Assessment of heat and mass transfer in a porous n-shaped heat exchanger using hybrid nanofluid under cross-diffusion and magnetic effects

Optimizing the geometry of cooling systems is vital for achieving the best thermal performance, ensuring energy efficiency, and supporting sustainability. This study introduces a novel approach by exploring the potential of a non-toxic hybrid nanofluid, an 80:20 water-propylene glycol blend combined with multi-walled carbon nanotubes (MWCNT) and iron oxide (Fe₃O₄) nanoparticles, within an innovative n-shaped heat exchanger. The research focuses on the impact of heat and mass sources on magnetohydrodynamic double-diffusive mixed convection (MHD-DDMC), emphasizing the intricate interactions between porous media, nanoparticle dynamics, cross-diffusion effects, and magnetic fields. Numerical simulations are conducted using the lattice Boltzmann method (LBM) to analyze the system's behavior. A sensitivity analysis, supported by Response Surface Methodology (RSM) and Analysis of Variance (ANOVA), quantifies the effects of various parameters on heat and mass transfer, establishing correlations for the average Nusselt number ($\overline{\mathrm{Nu}}$) and Sherwood number ($\overline{\mathrm{Sh}}$). Various dimensionless variables, including porosity (ε), nanoparticles volume fraction (ϕ), source size (a), Lewis number (Le), Richardson number (Ri), buoyancy ratio (Br), Darcy number (Da), Hartmann number (Ha), Soret number (S_r), and Du_four number ( D_f), were evaluated to understand their effect on fluid structure, heat, and mass transfer. The results show that as Le increases, $\overline{\mathrm{Nu}}$ decreases by 23 % at a= 0.1, while the average $\overline{\mathrm{Sh}}$ increases by 81 % at a= 0.3. Rising Ha from 0 to 90 causes $\overline{\mathrm{Nu}}$ to decrease by 58 %, and $\overline{\mathrm{Sh}}$ to decrease by 58 % at a= 0.3. Furthermore, reducing Da from 10⁻¹ to 10⁻⁵ results in the highest increase in $\overline{\mathrm{Nu}}$ by 56 %, and the largest rise in $\overline{\mathrm{Sh}}$ by 67 % at a= 0.3. Sensitivity analysis revealed that the ϕ, D_f, and parameters Br, S_r, and Ri are among the most influential parameters, with their effects on heat and mass transfer being statistically significant according to ANOVA results. At high concentrations, ϕ enhances heat transfer, while D_f significantly improves mass transfer. Additionally, $a$, Br, S_r, and ϕ positively contribute to both heat and mass transfer, while Ri shows a negative influence.