The study of heat transfer and peristaltic pumping of magnetohydrodynamic (MHD) biofluids have many physiological applications such as heart-lung machines during surgeries, dialysis, vitamin injections, cancer treatment. Also, it has many industrial applications such as pharmaceutical fluid production, filtration, dispensing cosmetic/glue emulsions with no contamination. Furthermore, the bi-viscous Bingham nanofluid model is the best model for several bio/industrial fluids. Therefore, the impact of thermal radiation and cross diffusion on the mixed convection peristaltic pumping of a bi-viscous Bingham nanofluid in a porous flexible conduit is considered. Also, we focus on the flexibility of the walls along with the convective boundary conditions. We adopted the lubrication strategy to reduce the system's complexity. The system of non-dimensional partial differential equations (PDEs) along with the pertinent boundary conditions is solved for several sets of values of the dimensionless parameters. The expressions for the temperature, concentration, velocity, and heat transfer coefficient are obtained analytically. The impact of the relevant parameters on the velocity, temperature, coefficient of heat transfer, concentration, and trapping are discussed in depth with the help of graphical illustrations. The results indicate that the velocity distribution is reduced with growing Darcy parameter and concentration Grashof number. Intensifying the magnetic parameter results in shrinking the trapped bolus. Decay in the heat transfer coefficient is observed for rising values of the radiation parameter. The current findings are compared with the existing studies in the literature and are found to agree very well for special cases.
