A gas heated steam reformer (GHR) which converts natural gas to synthesis gas for methanol or Fischer-Tropsch purposes has been modelled for steady state conditions. The model is in two dimensions and is made up of a fixed bed reactor model, representing one of the reactor tubes in the GHR, and an annulus model, representing the annular space on the shell side of the GHR where hot, fully converted syngas emits heat to the reactor tube. The annulus model is described and evaluated in this article. This is a plug flow model which involves heat transfer in radial direction caused by radiation and by turbulence. The gas radiation is modelled by the use of the discrete ordinates method and the effect on heat transfer from turbulence is modelled as an effective radial thermal conductivity. Both heat transfer mechanisms vary with the radial position. An additional annulus model, made in the commercial CFD code FLUENT and based on the k-? turbulence model and the discrete ordinates radiation model, is used to estimate effective radial thermal conductivities. These were implemented in the annulus model of the GHR model. The reactor and the annulus models were combined and linked by the wall temperature profile and the heat flux profile on the outer reactor tube wall. The simulation results were used to study the heat flux and temperature profiles along the reactor length and the radial temperature profiles in the annulus.