Sisko fluid flow through a non-Darcian micro-channel: An analysis of quadratic convection and electro-magneto-hydrodynamics

Microfluidics is used in a range of applications, including conversion of energy, biological diagnostics, and chemical processes. To improve these applications, it is essential to better understand the rheology of the non-Newtonian fluid movement through micro-channels. The purpose of this paper is to examine a Sisko fluid moving through a micro-channel in the presence of electro-magneto-hydrodynamic (EMHD) forces. The Darcy-Brinkmann-Forchheimer (DBF) model is applied. In addition, quadratic convection effects are used to investigate the rehology of the Sisko fluid model. Because it can accommodate a greater range of variables that can known experimental data, the Sisko fluid model is more suited for evaluating the flow dynamics. Furthermore, it is a simple model to apply and easier to adopt for a variety of industrial applications. Other elements, such as viscosity dissipation and Joule heating, are also incorporated in the model. Since the mathematical modeling is nonlinear we adopt a shooting numerical technique to solve it. The results of the computations are given in graphs and tables for all of the parameters in the governing equations. The velocity and temperature profiles are substantially enhanced as a result of the Brinkmann number’s strong influence. The opposite effect is observed when the generation parameter (generated by the interaction of electric and magnetic forces) increases. The velocity field and temperature profiles are adversely affected by the magnetic field, but they are enhanced by the electric field.