Linear stability analysis of the steady thermal regimes of a packed bed reactor with an organized structure

The linear stability of steady temperature distributions in a parallel-plane packed bed reactor is investigated analytically and numerically. A plane-parallel stratification of the reactive granular material is assumed which modulates the rate of the local volumetric heat generation by exothermic reactions. The approach is based on an exactly solvable nonlinear model which involves two experimentally accessible control parameters, the intensity parameter λ>0 and stratification parameter s⩾0. For a given value of s, an upper bound λmax(s) of λ exists, such that above of this maximum the reactor becomes thermally uncontrollable. Below λmax(s), unique as well as dual solutions exist. The former ones describe high temperature steady states of the reactor, while the dual solution branches are associated with low and high temperature reaction regimes, respectively. It is found that the low temperature branch is always linearly stable and the upper one unstable. The steady state of the reactor corresponding to the matching point λ=λmax(s) of the low- and high-temperature solutions is marginally stable for all s⩾0.