This work tackles the phenomenon of motile microorganisms and nanoliquid flow in the esteem of cross-flow (CF) and stream-wise (SW) direction. The analysis exposed to viscous dissipation, Brownian motion, thermal radiation, magnetic function, and thermophoresis impacts is encountered. The mathematical model consists of the partial differential equations (PDEs) switched into nonlinear ordinary differential equations (ODEs) through proper transformations of new variables. The multiple outcomes of the flow problem are achieved through the Lobatto IIIA formula. The features of controlling constraints are sketched for the motile organism, temperature, velocities (CF and SW), and concentration fields. Also, the Sherwood and the Nusselt numbers along with motile density and friction factor are sketched. One imperative numerical outcome of this research is the existence of dual numerical solutions for the nanofluid flow. The upshots indicate that the profiles of microorganisms decelerate due to bio-convection Schmidt and Péclet numbers. The magnetic function decelerates the velocity in the directions of SW and CF in the branch of the first solution and upsurges in the branch of the second solution. The concentration profile uplifts due to Nt in both solutions while the opposite behavior is observed for different values of Nb in both solutions. The temperature uplifts due to magnetic and radiation effects in both solutions.

中文翻译：

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包含纳米流体输送运动微生物的顺流和错流方向的生物对流的数值模拟：多种解决方案的分析

这项工作在交叉流 (CF) 和流向 (SW) 方向上解决了运动微生物和纳米液体流动的现象。遇到粘性耗散、布朗运动、热辐射、磁函数和热泳影响的分析。数学模型由偏微分方程 (PDE) 通过新变量的适当变换转换为非线性常微分方程 (ODE) 组成。流动问题的多个结果是通过 Lobatto IIIA 公式实现的。针对运动生物、温度、速度（CF 和 SW）和浓度场绘制了控制约束的特征。此外，还绘制了 Sherwood 和 Nusselt 数以及运动密度和摩擦系数。这项研究的一个必要的数值结果是纳米流体流动的双重数值解的存在。结果表明，由于生物对流 Schmidt 和 Péclet 数，微生物的分布会减速。磁函数在第一个解的分支中使 SW 和 CF 方向的速度减速，并在第二个解的分支中上升。浓度分布升高是由于ñ吨在两种解决方案中，而对于不同的值观察到相反的行为ñb在这两种解决方案中。由于两种解决方案中的磁效应和辐射效应，温度都会升高。