Natural or free convection is one mode of convection heat transfer where temperature changes leads to density variation. For example, free convection can happen in an enclosure that has two walls with different temperatures. In the present study, the heat transfer behavior of a cardioid shaped porous cavity is investigated. Regarding the situation of the inner cardioid, four modes can be considered for the problem that is called cases A, B, C and D. The Cu-water nanofluid has been selected as working fluid and the flow is affected by an external magnetic field. Non-dimensional governing equations (stream-vorticity functions) are solved numerically using the control volume finite element method (CVFEM). The ecological coefficient of performance (ECOP) as a criterion of cavity performance is evaluated. The effects of decision variables such as Darcy number, Hartmann number, Rayleigh number, and nanoparticle volume fraction on the entropy generation number, the ECOP and the average Nusselt number are studied. The results show that case C is better rather than other cases from the view point of the second law of thermodynamics.

中文翻译：

---

关于磁场下多孔外壳的熵产生：心形几何形状的不同方向


自然对流或自由对流是对流换热的一种模式，其中温度变化导致密度变化。例如，在具有两个不同温度的壁的外壳中可能会发生自由对流。在本研究中，研究了心形多孔腔的传热行为。对于内部心形的情况，可以考虑四种模式来解决称为情况A、B、C和D的问题。选择Cu-水纳米流体作为工作流体，并且流动受到外部磁场的影响。使用控制体有限元法 (CVFEM) 对无量纲控制方程（流涡函数）进行数值求解。生态性能系数（ECOP）作为空腔性能的标准进行了评估。研究了达西数、哈特曼数、瑞利数、纳米颗粒体积分数等决策变量对熵产生数、ECOP和平均努塞尔数的影响。结果表明，从热力学第二定律的角度来看，情况C优于其他情况。