Isothermal autocatalysis of homogeneous–heterogeneous chemical reaction in the nanofluid flowing in a diverging channel in the presence of bioconvection

Abstract

The nonlinear differential equations play a prominent role in the mathematical description of many phenomena that occur in our world. A similar set of equations appear in this paper that govern the homogeneous and heterogeneous chemical reactions in the nanofluid flowing between two non-parallel walls. Since the concentration of the homogeneous species is substantially high, quartic autocatalysis is considered for the analysis. It is found to be more effective than the cubic autocatalysis. Further, to avoid the deposition of nanoparticles on the surface, self-propelled microorganisms called gyrotactic microorganisms are allowed to swim in the nanofluid. This movement of microorganisms constitutes a major phenomenon called bioconvection. The set of governing equations thus formed are made dimensionless and the resulting system of equations are solved by Differential Transformation Method (DTM) with the help of Padé approximant that reduces the power series into rational function. This transformation helps in achieving a better convergence rate. The fluid flow analysis is interpreted through graphs and tables where it is observed that the heat source enhances the temperature of the nanofluid. Further, the homogeneous and heterogeneous chemical reaction parameters have significant impacts on the concentration of the reactants. Also, the outcomes indicated that the reaction profiles and motile density profiles increase with the increase in Schmidt number.