Numerical analysis of Nano-encapsulated PCM magnetohydrodynamics double-diffusive convection and entropy generation in vertical enclosures with porous layer

• NEPCMs enhance heat transfer by up to 48.4 % at higher Rayleigh numbers. • Magnetic fields reduce both heat and mass transfer significantly. • Total entropy generation rises sharply with Rayleigh number but falls with Ha. • Optimal fusion temperature for heat transfer is found to be θ f = 0.5. This study investigates the effects of Nano-Encapsulated Phase Change Materials (NEPCMs) on double diffusive free convection in a partially porous cavity, considering Soret-Dufour effects and magnetohydrodynamics. The problem is modeled using non-dimensional governing equations, solved numerically through a Galerkin finite element method. The research examines the influence of key parameters including Rayleigh number ( Ra : 10 3 –10 5 ), Darcy number ( Da : 10 –4 -10 –1 ), Hartmann number ( H a : 0 − 80 ), NEPCM volume fraction ( ϕ : 0 − 0.04 ), Lewis number ( L e : 0.1 − 10 ), fusion temperature ( θ f : 0.1 − 0.9 ), and Stefan number ( S t e : 0.1 − 0.9 ) on heat and mass transfer characteristics and entropy generation. Results show that increasing R a significantly enhances heat and mass transfer, with Nusselt and Sherwood numbers rising by 424.8 % and 547.3 % respectively as R a increases from 10 3 to 10 5 . Higher D a and ϕ improve heat transfer, while stronger magnetic fields suppress both heat and mass transfer. An optimal fusion temperature ( θ f = 0.5 ) is identified for maximum heat transfer enhancement. Total entropy generation, considering thermal diffusion, nanofluid friction, magnetic effects, porous medium, and mass diffusion contributions, increases by 15,957 % with R a and decreases by 42.5 % with increasing H a . The Bejan number analysis reveals that non-thermal irreversibilities become increasingly dominant at higher Ra and Ha values. The study concludes that NEPCMs can effectively enhance heat transfer in partially porous cavities, with their performance strongly influenced by R a , D a , and H a . The findings provide valuable insights for optimizing thermal management systems incorporating NEPCMs, particularly in applications involving porous media and magnetic fields.