Numerical study of entropy generation in magneto-convective flow of nanofluid in porous enclosure using fractional order non-Darcian model

The present numerical work examines the effect of fractional order parameter on heat transfer and entropy generation for a thermo-magnetic convective flow of nanofluid (Cu-water) in a square porous enclosure that contains semi-circular bottom wall. The Darcy–Brinkmann–Forchheimer model is utilized to evaluate the momentum transfer in porous media, and the Caputo-time fractional derivative term is introduced in momentum as well as in the energy equation. Further, non-dimensional governing equations are simulated through the penalty finite element method, and the Caputo time derivative is approximated by L1-scheme. The study is carried out for various parameters, including Rayleigh number (Ra), Darcy number (Da), radius of the semicircle (r), fractional order (α), and Hartmann number (Ha). The comprehensive results are presented by the contour variation of isotherms, streamlines, and total entropy generation at the selected range of parameters. In addition, thermal transport and irreversibilities due to heat transfer, fluid friction, and magnetic field have been accounted through the numerical variation of mean Nusselt number $( N u m )$ and Bejan number due to heat transfer $( B e h t )$⁠, fluid friction $( B e f f )$⁠, and magnetic field $( B e m f )$⁠, respectively. The key findings of the present study reveal that during the initial evolution period, the Nu_m value increases as $α → 1$⁠. Additionally, time taken to achieve the steady state condition varies and depends on fractional order α. Furthermore, in the absence of Ha, the heat transfer and entropy generation intensifies with augmentation of Ra and Da for all α, while, the increasing value of Ha shows an adverse impact on the heat transfer rate.