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.

这项研究工作突出了新开发的 Rosseland 近似和回旋微生物的概念，在稳定、二维、不可压缩的 Walter's-B 纳米流体（非牛顿流体）在片材的可拉伸表面上流动。Buongiorno 纳米流体模型代表七种重要的滑移机制（即布朗运动、惯性、马格努斯撞击、热泳、扩散泳、重力和流体排水），用于控制表达式的数学建模。在这项研究工作中，仅研究了七种滑移机制（布朗扩散、热泳）中的两个重要因素，其余因素被忽略。此外，在能量方程的建模中使用了 Rosseland 近似和热量产生/吸收效应。热和溶质分层效应的行为在片材的拉伸边界处得到解决。非线性多维流表达式通过适当的相似变换导致无量纲的普通方程。通过动量、温度、浓度和运动密度的同伦分析法 (HAM) 计算总残差。讨论并绘制了控制流动方程的重要流动参数的影响。将获得的结果与文献中富有成果和有价值的研究进行比较，发现与它们非常吻合。过度获得的结果突出表明，速度场下降，而魏森伯格数的估计值较高。还注意到温度场和浓度场具有受热泳参数影响的对比度影响。皮肤摩擦系数、运动密度、浓度和努塞尔数等物理量通过各种流动参数进行了物理讨论。