Natural Double-Diffusive Thermomagnetic Convection and Second-Law Examination in a Double-Slope Solar Still With a Non-Darcy Porous Bed Under LTNE Conditions

Abstract

The increasing global demand for potable water has driven growing interest in solar desalination as a sustainable and energy-efficient solution. This study presents a numerical investigation of coupled double-diffusive thermomagnetic natural convection and entropy generation of an air-vapor mixture within a symmetrical double-slope solar still equipped with a horizontal porous bed. The porous bed operates under local thermal nonequilibrium conditions with internal heat generation due to solar irradiance absorption, and is modeled using the extended Darcy-Brinkman-Forchheimer approach. The convective flow is subjected to a horizontal magnetic field with Joule heating effects accounted for. The dimensionless governing equations are solved numerically using the finite volume method under steady-state conditions. The analysis examines the effects of the thermal Rayleigh number (Ra), Hartmann number (Ha), heat generation parameter (Q), dimensionless interphase heat transfer coefficient (H), modified thermal conductivity ratio (gamma), and buoyancy ratio (N) on the double-diffusive flow structure, heat and mass transfer rates, and second-law performance. The results show that Ra enhances convective heat and mass transfer while Ha suppresses fluid motion through Lorentz forces, reducing flow intensity by approximately 54% as Ha varies from 0 to 50. Increasing Q reduces both fluid and solid-phase Nusselt numbers while leaving the Sherwood number unaffected, confirming the decoupling of solutal transport from the thermal state of the porous bed. Both H and gamma dramatically enhance solid-phase heat transfer with minimal influence on mass transport. Entropy generation analysis reveals that optimal thermal and mass transfer performance is achieved at Ra = 104, where the performance criteria reach their minimum. Thermal performance improves by 51.47% and 41.8% as H increases from 1 to 1000 and gamma increases from 1 to 100, respectively, while their influence on mass transfer efficiency remains negligible.