**8. Multi-step reaction models**

Models for premixed PM combustion are complicated by the highly nonlinear radiative exchange terms in the energy equation for the solid matrix in addition to the stiffness of the set of gas phase equations. Therefore researchers have simulated the gas phase reactions using single-step chemistry. However, few researchers had taken up this issue and presented multi-step reaction models. It was concluded that use multi-step kinetics is essential for accurate predictions of the temperature distributions, energy release rates, and emissions. Single-step kinetics was shown to be adequate for predicting all the flame characteristics except the emissions for the very lean conditions under which equilibrium favors the more complete combustion process dictated by global chemistry. full mechanism (49 species and 227 elemental reactions), skeletal mechanism (26 species and 77 elemental reactions), 4-step reduced mechanism 9 species and 1-step global mechanism.

In the open literature, there are few articles concerning the interaction between a fuel spray and a PM. The PM under study was of high porosity with uniformly distributed spheres and with uniform distribution of cavities with equal mean pore size in the porous medium. The interaction between droplets during evaporation was neglected. Physical properties of fuel such as latent heat of evaporation and healing value were constant. The temperature distribution inside of the fuel droplet was uniform, but time-varying. Laminar isobaric flow consits of air, fuel droplets, gaseous combustible mixture and hot products of combustion. After evaporation the fuel mixes immediately with air to form a homogeneous combustible mixture. Mass fraction of the liquid was negligible, and the gas was optically transparent. Also, radiative heat transfer between the skeleton surfaces of the porous medium can be considered.
