School of Engineering, Huzhou University, Huzhou, 313000, People's Republic of China.
Department of Mathematics, City University of Science and Information Technology, Peshawar, Pakistan.
Sci Rep. 2021 Jul 26;11(1):15142. doi: 10.1038/s41598-021-94543-4.
The present study explores incompressible, steady power law nanoliquid comprising gyrotactic microorganisms flow across parallel plates with energy transfer. In which only one plate is moving concerning another at a time. Nonlinear partial differential equations have been used to model the problem. Using Liao's transformation, the framework of PDEs is simplified to a system of Ordinary Differential Equations (ODEs). The problem is numerically solved using the parametric continuation method (PCM). The obtained results are compared to the boundary value solver (bvp4c) method for validity reasons. It has been observed that both the results are in best settlement with each other. The temperature, velocity, concentration and microorganism profile trend versus several physical constraints are presented graphically and briefly discussed. The velocity profile shows positive response versus the rising values of buoyancy convection parameters. While the velocity reduces with the increasing effect of magnetic field, because magnetic impact generates Lorentz force, which reduces the fluid velocity.
本研究探索了不可压缩的、稳定的幂律纳米流体在能量传递的情况下流过平行板，其中只有一个板相对于另一个板运动。非线性偏微分方程被用来建立问题的模型。利用廖的变换，将偏微分方程组简化为一个常微分方程组。利用参数连续法（PCM）对问题进行数值求解。为了验证结果的正确性，将得到的结果与边界值求解器（bvp4c）方法进行了比较。结果表明，这两种方法的结果非常吻合。给出了几个物理约束条件下温度、速度、浓度和微生物分布的趋势图，并进行了简要讨论。速度分布对浮力对流参数的增加呈正响应。而速度随着磁场影响的增加而减小，因为磁场产生洛伦兹力，从而降低了流体的速度。
