This research work highlight the newly developed concept of Rosseland approximation and gyrotactic microorganisms in steady, two-dimensional, incompressible flow of Walter's-B nanofluid (non-Newtonian) over a stretchable surface of sheet. Buongiorno nanofluid model, which represents seven important slip mechanisms (i.e., Brownian motion, inertia, Magnus impact, thermophoresis, diffusion-phoresis, gravity and fluid drainage) is utilized in the mathematical modeling of governing expressions. In this research work, only two important factors of seven slip mechanisms (Brownian diffusion, thermophoresis) are studied and the rest of neglected. Furthermore, the Rosseland approximation and heat generation/absorption effects are used in the modeling of the energy equation. The behavior of thermal and solutal stratification effects are addressed at the stretched boundary of the sheet. The nonlinear dimensional flow expressions lead to dimensionless ordinary equations through appropriate similarity transformations. The total residual error is calculated through Homotopy Analysis Method (HAM) for the momentum, temperature, concentration and motile density. The influences of important flow parameters of the governing flow equations are discussed and plotted graphically. The obtained results are compared with fruitful and valuable research in the literature and found very good agreement with them. Over obtained outcomes highlight that the velocity field, declined versus higher estimations of Weissenberg number. It is also remarked that the temperature and concentration fields have contrast impact subject to thermophoresis parameter. The physical quantities like skin friction coefficient, motile density, concentration and Nusselt number are discussed physically via various flow parameters.

Walter's-B nanofluid (non-Newtonian fluid) Rosseland approximation Gyrotactic microorganisms Heat generation/absorption Thermophoresis diffusion Brownian motion.