Physical aspects of radiative Carreau nanofluid flow with motile microorganisms movement under yield stress <i>via</i> oblique penetrable wedge

Abstract Oil extraction, renewable energy, and biological heat transfer are the major applications of radiative Carreau nanofluid flow in the existence of microorganisms moving around a permeable wedge. This work examines the time-dependent flowing of two-phase Carreau nanofluid containing gyrostatic motile bacteria via permeable oblique wedge in the existence of heat source (sink) and thermal radiation. Magnetoelectric effect and yield stress on the flow motion of Carreau nanofluid are considered, as Carreau nanofluid is most suitable for representing different types of physics problems because it can disclose the rheology of liquids with short-chain suspension molecules and fluid crystals and because of its many uses in detergents and blood mixing, biological and medical operations. Appropriate similarity conversions are used to produce equations characterizing the system in a nondimensional mathematical model, which are subsequently resolved computationally using Runge-Kutta methodology based on the shooting approach. Attendance of yield stress boosts the surface frictional force, upsurges rates of heat and mass transfers of nanofluid, and maintains the density of bacteria significantly. Magnetoelectric effect also diminishes the rates of heat and mass transfers and increases the density of microorganisms in the nanofluid, which is beneficial for its uses. Yield stress is the greatest way to increase heat transfer rates in this nanofluid for industrial cooling. Magnetoelectric action and yield stress maintain microbe density, making it valuable for medicinal and biological procedures using useful bacteria.