The simulation of correct flow and pressure fields in the radiation section of industrial thermal cracking furnaces is of practical interest since the amount of combustion air taken in by the burners in general is partly determined by the pressure field. For such engineering purposes often a (practical) simplified numerical treatment of the viscous terms in the flow equations is used to reduce the computational cost. It is shown that the interaction between such a simplified numerical treatment of the viscous terms and the alignment of the cell interfaces with the coordinate system can result in an erroneous (non-physical) calculation of the pressure field. This alignment problem is predominantly present when using a semi non-structured prismatic grid to solve the flow equations. Using a fully non-structured tetrahedral grid avoids this problem because of the random orientation of the cell interfaces for this type of grid. This is confirmed by assuring that the calculation results are independent with respect to grid refinement. At the same time the influence of the presence of the reactor tubes on the velocity field inside the furnace is examined: (C) 2003 Elsevier Ltd. All rights reserved.