Abstract The main purpose of this numerical investigation is to estimate energetically the thermo-magnetohydrodynamic (MHD) irreversibility arising in Stokes’ second problem by successfully applying the first and second thermodynamic laws to the unsteady MHD free convection flow of an electrically conducting dissipative fluid. This fluid flow is assumed to originate periodically in time over a vertical oscillatory plate which is heated with uniformly distributed temperature and flowing in the presence of viscous dissipation and Ohmic heating effects. Moreover, the mathematical model governing the studied flow is formulated in the form of dimensional partial differential equations (PDEs), which are transformed into non-dimensional ones with the help of appropriate mathematical transformations. The expressions of entropy generation and the Bejan number are also derived formally from the velocity and temperature fields. Mathematically, the resulting momentum and energy conservation equations are solved accurately by utilizing a novel hybrid numerical procedure called the Gear-Generalized Differential Quadrature Method (GGDQM). Furthermore, the velocity and temperature fields obtained numerically by the GGDQM are exploited thereafter for computing the entropy generation and Bejan number. Finally, the impacts of the various emerging flow parameters are emphasized and discussed in detail with the help of tabular and graphical illustrations. Our principal result is that the entropy generation is maximum near the oscillating boundary. In addition, this thermodynamic quantity can rise with increasing values of the Eckert number and the Prandtl number, whereas it can be reduced by increasing the magnetic parameter and the temperature difference parameter.

中文翻译：

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斯托克斯第二题磁流体动力耗散流中熵能收集的数值检验：利用齿轮广义微分求积法

摘要 本数值研究的主要目的是通过成功地将第一和第二热力学定律应用于导电耗散流体的不稳定 MHD 自由对流，在能量上估计 Stokes 第二个问题中出现的热磁流体力学 (MHD) 不可逆性。假定该流体流动在时间上周期性地起源于垂直振荡板，该板以均匀分布的温度加热并在存在粘性耗散和欧姆加热效应的情况下流动。此外，控制研究流动的数学模型以维数偏微分方程 (PDE) 的形式制定，借助适当的数学变换将其转换为无维数方程。熵生成和 Bejan 数的表达式也从速度场和温度场正式导出。在数学上，通过使用一种称为齿轮广义微分正交法 (GGDQM) 的新型混合数值程序，可以准确地求解得到的动量和能量守恒方程。此外，此后利用 GGDQM 数值获得的速度和温度场来计算熵生成和 Bejan 数。最后，在表格和图形说明的帮助下，强调并详细讨论了各种新出现的流动参数的影响。我们的主要结果是熵产生在振荡边界附近最大。此外，