Hall device impacts on ciliated pump-assisted blood flow of double-diffusion convection of nanofluid in a porous divergent channel

Motivated by bio-chemical systems and ciliated propulsion, we consider the steady laminar flow from a non-uniform wavy channel adjacent to a saturated porous medium which has been investigated analytically using an integration technique. A highly permeability domain is considered. We employed a sinusoidal complex wavy relation for the ciliated walls. A mathematical relation was used to convert the rheological equations from $$\big(\bar{X},\bar{\xi }\big)$$ coordinate system to a $$\big(\bar{x},\bar{\xi }\big)$$ dimensionless system. These rheological equations are simplified under two biological assumptions, one is creeping phenomena, and the second one is long-wavelength approximation. The solution of governing equations is obtained through Mathematica software 10.0 with the help of integration technique in a wave frame. The impacts of embedded hydro-mechanical parameters on the rheological features are studied. The boundary layer phenomena are obtained in the velocity profile under larger magnetic and porosity effects. The magnitude of pressure gradient is reduced under larger strength of magnetic and porosity effects. The cilia length parameter has a dynamic role in enhancement of the pressure gradient. The larger strength of the thermophoretic parameter has remarkable effects in augmentation of volumetric fraction, heat and mass transfer phenomena. The outcomes of current investigation are applicable in energy systems, manufacturing of ciliated micro-pumps, petroleum engineering, thermal augmentation of physiological and chemical fluids, and industrial magnetic materials processing.