In this study, MHD conjugate free convection of a porous cavity having a curved shape conductive partition is numerically analyzed by using the Galerkin weighted residual finite element method. The numerical simulation is performed for different values of pertinent parameters: Rayleigh number (between \(10^4\) and \(10^6\)), Hartmann number (between 0 and 60), Darcy number (between \(5 \times 10^{-4}\) and 0.05), porosity of the medium (between 0.25 and 0.75), curvature of the partition (minor axis radius of the horizontal ellipse, between 0.01H and 0.3H) and conductivity ratio (between 0.05 and 50). It was observed that the heat transfer rate enhances locally and in average for higher values of Rayleigh number, Darcy number, porosity of the medium and conductivity ratio, whereas the impact is opposite for higher values of Hartmann number. The amount of average Nusselt number reduction is obtained as \(22\%\) when Hartmann number is changed from 0 to 60 at Rayleigh number of \(10^5\). Curvature and conductivity of the curved partition affect the variation in fluid flow and heat transfer characteristics. Maximum of \(7\%\) variation in the average Nusselt number is achieved when the curvature of the conductive partition is varied but the effects of thermal conductivity ratio on heat transfer rate are higher. Long Short-Term Memory Networks are used for estimation of the velocity and temperatures in the computational domain for various values of pertinent input parameters variation in the system which includes conjugate heat transfer mechanism in a porous enclosure with complex-shaped conductive partition under the effects of magnetic field.

中文翻译：

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MHD共轭自然对流在包含弯曲导电隔板的多孔腔中，并通过使用长短期记忆网络进行估计

在这项研究中，通过使用Galerkin加权残差有限元方法，对具有弯曲形状的导电隔板的多孔腔的MHD共轭自由对流进行了数值分析。对相关参数的不同值进行了数值模拟：瑞利数（在（（10 ^ 4 \）和\（10 ^ 6 \）之间），哈特曼数（在0和60之间），达西数（在（（5 \乘以10 ^ {-4} \）和0.05），介质的孔隙率（在0.25和0.75之间），隔板的曲率（水平椭圆的最小轴半径，在0.01 H和0.3 H之间））和电导率比（介于0.05和50之间）。观察到，对于较高的瑞利数，达西数，介质的孔隙率和电导率比，传热速率局部地和平均地提高，而对于较高的哈特曼数，传热效果相反。当哈特曼数在瑞利数为\（10 ^ 5 \）时从0变为60时，平均努塞尔特数减少量为\（22 \％\）。弯曲隔板的曲率和电导率会影响流体流量和传热特性的变化。最高\（7 \％\）当改变导电隔板的曲率时，平均努塞尔数会发生变化，但是热导率对传热率的影响更大。长短期记忆网络用于估算系统中相关输入参数变化的各种值在计算域中的速度和温度，该系统包括在具有复杂形状的导电隔板的多孔外壳中的共轭传热机制，其作用是磁场。