Natural convection in the annulus bounded by two wavy wall cylinders having a chemically reacting fluid

Abstract

Abstract We study the flow characteristics of natural convection induced by exothermic reaction in an annulus bounded by two wavy wall cylinders. With a view to achieving the target the dimensionless equations are transformed for the present problem using suitable functions. We solve the new system of equations with the use of finite difference method. Numerical results demonstrate that an increase of the number of crests or troughs of the inner or outer walls of the enclosed domain considerably reduces the strength of streamlines and the maximum temperature. Due to the augmentation of the Frank-Kamenetskii number the intensity of the streamlines and the maximum temperature are found to increase but the minimum value of the concentration decreases. When the Rayleigh number for thermal diffusion is increased, the magnitude of streamlines noticeably increases, whereas there is little effect on the isotherms and isolines of concentration. For larger value of the amplitude of the inner or outer cylinder walls the intensity of streamlines considerably decreases, but the isotherms and the isolines of concentration change a little bit. The remarkable findings are that when Le\u202f=\u202f0.5 and 1.0, the inner and outer major vortices contain two and three eyes respectively. But the streamlines for Le\u202f=\u202f2.0 show distinct characteristics from those for Le\u202f=\u202f0.5 and 1.0. In this case, there occur two elongated and two elliptic vortices adjacent to the inner and outer cylinder walls. The inner elongated vortices hold a single eddy whereas the elongated vortices neighboring the outer cylinder consist of two eddies. Contrary to this, in presence of thermal convection or combined convection for thermal and mass diffusion the inner and outer major vortices have two and three eddies respectively. However, the convection due to mass diffusion yields an astonishing result. Two vortices are recognized near the outer wall while a single vortex is observed adjacent to the inner wall. Both of the inner and the outer elongated vortices consist of two eyes. It is worthy of mentioning that the concept of constructing such a geometry by means of simple transformations might encourage the researchers to think for generating a more complex geometry. Moreover, these results could be useful for the advancement in science, engineering and technology.