A steam reformer is a chemical reactor to produce high purity hydrogen from fossil fuel. In the steam reformer, since endothermic steam reforming is heated by exothermic combustion of fossil fuel, the heat transfer between two reaction zones dominates conversion of fossil fuel to hydrogen. Steam Reforming is complex chemical reaction, mass and heat transfer due to the exothermic methane/air combustion reaction and the endothermic steam reforming reaction. Typically, a steam reformer employs burner to supply appropriate heat for endothermic steam reforming reaction which reduces system efficiency. In this study, the heat of steam reforming reaction is provided by anode-off gas combustion of stationary fuel cell. This paper presents a optimization of heat transfer effect and average temperature of cross-section using two-dimensional models of a coaxial cylindrical reactor, and analysis three-dimensional models of a coaxial cylindrical steam reformer with chemical reaction. Numerical analysis needs to dominant chemical reaction that are assumed as a Steam Reforming (SR) reaction, a Water-Gas Shift (WGS) reaction, and a Direct Steam Reforming(DSR) reaction. The major parameters of analysis are temperature, fuel conversion and heat flux in the coaxial reactor.