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 lambda > 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 lambda(max)(s) of the intensity parameter has been found, such that above of this Maximum value of lambda the reactor becomes thermally uncontrollable. Below unique as well as dual solutions exist. The former ones describe high temperature steady states lambda(max)(s). 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. (c) 2008 Elsevier B.V. All rights reserved.