Numerical analysis of MHD double-diffusive convection and entropy generation in a wavy porous cavity filled with NEPCM suspension

Effective thermal and mass transport management in double-pipe heat exchangers remains a critical challenge in energy storage, electronics cooling, and industrial process optimization. This study numerically investigates the combined effects of nano-encapsulated phase change material (NEPCM) concentration and magnetohydrodynamics (MHD) on double-diffusive natural convection and entropy generation within a partially porous wavy-wall cavity representative of a double-pipe heat exchanger. The Finite Element Method (FEM) (Galerkin weighted residual approach) is employed across a wide parametric range: Rayleigh number ( 10³ ≤ Ra ≤ 10⁶ ), Lewis number ( 0.1 ≤ Le ≤ 10 ), buoyancy ratio ( 1 ≤ N ≤ 4 ), Hartmann number ( 0 ≤ Ha ≤ 60 ), fusion temperature ( 0.1 ≤ θ f ≤ 0.9 ), Stefan number ( 0.1 ≤ Ste ≤ 0.9 ), Darcy number ( 10⁻⁵ ≤ Da ≤ 10⁻¹ ), and NEPCM volume fraction ( 0 ≤ φ ≤ 0.05 ). Key findings demonstrate that Nu avg and Sh avg increase by 88% and 91% respectively as Ra rises from 10³ to 10⁶, while declining by 33% and 15% when Ha increases from 0 to 50. Fusion temperature exhibits negligible influence on bulk heat and mass transfer but governs the position of the melting/solidification zone. Total entropy generation increases by 99% with Ra elevation from 10³ to 10⁵, while rising Le suppresses entropy by 84%. These results provide quantitative design guidelines for MHD-controlled double-pipe heat exchangers incorporating NEPCM and porous inserts.