The highest number of non-orthogonal cells and consequently the largest effect of the secondary gradient on the simulation results is expected for unstructured meshes of complex geometries. Therefore, the influence of the secondary gradient on integral and distributed quantities is investigated for the flow through a short packed bed containing ring shaped VPO catalyst particles. The simulation setup described in section 4.3 is calculated once with consideration of the secondary gradient and once without it ( Ṡκ = 0). The quotient Â• Â Â•êb can be used to quantify the level of non-orthogonality of an interfacenearest computational cell. The closer this quotient is to unity the more similar the cell is to a perfectly orthogonal cell. Figure shows the probability distribution of Â• Â Â•êb for the interface-nearest cells and illustrates that a large percentage of the interfacenearest cells on the fluid and solid side can be assumed to be approximately orthogonal. However, especially at the fluid side, there are a few cells, which significantly deviate from orthogonality. Table lists various integral quantities characteristic of catalyst performance and heat removal obtained from simulations with and without secondary gradient. The values calculated neglecting the secondary gradient differ only slightly from the values computed considering the secondary gradient. This indicates that applying the secondary gradient has a minor impact on the integral results of the simulation even for calculations with complex geometries. The small effect of the secondary gradient on integral quantities can be attributed to the high percentage of approximately orthogonal cells shown in Figure . This is in line with the finding of , who concluded that the secondary gradient can be neglected for cells close to orthogonality. To study the impact of the secondary gradient on distributed quantities, the deviation between the simulation with and without secondary gradient for the temperature and the mass fraction of n-butane at the fluid-solid interface is calculated and shown in Figure . Due to the large number of approximately orthogonal cells, the difference between the simulations with and without secondary gradient is negligible for most of the temperatures and C 4 H 10 mass fractions at the interface. Nevertheless, there are regions on the particle surface at which the non-orthogonality of the interface-nearest cells results in deviations between simulation with and without secondary gradient by up to 0.5 % in the temperature and by up to 8.2 % in the C 4 H 10 mass fraction. As illustrated in the supplementary information (SI Section S8), these regions are frequently located around particle-particle and particle-wall contacts, where the close proximity between surfaces results in non-orthogonal computational cells. In these regions, the high value of the quotient Â• Â Â•êb results in an increase of the secondary gradient term (see Equation ) and consequently its value becomes more important for the calculation of the scalar or scalar flux value at the fluid-solid interface. This demonstrates that neglecting the secondary gradient can locally have a significant effect on the temperatures and mass fractions at the particle surface. Not applying secondary gradients in the conjugated heat and mass transfer model results in similar integral quantities as considering the secondary gradient, but may causes local deviations in the temperature and mass fractions distribution. For computational meshes with a higher amount of strongly non-orthogonal cells at the particle surface, it can be assumed that the local influence of the secondary gradient also effects integral quantities. Both simulations, with and without secondary gradient, reach convergence after 10, 000 iteration steps. The CPU time per iteration of the simulation neglecting the secondary gradient is 252.67 s, while for the simulation considering the secondary gradient this value increases slightly to 252.85 s. Since significant differences in computational time and numerical stability between the simulation with and without secondary gradient cannot be found, it is recommended to consider the secondary gradient in the CHT and CMT model. Therefore, all further results presented in this study are based on the simulation with secondary gradient.