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The steady conduction regime of exothermic chemical reactions in a packed bed reactor is investigated analytically. A plane-parallel stratification of the reactive granular material is assumed which modulates the rate of the local volumetric heat generation in the reactor. The approach is based on an exactly solvable nonlinear mathematical model which involves two experimentally accessible control parameters, the intensity parameter λ > 0 and stratification parameter s ≥ 0, respectively. In terms of these parameters, the existence domain of the steady temperature solutions and the occurrence of hot spots are discussed. For a given value of the stratification parameter, an upper bound λmax(s) of the intensity parameter has been found, such that above of this maximum value of λ 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. The features of the corresponding temperature distributions are examined in detail.
Journal: Chemical Engineering Journal - Volume 146, Issue 1, 15 January 2009, Pages 136–142