Numerical simulation of bio‐convection radiative heat transport flow of MHD Carreau nanofluid

Abstract To report the challenges and advance of heat transport performance, we aim to scrutinize the motile microbe's phenomenon in mixed convection Carreau nanofluid considering the properties of Soret and Dufour, non‐uniform heat sink/source, radiation and magnetohydrodynamic (MHD). The new mass flux and convective phenomenon are also considered. The inclusion of motile microbe phenomenon in conjunction with Soret and Dufour effects, non‐uniform heat sink/source, radiation, and MHD presents a multifaceted approach to studying heat transport in Carreau nanofluids. By integrating these factors, we gain insights into the complex interplay between thermal conductivity variations, convective heat transfer, and fluid flow behavior. This comprehensive analysis allows for a deeper understanding of how various mechanisms influence heat transport performance, offering valuable insights for optimizing nanofluid‐based heat transfer systems and enhancing their efficiency. The highly nonlinear and coupled partial differential equations (PDE) are transformed using similarity conversion and attained required ordinary differential equations (ODE). The bvp4c algorithm works to derive the solutions subjected to appropriate norms and physical boundary conditions. Furthermore, an assessment made with the obtainable works shows worthy outcomes. The controlling variables influence on the microorganisms, concentration, temperature, and velocity fields are scrutinized graphically for shear thinning and thickening phenomena. Skin frictions, motile density number, and Nusselt numbers of tables are prepared. Additionally, the cases of shear thinning/thickening are discussed in tables. The radiation and Biot factors exaggerate the temperature field; however, Brownian factor decay the fluid concentration. The bioconvection Rayleigh factor decreases and mixed convection factor increases the velocity field. Furthermore, the bioconvection Lewis factor declines the motile microbe's field. The graphs of controlling factors for followings values are plotted for accurate convergence that is, , , , , , , , ,