Abstract One of the most concerned subjective in Mechanical science is natural convection study in a cavity. Furthermore, the investigation of entropy generation can be useful for better designing of the thermal systems. In the present study, natural convection flow and entropy generation are numerically investigated in the presence of a magnetic field in a square inclined cavity which known as the effect of magneto-hydrodynamic (MHD). Firstly, governing equations, including mass, momentum, and energy balance equations are applied to the problem. Then, governing equations are rewritten in dimensionless form using non-dimensional parameters, vorticity, and stream function. Furthermore, the entropy generation equation is written as a non-dimensional equation. Then, the contribution of the heat transfer entropy generation into the total entropy generation rate is determined using the Bejan number. A new measure for evaluation of the thermal performance of the cavity is presented that is the so-called ecological coefficient of performance (ECOP) based on the second law of thermodynamics. Flow and heat transfer characteristics are investigated for different values of the Rayleigh number, inclination angle, and Hartmann number. The new correlations of entropy generation as a function of Rayleigh number are obtained using the two-dimensional version of quadratic Lagrange interpolation functions (QLIFs). The obtained values for the average Nusselt number and the entropy generation number are compared with those of the literature and excellent agreement is observed. The results show that the entropy generation number rises with increasing of Hartmann number and whereas it has a maximum value for a specified inclination angle. Also, ECOP increases with increasing of Hartmann number for low values of Rayleigh number. The results discover that the optimum values of the inclination angle are 20°, 35° and 48°for Hartmann number 0, 25 and 75 at Ra = 105, respectively. Also, with increasing Ha from 25 to 75, the contribution of the Ngen due to magnetic field decreases from 23% to 9% for β = 0° and it decreases from 24% to 6% for β = 45°.

中文翻译：

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使用辅助二次拉格朗日插值函数的控制体积有限元方法研究方形倾斜腔中的熵生成

摘要 机械科学中最受关注的学科之一是空腔中的自然对流研究。此外，熵生成的研究有助于更好地设计热系统。在本研究中，在方形倾斜腔中存在磁场的情况下，对自然对流和熵产生进行了数值研究，这被称为磁流体动力学 (MHD) 效应。首先，将控制方程，包括质量、动量和能量平衡方程应用于该问题。然后，使用无量纲参数、涡度和流函数以无量纲形式重写控制方程。此外，熵生成方程被写为无量纲方程。然后，传热熵产生对总熵产生率的贡献是使用 Bejan 数确定的。提出了一种评估腔体热性能的新方法，即基于热力学第二定律的生态性能系数 (ECOP)。研究了瑞利数、倾角和哈特曼数的不同值的流动和传热特性。使用二维版本的二次拉格朗日插值函数 (QLIF) 获得作为瑞利数函数的熵生成的新相关性。将获得的平均 Nusselt 数和熵生成数的值与文献中的值进行比较，观察到极好的一致性。结果表明，熵生成数随着哈特曼数的增加而增加，并且在指定的倾角下具有最大值。此外，对于低瑞利数值，ECOP 随着哈特曼数的增加而增加。结果发现，在 Ra=105 时，Hartmann 数 0、25 和 75 的倾角最佳值分别为 20°、35°和 48°。此外，随着 Ha 从 25 增加到 75，对于 β = 0°，由磁场引起的 Ngen 的贡献从 23% 减少到 9%，对于 β = 45°，它从 24% 减少到 6%。哈特曼数 0、25 和 75 在 Ra = 105 时分别为 35° 和 48°。此外，随着 Ha 从 25 增加到 75，对于 β = 0°，由磁场引起的 Ngen 的贡献从 23% 减少到 9%，对于 β = 45°，它从 24% 减少到 6%。哈特曼数 0、25 和 75 在 Ra = 105 时分别为 35° 和 48°。此外，随着 Ha 从 25 增加到 75，对于 β = 0°，由磁场引起的 Ngen 的贡献从 23% 减少到 9%，对于 β = 45°，它从 24% 减少到 6%。