Here theoretical analysis of heat, mass and motile microorganisms transfer rates in Casson fluid flow over stretched permeable surface of cylinder is studied. Investigated is carried out in the presence of suspended nanoparticles and self-propelled gyrotactic microorganisms. The effects of buoyancy forces, magnetic field and thermal radiation are considered. The nanoparticles with suitable suspension are stabilized through mutual effects of buoyancy forces and bioconvection. Furthermore, activation energy and Darcy- Forchheimer effects on bio nanofluid flow are accounted. The constitutive theories are executed to develop the model formulation. The obtained model is made dimensionless trough appropriate transformations. The dimensionless flow model is tackled by built-in algorithm of shooting technique. Impact of flow controlling constraints parameters is physically elaborated by making graphical illustrations. The outcomes based on numerical data against essential engineering formulations like surface drag force, Nusselt, density and Sherwood numbers are tabulated. Main outcomes are successfully summarized in terms of closing remarks.

这里研究了卡森流体流过圆柱体可渗透表面的热量、质量和活动微生物传递速率的理论分析。研究是在悬浮的纳米粒子和自推进回旋微生物存在的情况下进行的。考虑了浮力、磁场和热辐射的影响。具有合适悬浮液的纳米颗粒通过浮力和生物对流的相互影响而稳定。此外，还考虑了活化能和 Darcy-Forchheimer 对生物纳米流体流动的影响。执行本构理论以开发模型公式。通过适当的变换，获得的模型是无量纲的。无量纲流模型由内置的射击技术算法处理。流量控制约束参数的影响是通过制作图形说明来物理阐述的。表中列出了基于数值数据与基本工程公式（如表面阻力、努塞尔特、密度和舍伍德数）的结果。在结束语中成功总结了主要成果。