Transport effects on pattern formation and maximum temperature in homogeneous-heterogeneous combustion

We study the impact of the Lewis number, Lef (thermal diffusivity of the reaction mixture to the molecular diffusivity of the limiting reactant) and the Peclet numbers on the maximum temperature attained for coupled homogeneous-heterogeneous combustion process in a parallel plate reactor using one, two and three-dimensional models. For the case of 1-D models, we find that the maximum temperature never exceeds the adiabatic value for physically consistent boundary conditions. For 2-D models, we find that for Lef<1, the hot spot temperature can exceed the adiabatic value, it is always located on the wall and its distance from the inlet and magnitude increase with increasing radial Peclet number. However, for Lef>1, contrary to some literature claims (Zheng and Mantzaras, 2014), the peak temperature never exceeds the adiabatic value, though the temperature can be non-monotontic across the channel. We show that 3-D solutions can bifurcate either from 1-D or 2-D solutions irrespective of the value of the Lewis number. It is also shown that an infinite number of solutions that are discontinuous in the axial coordinate can exist for the common case of large axial heat Peclet number. The implications of these observations for catalyst and process design in systems in which both homogeneous and catalytic reactions occur are discussed.