EMHD creeping rheology of nanofluid through a micro-channel via ciliated propulsion under porosity and thermal effects

The mathematical study is modeled to examine the physical impacts of porosity and thermal slip on flow features of nanofluid through an asymmetric micro-channel. Additionally, the effects of electro-osmosis and magnetic field are also under consideration. Convective boundary conditions are used in the current study by neglecting thermal and buoyancy forces. The obtained rheological equations are transformed into non-dimensional flow systems by using scaling variables. These rheological equations are elucidated by using the creeping approximation and low zeta potential (the Debye–Hückel linearization). The exact solutions of rheological equations are evaluated via Mathematica software 11.0. The dynamic impacts of embedded parameters such as Hartmann number, electro-osmosis parameter, Darcy's number, Brinkman number, Helmholtz–Smoluchowski velocity, slip parameter, thermal radiation, cilia length parameter and Prandtl number on the rheological features are presented graphically via Mathematica software 11.0. The whole analysis is based upon train waves of metachronal propulsion. Three-dimensional graphs are plotted in the current investigation to get more obvious behavior of embedded on the flow features. The cilia length parameter has a remarkable character in enhancing the magnitude of velocity profiles, while, and opposite actions is perceived in the graph of pressure gradient. The thermal slip parameters have an energetic impact in reducing the temperature profile magnitude. The outcomes revealed a good understanding into biomimetic energy frameworks taking advantage of electroosmosis, magnetism and nanotechnology, and, besides, they outfit a valuable benchmark for numerical and experimental multi-physics recreations.