Abstract
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.
Highlights
The assortment of the structure, propulsive movement, and nutritive behavior of phytoplankton has long motivated the fluid physicists
Palwasha et al.[17] analyzed porous medium in a nonNewtonian nanofluid thin films flow with magnetotactic microbes using the passively controlled nanofluid model and discussed the effects of different parameters on heat and mass transfer as well as gyrotactic microorganisms
It is attempted to analyze the behaviors of homogeneous–heterogeneous chemical reactions and gyrotactic microorganisms in gravity-driven Casson and Williamson nanofluids flow through a porous medium with heat transfer
Summary
The assortment of the structure, propulsive movement, and nutritive behavior of phytoplankton has long motivated the fluid physicists. Zuhra et al.[11] discussed thin film nonNewtonian Casson and Williamson nanofluids flow in the presence of heat transfer properties with water as the base fluid which contains graphene nanoparticles. Palwasha et al.[17] analyzed porous medium in a nonNewtonian nanofluid thin films flow with magnetotactic microbes using the passively controlled nanofluid model and discussed the effects of different parameters on heat and mass transfer as well as gyrotactic microorganisms. Interest toward this side is rare in literature For this purpose, it is attempted to analyze the behaviors of homogeneous–heterogeneous chemical reactions and gyrotactic microorganisms in gravity-driven Casson and Williamson nanofluids flow through a porous medium with heat transfer. The basic governing boundary layer equations of 2D, steady thin film heat and mass transfer flow with gyrotactic microorganisms and heterogenous– homogeneous chemical reactions are as in literature[17,21]. Using equation (10) in equations (2)–(6), (8), and (9), the final set of governing non-dimensional equations of flow, temperature, homogeneous–heterogeneous chemical reactions and gyrotactic microorganisms concentration are achieved as q
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