Modelling of a closed two-dimensional reactor bounded by a wavy wall

In this paper, we propose a model for a two-dimensional closed reactor bounded by a wavy wall. The left, right and top walls of the reactor are assumed to be flat surfaces while the bottom wall is a wavy surface. In order to formulate a model for such a reactor, we introduce a coordinate transformation into the dimensionless equations of a rectangular closed domain. Then the resulting equations illustrate the phenomena for a closed reactor bounded by a wavy wall. We solve these equations using the finite difference method. The astonishing results are that the intensity of streamlines and the maximum temperature within the reactor significantly increase with an increase of the number of waves in the bottom wall, the amplitude of waves and the Frank-Kamenetskii number. Converse characteristics are observed for higher values of the enlargement of a wave. Moreover, larger Rayleigh number induces stronger vortices in the flow field and reduces the maximum temperature. The Nusselt number at the bottom wavy wall is found to increase for higher values of the Frank-Kamenetskii number and the amplitude of a wave. A transition from the steady-state to the oscillatory convection is identified for a certain value of the Frank-Kamenetskii number. However, for a low value of the Rayleigh number, there occurs a transition from the steady-state to an explosion for increasing value of the Frank-Kamenetskii number. Results also demonstrate that the critical value of the Frank-Kamenetskii number, for which a transition from the steady-state to the oscillatory convection occurs, is higher for increasing values of the number of waves, the enlargement of a wave and the amplitude of a wave.