Abstract
A Generalized Integral Transform Technique (GITT) solution scheme for transient non-linear heat and mass diffusion in chemically reacting systems with Michaelis–Menten type kinetics has been developed. A model with two one-dimensional coupled PDEs was selected for illustrating the solution methodology, in which temperature and substrate concentration are the dependent variables. Although the model is one-dimensional, a generalized formulation valid for both plane and curved systems was employed. The main novelty of this investigation is the treatment of the reaction kinetics term, whose functional form is a major obstacle for GITT solutions. This term was resolved by an automatic scheme based on Taylor Series approximations for which the expansion point can be progressively updated with the numerical time-integration, using data from the previous time-step. The outcome of the solution implementation is then verified with data from a reference finite-volumes solution, exhibiting a very good agreement. Finally, illustrative results of averaged temperature and substrate concentration are presented, showing that different type of solutions are obtained within the considered range of dimensionless parameters.
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