A mathematical analysis for slip effects on MHD nanofluid in the presence of electromagnetic field and gyrotactic microorganisms is considered. The influence of activation energy and thermal radiation are also discussed. The transportation of nanofluids provides a feasible option for the enhancement of thermal distribution. A rather new aspect of this work is the diffusion and bioconvection of motile microorganisms. It may avoid possible settling of nano-entities. A system of highly non-linear partial differential equations is transformed into Ordinary differential equations by using suitable similarity transformation. The converted ordinary differential equations are then solved numerically by utilizing the shooting technique is built-in function bvp4c solver on the plate form of commercial software Matlab. The results obtained are verified through acceptable agreement with those of the existing one as a special case. The quantities of interest are observed physically. The characteristics of various emerging parameters on the velocity field, temperature distribution and volumetric concentration of nanoparticles, microorganism concentration as well as skin friction coefficient, the gradient of temperature, local Sherwood number, and density number of motile microorganisms are interpreted and reflected in tabulated and graphical form. It is noticed that velocity decreases with the rising values of M. Also, the temperature rises directly with Nb and Nt. With the growing values of Lb, the microorganism profile does down.

考虑了在电磁场和回旋微生物存在下对 MHD 纳米流体的滑移效应的数学分析。还讨论了活化能和热辐射的影响。纳米流体的运输为增强热分布提供了可行的选择。这项工作的一个相当新的方面是活动微生物的扩散和生物对流。它可以避免纳米实体的可能沉降。一个高度非线性的偏微分方程组通过适当的相似变换被转化为常微分方程。然后利用商业软件Matlab平板形式的内置函数bvp4c求解器拍摄技术对转换后的常微分方程进行数值求解。获得的结果通过与现有结果的可接受一致作为特例进行验证。感兴趣的量是物理观察的。对纳米粒子的速度场、温度分布和体积浓度、微生物浓度以及皮肤摩擦系数、温度梯度、局部舍伍德数和运动微生物密度数等各种新兴参数的特征进行了解释和反映在表格和图形形式。可以看到，速度随着值的增加而减小 纳米颗粒的温度分布和体积浓度、微生物浓度以及皮肤摩擦系数、温度梯度、局部舍伍德数和活动微生物的密度数以表格和图形形式进行解释和反映。可以看到，速度随着值的增加而减小 纳米颗粒的温度分布和体积浓度、微生物浓度以及皮肤摩擦系数、温度梯度、局部舍伍德数和活动微生物的密度数以表格和图形形式进行解释和反映。可以看到，速度随着值的增加而减小米。此外，温度直接随Nb和Nt升高。随着Lb值的增加，微生物分布下降。