Analysis of couple stress nanofluid flow under convective condition in the temperature-dependent fluid properties and Lorentz forces

In recent years, a great deal of interest has been generated in modern micro- and nanotechnologies for micro/nano-electronic devices. These technologies are increasingly utilizing sophisticated fluid media to enhance performance. Among the new trends is the simultaneous adoption of nanofluids and biological micro-organisms. Motivated by bio-nanofluid vertical channel oxygenators in medical engineering, in the current work, a mathematical model is developed to examine the flow of mixed convective couple-stress nanofluids in a vertical channel with a transverse magnetic field, fluid viscosity that changes with temperature, and thermal conductivity. The non-Newtonian model follows Brownian motion and heat spread by nanoparticles in a fluid under coupled stress. Highly linked, nonlinear regulating equations are translated into non-dimensional equations using relevant variables. The governing equations are then turned into a form with no dimensions. The Kellerbox technique, a second-order finite difference method for solving second-order equations, is used to solve them numerically. On the other hand, the effects of different non-Newtonian flow parameters, such as the couple stress fluid parameter, the magnetic parameter, the variable fluid viscosity, the variable thermal conductivity parameters, the Brinkman number, the nanofluid and buoyancy parameters, and the rate of chemical reaction parameter, are carefully studied. The velocity, temperature, and concentration fields are calculated over a wide range of possible values for the relevant parameters.