Magnetic Dipole and Thermophoretic Particle Deposition Impact on Bioconvective Oldroyd-B Fluid Flow over a Stretching Surface with Cattaneo–Christov Heat Flux

This study emphasizes the performance of two-dimensional electrically non-conducting Oldroyd-B fluid flowing across a stretching sheet with thermophoretic particle deposition. The heat and mass transfer mechanisms are elaborated in the presence of a magnetic dipole, which acts as an external magnetic field. The fluid possesses magnetic characteristics due to the presence of ferrite particles. The gyrotactic microorganisms are considered to keep the suspended ferromagnetic particles stable. Cattaneo–Christov heat flux is cogitated instead of the conventional Fourier law. Further, to strengthen the heat transfer and mass transfer processes, thermal stratification and chemical reaction are employed. Appropriate similarity transformations are applied to convert highly non-linear coupled partial differential equations into non-linear ordinary differential equations (ODEs). To numerically solve these ODEs, an excellent MATLAB bvp4c approach is used. The physical behavior of important parameters and their graphical representations are thoroughly examined. The tables are presented to address the thermophoretic particle velocity deposition, rate of heat flux, and motile microorganisms’ density number. The results show that the rate of heat transfer decreases as the value of the thermal relaxation time parameter surges. Furthermore, when the thermophoretic coefficient increases, the velocity of thermophoretic deposition decreases.