In the present paper, bioconvective stagnation point flow of nanofluid containing gyrotactic microorganisms over a nonlinearly stretching sheet embedded in a porous medium is considered. The scaling group transformation method is introduced to obtain the similarity transformation to convert the governing partial differential equations to a set of ordinary differential equations. The reduced governing nonlinear differential equations are then solved numerically with Runge–Kutta–Fehlberg method. Differential transform method is employed to justify the results obtained by the numerical method. It is found that both the results matched nicely. It is noticed that the density of motile microorganism distribution grows high with an increase in the values of the bioconvection Peclet number. Further, the rate of heat transfer and the rate of mass transfer increase rapidly with an increment in the thermophoresis parameter, heat source parameter, chemical reaction parameter, and Brownian motion parameter, respectively. This work is relevant to engineering and biotechnological applications, such as in the design of bioconjugates and mass transfer enhancement of microfluidics.

中文翻译：

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使用DTM和RKF方法对纳米流体中非线性热生物对流停滞点流的布朗运动进行数学分析

在本文中，考虑了包含旋流微生物的纳米流体在悬浮于多孔介质中的非线性拉伸片上的生物对流停滞点流动。引入标度群变换法获得相似度变换，将控制性偏微分方程转换为一组常微分方程。然后用Runge–Kutta–Fehlberg方法对简化的控制非线性微分方程进行数值求解。采用微分变换法对通过数值方法获得的结果进行证明。发现两个结果很好地匹配。值得注意的是，随着对流佩克雷特数的增加，运动微生物分布的密度也随之增加。进一步，随着热泳参数，热源参数，化学反应参数和布朗运动参数的增加，传热速率和传质速率迅速增加。这项工作与工程和生物技术应用有关，例如生物共轭物的设计和微流体传质的增强。