Modeling of a reactor with exothermic reaction bounded by two concentric cylinders

Abstract

A model is developed to investigate the natural convection flow in a reactor bounded by two concentric cylinders. Using a simple transformation, the governing equations for a rectangular closed domain are transformed into a system of equations which are valid for a reactor of concentric annulus. These equations have been solved using an implicit finite difference method. Numerical solutions reveal that two counter-rotating vortices are built up in each half of the annulus. The clockwise flow circulation in the inner vortex and the anticlockwise flow circulation in the outer vortex are found in the left half of the annulus. However, the reverse characteristics are observed in the right half of the annulus. The remarkable results are that the concentric characteristics of isotherms are not maintained for higher values of the Frank-Kamenetskii number, Rayleigh number, and outer radius of the annulus. In this case, a local maximum value of the Nusselt number at the inner cylinder wall is identified at the bottom of the annulus. For a fixed value of the Rayleigh number and outer radius of the annulus, an explosion occurred in the system for a higher value of the Frank-Kamenetskii number. With the increase of the Rayleigh number, the critical limit of the Frank-Kamenetskii number for the explosion of the system is found to increase. On the contrary, it significantly reduces owing to the increase of the outer radius of the annulus.