In this study, we aim to deal with the flow behavior betwixt a pair of rotating circular plates filled with Carreau fluid under the suspension of nanoparticles and motile gyrotactic microorganisms in the presence of generalized magnetic Reynolds number. The activation energy is also contemplated with the nanoparticle concentration equation. The appropriate similarity transformations are used to formulate the proposed mathematical modeling in the three dimensions. The outcomes of the torque on both plates, i.e., the fix and the moving plate, are also contemplated. A well-known differential transform method (DTM) with a combination of Padé approximation will be implemented to get solutions to the coupled nonlinear ordinary differential equations (ODEs). The impact of different nondimensional physical aspects on velocity profile, temperature, concentration, and motile gyrotactic microorganism functions is discussed. The shear-thinning fluid viscosity decreases with shear strain due to its high velocity compared to the Newtonian and shear-thickening case. The impact of Carreau fluid velocity for shear-thinning , Newtonian case , and shear-thickening cases on axial velocity distribution has been discussed in tabular form and graphical figures. For the validation of the current methodology, a comparison is made between DTM-Padé and the numerical shooting scheme.

中文翻译：

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一对旋转圆盘之间多相流的阿里尼乌斯动力学分析

在这项研究中，我们的目的是在存在广义磁雷诺数的情况下，处理一对旋转的圆盘之间的流动行为，该圆盘充满了Carreau流体，在纳米粒子和运动性回旋微生物的悬浮液下。纳米粒子浓度方程还考虑了活化能。适当的相似度转换用于在三个维度上拟议的数学建模。还可以预期在两个板（即固定板和移动板）上的扭矩结果。将实现结合了Padé逼近的众所周知的微分变换方法（DTM），以获取耦合的非线性常微分方程（ODE）的解。不同的无量纲物理方面对速度分布，温度，浓度，以及运动的回旋微生物功能。与牛顿和剪切增稠的情况相比，剪切稀化流体的粘度因其高速度而随剪切应变而降低。Carreau流体速度对剪切稀化的影响，牛顿的情况下，和剪切稠化以表格形式和图形形式讨论了轴向速度分布情况。为了验证当前的方法，在DTM-Padé和数字拍摄方案之间进行了比较。