Abstract The thermal transfer in the water-based ferrofluid enclosed porous cavity attached with a novel permeable (suction/injection) chamber is investigated within this research. The mathematical analysis of the problem is fulfilled with the modified Rosensweig-model (mRm) accounting for the Darcy porous medium in cooperation with the energy equation. The relevant governing equations are numerically treated via the successive-over-relaxation method (SOR) based on a special finite difference scheme. The pertinent effects of physical parameters on the convection and heat transfer of the ferrofluid inside the cavity are examined in detail. It is determined that the Nusselt number enhances at the left wall but it is reduced at the right wall if one increases either (i) the concentration of the ferroparticles or (ii) the Lorentz force. But the effect of Kelvin force is different from the effect of the Lorentz force on the Nusselt number in the sense that; the Nusselt number decays at the left wall but it intensifies at the right wall if we increase the Lorentz force or its representative the Hartmann number. In addition, the Nusselt number at the left wall of the cavity rises about 1.4 times if the Hartmann number increases from 0 to 50. The problem setup in the current work may be useful in the applications regarding bio-medical, pharmaceutical and engineering industries. The generated results from the present work quantitatively as well as qualitatively match with the existing literature.

中文翻译：

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封闭在多孔和可渗透腔中的铁磁流体中的自然对流

摘要 在这项研究中，研究了水基铁磁流体封闭多孔腔中的热传递，该腔附有新型渗透（吸入/注入）室。该问题的数学分析是通过修正的 Rosensweig 模型 (mRm) 与能量方程一起解释达西多孔介质来完成的。相关控制方程通过基于特殊有限差分格式的逐次超弛豫方法（SOR）进行数值处理。详细研究了物理参数对腔内铁磁流体的对流和热传递的相关影响。确定努塞尔数在左壁增强，但如果 (i) 铁粒子浓度或 (ii) 洛伦兹力增加，则它在右壁减小。但是开尔文力的作用不同于洛伦兹力对努塞尔数的作用，意义在于：如果我们增加洛伦兹力或其代表哈特曼数，努塞尔数在左壁衰减，但在右壁会增强。此外，如果哈特曼数从0增加到50，腔左壁处的努塞尔数增加约1.4倍。当前工作中的问题设置可能对生物医学、制药和工程行业的应用有用。当前工作产生的结果在数量上和质量上都与现有文献相匹配。如果我们增加洛伦兹力或其代表哈特曼数，努塞尔数在左壁衰减，但在右壁会增强。此外，如果哈特曼数从0增加到50，腔左壁处的努塞尔数增加约1.4倍。当前工作中的问题设置可能对生物医学、制药和工程行业的应用有用。当前工作产生的结果在数量上和质量上都与现有文献相匹配。如果我们增加洛伦兹力或其代表哈特曼数，努塞尔数在左壁衰减，但在右壁会增强。此外，如果哈特曼数从0增加到50，腔左壁处的努塞尔数增加约1.4倍。当前工作中的问题设置可能对生物医学、制药和工程行业的应用有用。当前工作产生的结果在数量上和质量上都与现有文献相匹配。制药和工程行业。当前工作产生的结果在数量上和质量上都与现有文献相匹配。制药和工程行业。当前工作产生的结果在数量上和质量上都与现有文献相匹配。