The fixed-bed reactors of circular cylindrical geometry with heated or cooled walls are frequently used to carry out heterogeneous reactions of solid-gas type in engineering applications. The design of a fixed bed reactor requires an extensive knowledge of heat transfer characteristics within the packed bed. In this sense, this work presents a three-dimensional mathematical model to predict the heat transfer inside a fixed bed elliptical cylinder heat exchanger. The model considers uniform velocity and temperature profiles of the fluid phase at the entrance of the reactor, and constant thermo-physical properties. The surface of the equipment convective boundary condition is assumed to be constant. The energy equation, written in the elliptical cylindrical coordinates, was discretized using a finite-volume method considering a fully implicit formulation, and WUDS interpolation scheme. Numerical results of the dimensionless temperature profiles inside the packed bed reactor at a steady state are presented and temperature distribution is interpreted. To validate the model, numerical results obtained for the circular cylinder are compared with analytical results from literature and a good agreement was obtained.