Furthermore, the work of is also directly related to the study presented herein. The authors developed a semi-analytical solution for an isothermal wall MBR model to distributed parameters in the particles and to lumped parameters in the fluid phase (hereinafter this model and the semianalytical solution of will simply be referred to as DM and SA, respectively), assuming -among other simplifications -irreversible chemical reaction occurring uniformly within spherical particles, and constant radiative heat transfer coefficient ℎ $ -this hypothesis was mitigated by means of a corrective step, in which ℎ $ is taken equal to the arithmetic mean between its value at the reactor inlet and its value at the discretization point. The solution was developed from the analytical solution of the associated homogeneous (linear) problem and the spectral expansion of the nonhomogeneous vector. The simulations accurately predicted kaolinite flash calcination's temperature and conversion profiles . The main distinctions between DM and the model of this study are as follows: in the latter, the particle is modeled to lumped parameters, a strategy that simplifies the model. Regarding the implementation of the solutions, in SAS, ℎ $ is evaluated locally, i.e., at the discretization point, in better correspondence to physical reality. In SA, however, it is assumed to be constant throughout the reactor (or corrected, as described above). Furthermore, although the DM is to distributed parameters for the solid phase, the SA assumes, for each discretization interval, a uniform reaction rate for the particle (calculated at a volumetric average particle temperature). SAS will be developed using FAM concepts : decomposition of the problem region into small intervals; maintaining terms as linear and evaluated under the conditions at the beginning of each interval; obtaining local analytical solutions in these intervals. Although there are studies/applications aiming to generalize the FAM (e.g., ; de Almeida Jr., 2016; , one of the difficulties in applying of the original finite analytical method is since for each case there is a solution. Several applications of the method (see, ) demonstrate this difficulty. Among the applications of FAM for chemically reactive systems is the work of , who used the practical FAM proposed by to solve a model to describe the transport of contaminants dissolved in groundwater.