Bioconvection and radiation effects on thermally enhanced Carreau–Yasuda nanofluid peristalsis using Buongiorno nanofluidic mathematical model

The aim of this research is to investigate the peristaltic flow of a Carreau–Yasuda nanofluid with mixed bioconvective properties under slip conditions. The porous medium is modeled using a modified Darcy's equation. In addition, motile microorganisms are introduced into the flow. The momentum equation is formulated by accounting for the effects of a magnetic field, mixed convection, Hall current and the modified Darcy model. The energy and concentration equations are derived using the Buongiorno model for nanofluids. Wall slip and convective boundary conditions are imposed at both walls. Conservation laws are used to model the governing fluid equations incorporating the effects mentioned above. The system is simplified using the assumptions of small wave number and dominant viscous effects (i.e. large wavelength and small Reynolds number approximations), which reduce the governing equations. However, the resulting reduced system remains highly complex due to nonlinearity and coupling among the equations, making analytical treatment difficult; therefore, it is solved numerically using the NDSolve method. The influence of relevant parameters on velocity, temperature, concentration and motile microorganisms is examined using graphs. The transfer rates of nanofluid heat, concentration and motile microorganisms at both walls are presented in the tables. The results show that, due to the modified Darcy consideration, the fluid velocity decreases. Additionally, Brownian motion and thermophoresis in the nanofluid affect the temperature profile in opposite ways.