The Process and Energy department of the 3mE faculty of TU Delft and the Dutch company Petrogas Gas-Systems B.V. are working together on the commissioning of a small 50 kWth Indirectly Heated Bubbling Fluidized Bed Steam Reformer (IHBFB-SR) heated by two radiant tube burners placed vertically inside the reactor. This is a new approach on indirectly heating as the heat is released from the inside to the outside, compared to existing indirectly heated gasifiers, where the heat is released from the outside to the inside. The main objective of this thesis has been to analyze the hydrodynamics and heat transfer occurring within the reactor, by applying "Computational Fluid Dynamics" (CFD) techniques. The analysis has been carried out using the commercial CFD software ANSYS® FLUENT. First the physical phenomena occurring within the reactor have been identified and then research was done on the models and parameters developed to describe the physical phenomena. First the hydrodynamic behaviour was evaluated and then it was looked into how the heat transfer can be coupled to the hydrodynamics in the reactor. In regards to the hydrodynamics, the Euler-Euler Two-Fluid Model (TFM) has been found to be appropriate, and the inter-phase drag coefficient was chosen as a parameter of interest. The Gidaspow drag model and the Syamlal-O-Brien modelwere compared to one another, and the solid volume fraction, pressure, axial velocity and granular temperature within the reactor were evaluated. The results were compared to the numerical solutions obtained in previous work, in order to understand which model gives a better prediction. The Gidaspow drag model was found to provide a better prediction of the core annular flow in the bed zone, and was therefore implemented in the heat transfer evaluation. In regards to the heat transfer, models were already developed for the conductive and convective heat transfer in multiphase flows. For radiation there is still a lack of rigorous coupling between radiative heat transfer and hydrodynamics in simulations of non-dilute multiphase flows. The heat transfer simulation was performed in two steps, first with only the conductive and convective heat transfer, and then with radiation added to the system. The thermal properties such as the thermal conductivity, absorption and scattering coefficient have been made dependent of the volume fraction. For the case without radiation, a small temperature increase was observed with high temperature gradients near the wall. For the case with radiation, the Discrete-Ordinates (DO) Radiation model was evaluated. From the results it can be concluded that the DO Radiation model overpredicts the radiation that is emitted and scattered from the bed, causing the bed to heat up continuously to temperatures much higher than the radiant tube. More research and experimental validation is required in order to improve the coupling of the radiative heat transfer to the hydrodynamics.