Investigation of Magneto Hydrodynamics Properties of Reiner–Philippoff Nanofluid with Gyrotactic Microorganism in a Porous Medium

Investigation of Magneto Hydrodynamics Properties of Reiner–Philippoff Nanofluid with Gyrotactic Microorganism in a Porous Medium Nanofluids have many potential applications in engineering, medicine, and biotechnology due to their enhanced thermal, electrical, and optical properties. However, the flow and heat transfer characteristics of nanofluids are influenced by various factors, such as the type and size of nanoparticles, the base fluid, the magnetic field, the radiation, the chemical reaction, and the presence of microorganisms. Therefore, it is important to study the effects of these factors on the nanofluid flow and heat transfer using mathematical models and numerical methods. One of the mathematical models that can describe the nanofluid flow is the Reiner-Philippoff model, which is a classical non-Newtonian fluid model that accounts for the shear-thinning behaviour of some fluids. The Reiner-Philippoff model has been used to study the nanofluid flow over a stretching sheet, which is a simplified model of many industrial processes involving stretching or shrinking surfaces. However, most of the previous studies have neglected the effects of the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection on the nanofluid flow over a stretching sheet. The objective of this paper is to fill this gap by conducting a numerical investigation of the effects of the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection on a Reiner-Philippoff nanofluid of MHD flow through a stretching sheet. This also considers the effects of thermophoresis and Brownian motion, which are two mechanisms that govern the transport of nanoparticles in nanofluids. The article utilized a similarity transformation to reduce the governing partial differential equations into ordinary differential equations, which are then solved by using the MATLAB computational tool bvp4c technique. The paper also employs a hybrid numerical solution method using Runge-Kutta fourth order with a shooting technique and an optimization technique using the Bayesian regularization method for Runge-Kutta to improve the accuracy of the prediction outcomes. The main finding of this paper is that the Arrhenius reaction, thermal radiation, viscous dissipation, and bio-convection have significant effects on the velocity, temperature, concentration, and motile microorganism profiles of the nanofluid flow over a stretching sheet. The paper also discusses how these effects can be controlled by varying the relevant parameters. This provides graphical results for the profiles of velocity, temperature, concentration, and motile microorganisms for different values of these parameters. The study also compares its results with some existing results in the literature and finds good agreement.