No alternatives are currently available to operate industrial furnaces, except for hydrocarbon fuels. Plant managers, therefore, face at least two challenges. First, environmental legislation demands emission reduction. Second, changes in the origin of the fuel might cause unforeseen changes in the heat release. This paper develops the hypothesis for the detailed control of the combustion process using computational fluid dynamic models. A full-scale mock-up of a rotary cement kiln is selected as a case study. The kiln is fired by the non-premixed combustion of Dutch natural gas. The gas is injected at Mach 0.6 via a multi-nozzle burner located at the outlet of an axially mounted fuel pipe. The preheated combustion air is fed in (co-flow) through a rectangular inlet situated above the attachment of the fuel pipe. The multi-jet nozzle burner enhances the entrainment of the air in the fuel jet. A diffusion flame is formed by thin reaction zones where the fuel and oxidizer meet. The heat formed is transported through the freeboard, mainly via radiation in a participating medium. This turbulent combustion process is modeled using unsteady Favre-averaged compressible Navier–Stokes equations. The standard k-ϵ equations and standard wall functions close the turbulent flow description. The eddy dissipation concept model is used to describe the combustion process. Here, only the presence of methane in the composition of the fuel is accounted for. Furthermore, the single-step reaction mechanism is chosen. The heat released radiates throughout the freeboard space. This process is described using a P1-radiation model with a constant thermal absorption coefficient. The flow, combustion, and radiative heat transfer are solved numerically using the OpenFoam simulation software. The equations for flow, combustion, and radiant heat transfer are discretized on a mesh locally refined near the burner outlet and solved numerically using the OpenFoam simulation software. The main results are as follows. The meticulously crafted mesh combined with the outlet condition that avoids pressure reflections cause the solver to converge in a stable manner. Predictions for velocity, pressure, temperature, and species distribution are now closer to manufacturing conditions. Computed temperate and species values are key to deducing the flame length and shape. The radiative heat flux to the wall peaks at the tip of the flame. This should allow us to measure the flame length indirectly from exterior wall temperature values. The amount of thermal nitric oxide formed in the flame is quantified. The main implication of this study is that the numerical model developed in this paper reveals valuable information on the combustion process in the kiln that otherwise would not be available. This information can be used to increase fuel efficiency, reduce spurious peak temperatures, and reduce pollutant emissions. The impact of the unsteady nature of the flow on the chemical species concentration and temperature distribution is illustrated in an accompanying video.