Owing to the magnified thermal performances of nanoparticles and essential applications in various industrial and engineering processes like heat exchangers, cooling systems, boilers, MEMS, chemical engineering, laser diode arrays and cool automobile engines, variety of research is presented in this topic. On this end, current investigation deals with the unsteady flow of Williamson nanofluid containing the gyrotactic microorganisms over a rotating cylinder. The additional features like activation energy, chemical reaction and variable thermal conductivity are also composed in the current flow problem. The whole flow model is subjected to the second order slip from which results two slip parameters that effectively control the associated boundary layers. The formulated problem is based on the utilization of governing equations which are converted into dimensionless form with help of appropriate transformation. The self similar solution of constituted equations is followed by using shooting technique. The obtained results are confirmed by comparing already reported investigations with convincible agreement. The graphical analysis for involved parameters is comprehensively presented for both circular cylinder and flat plat as a liming case. The physical aspects of each flow parameter are discussed. The numerical illustration for local Nusselt number, local Sherwood number and motile density number are also presented in tabular form. The results show that temperature ratio parameter and slip constant increase the nanofluid temperature which is more prominent in case of circular cylinder. The concentration and microorganism distributions enhances with unsteady parameter. Moreover, a declining microorganism distribution is observed with mixed convection parameter, Peclet number and bioconvection Lewis number.

由于纳米颗粒的放大热性能以及在各种工业和工程过程中的重要应用，例如热交换器，冷却系统，锅炉，MEMS，化学工程，激光二极管阵列和凉爽的汽车发动机，因此在本主题中进行了各种各样的研究。为此，目前的研究涉及在旋转的圆柱体上不稳定的含有回转活性微生物的威廉姆森纳米流体的流动。电流问题还包括诸如活化能，化学反应和可变的热导率的附加特征。整个流动模型受到二阶滑移的影响，由此产生两个滑移参数，可以有效地控制关联的边界层。提出的问题是基于控制方程的利用，该控制方程在适当的变换的帮助下转换为无量纲形式。使用射击技术遵循构成方程的自相似解。通过将已有报告的调查结果与令人信服的协议进行比较，可以确认获得的结果。对于涉及的参数的图形分析，全面介绍了圆柱和平板的情况。讨论了每个流量参数的物理方面。表格中还显示了本地Nusselt数，Sherwood数和运动密度数的数字图示。结果表明，温度比参数和滑移常数提高了纳米流体的温度，在圆柱体的情况下更为突出。浓度和微生物分布随不稳定参数而增加。此外，混合对流参数，Peclet数和生物对流路易斯数观察到微生物分布下降。