LAUSR

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 $$10^4$$ 10 4 and $$10^6$$ 10 6 ), Hartmann number (between 0 and 60), Darcy number (between $$5 \times 10^{-4}$$ 5 × 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 0.01 H and 0.3 H ) 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 $$22\%$$ 22 % when Hartmann number is changed from 0 to 60 at Rayleigh number of $$10^5$$ 10 5 . Curvature and conductivity of the curved partition affect the variation in fluid flow and heat transfer characteristics. Maximum of $$7\%$$ 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.