Convective stability of a chemically reacting fluid in an annulus

Linear stability of a steady convective motion of a viscous incompressible fluid generated by internal heat sources in a tall vertical annulus is investigated. The heat sources are distributed within the fluid in accordance with the Arrhenius law. The problem for the determination of base flow in this case is nonlinear. The base flow velocity and temperature distribution is obtained numerically using Matlab. Linear stability of the base flow is investigated with respect to asymmetric perturbations. The stability bound- ary depends on the two parameters: the Prandtl number and the Frank-Kamenetskii parameter. It is shown that even for small Prandtl numbers (in contrast with the case of uniformly distributed heat sources) marginal stability curves consist of two separate brances. Calculations show that the base flow is destabilized as both parameters (the Prandtl number and the Frank-Kamenetskii parameter) increase