Mathematical modelling of thermal microexplosion in a catalyst granule with point sources of heat release

A mathematical model of heat and mass transfer in a spherical catalyst granule is proposed. Exothermic synthesis reactions are carried out on point active centres located inside a porous ceramic granule. From the surface of the granule the heat of catalytic reactions is removed into liquid synthesis products. The rate of a chemical reaction is modelled by a modified Arrhenius law. In contrast to the homogeneous model of a catalytic granule methods for calculating heat transfer processes in a system of point, active centres do not develop. An iterative procedure is suggested to calculate the unknown temperature and concentration of the reagent at the active centre. It is shown that the temperature of the active centres is significantly higher than in the volume of the granule. The results of modelling a thermal explosion with increasing granule size and reactor temperature are presented.

On some wavelet solutions of singular differential equations arising in the modeling of chemical and biochemical phenomena

This paper is concerned with the Lane–Emden boundary value problems arising in many real-life problems. Here, we discuss two numerical schemes based on Jacobi and Bernoulli wavelets for the solution of the governing equation of electrohydrodynamic flow in a circular cylindrical conduit, nonlinear heat conduction model in the human head, and non-isothermal reaction–diffusion model equations in a spherical catalyst and a spherical biocatalyst. These methods convert each problem into a system of nonlinear algebraic equations, and on solving them by Newton’s method, we get the approximate analytical solution. We also provide the error bounds of our schemes. Furthermore, we also compare our results with the results in the literature. Numerical experiments show the accuracy and reliability of the proposed methods.

Multi-objective optimization and decision visualization of batch stirred tank reactor based on spherical catalyst particles

This paper presents a Bayesian approach rooted algorithm oriented to the properties of multi-objective optimization problems. The performance of the developed algorithm is compared with several other multi-objective optimization algorithms. The approach is applied to the multiobjective optimization of a batch stirred tank reactor based on spherical catalyst microreactors. The microbioreactors are computationally modeled by a two-compartment model based on reaction–diffusion equations containing a nonlinear term related to the Michaelis–Menten enzyme kinetics. A two-stage visualization procedure based on the multi-dimensional scaling is proposed and applied for the visualization of trade-off solutions and for the selection of favorable configurations of the bioreactor.