The increasing demand need for efficient thermal management systems across various industrial applications is effectively being addressed by the utilization of nanofluids, which possess superior thermal performance character relative to conventional typical fluids. Nanomaterials offer a promising solution for enhancing heat transfer in diverse engineering systems, particularly where traditional fluids are insufficient for optimizing thermal performance. The primary goal of this work is to investigate the gyrotactic microorganisms with magnetohydrodynamic 2D unsteady mixed bioconvective flow of electrically conducting nanofluid flow across two extended parallel plates through convective conditions is considered and analyzed. Possessions of chemical reaction, magnetic field, thermophoretic diffusion, Soret and Dufour impacts are also deliberated. The consequences of the density of living microbes are incorporated into the model. The flow problem developed using a system of coupled nonlinear partial differential equations (PDEs) derived from flow assumptions. Suitable transformation techniques are introduced to reduce resulting PDEs into a system of nonlinear ordinary differential equations (ODEs). The resulting transformed ODEs are then solved numerically using the RKF45 method combined with Nactsheim–Swigert shooting techniques on the MATLAB programming platform. The effects of the pertinent physical parameters on different flow profiles are offered and discussed in detail, accompanied by graphics and tabulated data. Finally, the accuracy of the computational technique employed is verified by comparing the numerical results with those obtained using the homotopy analysis method (HAM). This comparison assesses the validity of the RKF45 technique and provides tabulated data and graphical results for various flow profiles. The results demonstrate excellent correlation, providing assurance that the computational outcomes in our study are valid.