On the Stability of a Steady Convective Flow in a Vertical Layer of a Chemically Reacting Fluid

Abstract

Linear stability of a steady flow of a chemically reacting fluid located in a vertical fluid layer bounded by two infinite parallel planes is investigated. Steady convective flow in the vertical direction is initiated due to the combined effect of internal heat generation and the temperature difference between the planes. Imposing small perturbations on the base flow, linearizing equations of thermal convection under the Boussinesq approximation in the neighbourhood of the base flow and using the method of normal modes we obtain an eigenvalue problem for a system of ordinary differential equations. Collocation method is used to discretize the problem. Numerical calculations are performed in Matlab. Fluid velocity, pressure, and temperature are the solutions of a nonlinear boundary value problem. Properties of the nonlinear boundary value problem for the base flow are investigated numerically using bifurcation analysis. It is shown that both the temperature difference between the planes and intensity of internal heat generation have a destabilizing influence on the base flow. The intensity of heat transfer in the direction perpendicular to the main flow can promote instability and leads to more intensive mixing. This fact can be used in design of bioreactors for biomass thermal conversion.