. The studied reactor is inserted in an electric furnace where the heat requirement of the endothermic reaction is supplied by electric heating system. During the heat supply, an unknown heat flux density, received by the reactive flow, is estimated using inverse methods. In the basis of the catalytic-wall reactor model, an experimental setup is engineered in situ to measure the temperature distribution. Then after, the measurements are injected in the numerical heat flux estimation procedure, which is based on the Function Specification Method (FSM). The measured and estimated temperatures are confronted and the heat flux density which crosses the reactor wall is determined. [ABSTRACT FROM AUTHOR]