摘要
本研究采用微分变换法和Akbari-Ganji法,研究了施加均匀磁场对纳米流体在两个无限平行板间流动的自然对流传热的影响。在得到控制方程并在特定边界条件下求解问题后,研究了Prandtl数、挤压次数、Schmidt数、Hartmann数、Eckert数、布朗运动参数和热电泳参数等主要参数的影响。将相似变换用于求解常微分方程组,并与Rung-Kutta四阶数值法进行对比。研究结果表明,增加挤压次数会导致速度减慢,增加Hartman数也有类似的影响。此外,温度随着Hartman数、Eckert数和热电泳参数的增大而升高,且与Prandtl数成正比。我们对比研究了Akbari-Ganji法和微分变换法求解非线性微分方程,结果表明,前者需要的计算步骤更少和计算时间更短,是一种更有效的方法。使用建议的方法获得的解与文献中的解一致。这些结果有助于研究人员更快、更容易地进行分析,并为纳米流体在电磁场存在下流动的复杂行为提供重要见解。
In this study,we use the differential transform method and Akbari-Ganji method to examine the influence of uniform magnetic field on the natural convection heat transfer of nanofluids flowing between two infinite parallel plates.The effects of the primary parameters of Prandtl number,squeeze number,Schmidt number,Hartmann number,Eckert number,Brownian motion parameter,and thermophoresis parameter have been investigated after obtaining the governing equations and solving the problem with specified boundary conditions.The similarity transformation is used to find the system of ordinary differential equations,and the Rung-Kutta fourth-order numerical technique is contrasted.The findings suggest that increasing the squeeze number leads to a decrease in velocity,while increasing the Hartman number has a similar effect.Moreover,the temperature rises with an increase in Hartman number,Eckert number,and thermophoretic parameters and is directly proportional to Prandtl number.Our study compares Akbari-Ganji and differential transform methods for solving nonlinear differential equations.It demonstrates that the former requires fewer computational steps and less computational time,making it a more efficient approach.The answers acquired using the suggested methods are consistent with those found in the literature.These results can help researchers to analyze quicker and easier and provide important insights into the complex behavior of nanofluid flow in the presence of electromagnetic fields.
