Buoyancy effects on nanoliquids film flow through a porous medium with gyrotactic microorganisms and cubic autocatalysis chemical reaction

This article is based on the mathematical model constructed to analyze the simultaneous flow and heat transfer of two nanoliquids (Casson and Williamson) in the presence of gyrotactic microorganisms and cubic autocatalysis chemical reaction through a porous medium under the potentiality of buoyancy forces. Heterogeneous reaction existing on the surface is described by isothermal cubic autocatalytic chemical reaction, whereas homogeneous reaction is taking place at far field described by first-order kinetics. Similarity transformations are used to get the different order differential equations from the governing equations which are solved via an efficient technique namely homotopy analysis method. The effects of all the non-dimensional parameters on velocity, temperature, concentration, and density of motile microorganisms are shown through graphs and elucidated. Velocity increases with the Weissenberg parameter and decreases with the Casson nanofluid parameter in the presence of magnetic field and porous medium. Temperature decreases with the high values of slip condition. The dual behavior of concentration profile for the strength of homogeneous reaction parameter is observed. Flow of microorganisms decreases based on the parameters of porous medium, magnetic field, and heterogeneous chemical reaction. There exists an excellent agreement between the present and published work.