Thermophoretic and Brownian motion in magnetized flow of Ree–Eyring nanofluid containing microorganisms over a curved surface by using Keller-box method

This theoretical study aims to investigate the heat and mass transference features in the magnetized flow of Ree–Eyring nanofluid comprising both nanoparticles and gyrotactic microorganisms with Joule heating over a curved stretchable surface. By employing the Buongiorno nanofluid model, we examine the influences of thermophoresis and Brownian diffusions which are essential to accurately capture the behavior of nanofluids under thermal and magnetic affects. The presence of nanoparticles and gyrotactic microorganisms enhances the thermal conductivity and stability of the fluid making it suitable for various industrial applications, such as cooling systems, biomedical devices, and enhanced oil recovery. The flow configuration in the form of a mathematical expression of the present boundary layer problem is obtained as a set of partial differential equations (PDEs) after utilizing the curvilinear coordinate systems. To simplify the complexity of these equations, we apply similarity transformations that reduce the PDEs to a system of nonlinear ordinary differential equations (ODEs). This transformed set of ODEs is then solved numerically by using the Keller-box method a robust technique for handling boundary layer problems in fluid dynamics. A detailed graphical and tabular analysis is performed to illustrate the influence of numerous variables on the concerned profiles. The graphical results reveal that the microorganism’s concentration profile reduces for the higher values of the bioconvective Lewis number, radius of curvature parameter, Peclet number, and microorganism difference constant. However, the profile of the Motile number shows a favorable response for upshot values of all the above-defined parameters.