Unsteady behaviors of natural convection flow of a reactant in a thin finned enclosure

Steady, oscillating, and chaotic behaviors of natural convection flow of a reacting chemical are investigated taking into account the effects of a fin attached to the left vertical wall of a square enclosure. The steady-state results expose that an increase in the Rayleigh number for thermal diffusion leads to higher convection but lower temperature. On the other hand, the magnitude of the stream function, maximum temperature, and heat transfer through the walls of the cavity significantly increase with higher Frank-Kamenetskii number. When the height of the fin is increased, the convective flow and the maximum temperature are found to considerably decrease. For continued increasing of Rayleigh number and Frank-Kamenetskii number from their lower values, the convection demonstrates steady-state, oscillating to steady-state, single-periodic oscillating, multi-periodic oscillating, and chaotic characteristics. Moreover, the region of the steady-state convection for the fin in the middle of the left vertical wall is wider in comparison to that of the fin at 0.7. However, the converse results have been recognized for single-periodic and multi-periodic regions.