Natural convective flow of a chemically reacting fluid in an annulus

We examine the heat transfer and flow properties induced by natural convection in an annulus between a square enclosure and a circular cylinder filled with a chemically reacting fluid. During the exothermic reaction process in the reacting fluid, there generates heat that induces natural convection in the annulus. The problem is developed defining the vorticity-stream function. We solve it with the use of the finite difference method. The results show that two counter-rotating vortices generate in each half about the vertical symmetry line through the center of the inner cylinder. The lower eddies of the inner vortices get closer and closer with the decrease of the aspect ratio and the increase of the Rayleigh number, Frank-Kamenetskii number, buoyancy force parameter, and Lewis number. Besides this, the eyes of the outer vortices expose similar characteristics for increasing values of the Rayleigh number and buoyancy force parameter, and for decreasing values of the aspect ratio and the Lewis number. It is remarkable that the flow field and the Nusselt number demonstrate completely distinct characteristics for the Lewis number unity, the aspect ratio equal to 0.1, and in the absence of the buoyancy force parameter.