In the current article, a mathematical model is developed to visualize the flow of non-Newtonian magneto cross nanofluid with mass and heat transport rates having activation energy, motile microorganisms and bioconvection over the wedge. The phenomena of microorganisms is implemented to control the suspension of nanomaterials. The results of hydromagnetic are also integrated into the momentum expression. Nanofluid is developed by dispersing the nanosized particles in the regular fluid. Nanosized solid materials like carbides, ceramics, graphene, metal, alloyed CNTs etc. have been utilized for the preparation of nanofluid. Physically regular fluids have low thermal efficiency. Therefore, the nanosize particles can be utilized to enhance the thermal efficiency of the regular fluids. Nanofluids have many features in hybrid power engine, heat transfer and can be useful in cancer therapy and medicine. The constructed system is first simplified into nonlinear form by introducing similarity variables. Then obtained ordinary differential equations (ODEs) which are evaluated for numerical solution. Further, for numerical approximation, the popular bvp4c scheme built-in function in MATLAB is utilized. Reliable outcomes are achieved for the temperature, velocity, concentration and motile microorganism density profiles. Results for numerous essential flow parameters are shown via numerical outcomes and graphs. It is revealed that velocity upsurges with enhancement in mixed convection parameter while reduces for bioconvection Rayleigh and buoyancy ratio parameters. Furthermore, the volumetric concentration of nanoparticles boost up for growing estimations of activation energy parameter. The microorganisms field upsurges with larger microorganism slip parameters while reduces with the augmentation in magnitude of bioconvection Lewis number and Peclet number. The obtained numerical results are compared with the available data and found good agreement.

在当前文章中，开发了数学模型以可视化具有质量和热传输速率的非牛顿磁交叉纳米流体的流动，该质量和热传输速率具有激活能，活动微生物和楔形物上方的生物对流。实施微生物现象以控制纳米材料的悬浮。水磁的结果也被整合到动量表达式中。纳米流体是通过将纳米尺寸的颗粒分散在常规流体中而开发的。诸如碳化物，陶瓷，石墨烯，金属，合金化的CNT等纳米级固体材料已用于制备纳米流体。物理上规则的流体的热效率低。因此，可以利用纳米级颗粒来提高常规流体的热效率。纳米流体在混合动力发动机中具有许多功能，传热，可用于癌症治疗和医学。首先通过引入相似性变量将构建的系统简化为非线性形式。然后获得常微分方程（ODE），并对其进行数值求解。此外，为了进行数值逼近，利用了MATLAB中流行的bvp4c方案内置函数。在温度，速度，浓度和运动微生物密度分布方面均获得了可靠的结果。通过数值结果和图表显示了许多基本流量参数的结果。结果表明，随着混合对流参数的增加，速度激增，而生物对流瑞利和浮力比参数则减小。此外，纳米颗粒的体积浓度增加，用于增长估计活化能参数。随着较大的微生物滑动参数，微生物场激增，而随着生物对流路易斯数和佩克雷特数的增加而减小。将获得的数值结果与可用数据进行比较，并发现很好的一致性。