The existing study observed 3-D Darcy-Forchheimer MHD Casson fluid, steady flow between the gap of a disk and a cone in a spinning scheme. Energy ascription is considered in the existence of thermophoresis effect and Brownian motion. Mass transfer and gyrotactic microorganism are also considered, and the impact of the various embedded constraints has been observed on these profiles. The similarity alterations are used to transform the partial differential equations into the set of ordinary differential equations (ODEs). To solve the ODEs, we have chosen the homotopy analysis method of BVPh 2.0 package. The important physical parameters of interest like, heat transfer rate, mass transfer, and motile have been calculated numerically and discussed. The obtained results show that the velocity profiles decreased for inertial parameter \(F_{1}\), magnetic field \(M\), and permeability constraint \(Kr\). The effects of other constraints such as Brownian motion constraint \(N_{b}\), Schmidt number \(Sc\), Prandtl number \(\Pr\), and thermo physical constraint on the concentration and temperature fields have been analyzed and debated. The accumulative standards of the Casson constraint are declining the fluid motion. But the temperature field is rising with growing Casson parameter. It is detected that the motile density of microorganisms displays a falling behavior for rising values of Lewis and Peclet numbers.

现有研究观察到3-D Darcy-Forchheimer MHD Casson流体，在纺丝方案中，圆盘间隙与圆锥体之间稳定流动。在存在热泳效应和布朗运动的情况下考虑了能量归因。还考虑了传质和旋回微生物，并且已经观察到各种嵌入的限制因素对这些分布的影响。相似性更改用于将偏微分方程转换为一组常微分方程（ODE）。为了解决ODE，我们选择了BVPh 2.0软件包的同伦分析方法。感兴趣的重要物理参数，如传热速率，传质和运动性已通过数值计算并进行了讨论。结果表明，惯性参数的速度分布减小\（F_ {1} \），磁场\（M \）和磁导率约束\（Kr \）。分析了布朗运动约束\（N_ {b} \），施密特数\（Sc \），普朗特数\（\ Pr \）和热物理约束等其他约束对浓度和温度场的影响，并辩论。卡森约束的累积标准正在使流体运动下降。但是温度场随Casson参数的增加而上升。据检测，微生物的运动密度随着路易斯和佩克雷特数的升高而显示出下降的行为。