A numerical study is performed to investigate the magnetic field effects on steady laminar natural convection heat transfer between two concentric horizontal cylinders filled with a porous medium. The inner cylinder surface is maintained at a hot temperature (T_h), while the outer cylinder surface is at a cold temperature (T_c). The external magnetic field is applied parallel to the gravity. A non-Darcian model is used to simulate the flow in the porous medium. The governing equations in a body-fitted coordinate system were solved numerically using the finite difference method. Numerical results have covered a wide range of the modified Rayleigh number (25 ≤ Ra* ≤ 800) and the Hartmann number (0 ≤ Ha ≤ 10). The porosity of porous medium, Prandtl number, and Darcy number were taken as, 0.8, 0.7, and 3.2 × 10^-6, respectively. The obtained results are depicted in terms of the streamlines, isotherms, and local and average Nusselt numbers, which show significant effects of Hartmann number and modified Rayleigh number on the fluid flow and temperature distribution inside the annulus. Also, it was found that the increase of magnetic field cause a reduction in the average Nusselt number, which leads to increasing in the thermal insulation.

中文翻译：

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多孔水平圆柱环内自然对流磁场影响的数值研究

进行了数值研究，以研究磁场对填充有多孔介质的两个同心水平圆柱之间稳定的层流自然对流换热的影响。汽缸内表面保持高温（T _h），汽缸外表面保持低温（T _c））。外部磁场平行于重力作用。使用非达西人模型来模拟多孔介质中的流动。使用有限差分法数值求解了人体坐标系中的控制方程。数值结果涵盖了广泛的修正瑞利数（25≤Ra *≤800）和哈特曼数（0≤Ha≤10）。多孔介质的孔隙率，Prandtl数和Darcy数分别为0.8、0.7和3.2×10 ^-6， 分别。获得的结果以流线，等温线以及局部和平均Nusselt数表示，这表明Hartmann数和修正的Rayleigh数对环空内的流体流动和温度分布有显着影响。另外，发现磁场的增加引起平均努塞尔数的减少，这导致热绝缘性的增加。