Coupled Thermal and Solutal Transport in Magnetic Nanofluids with Field-Dependent Viscosity in Porous Media: A Stability Perspective

Abstract

This study investigates the linear stability of double-diffusive convection in magnetic nanofluids (MNFs) within a horizontal porous medium, accounting for field–dependent viscosity (FDV). A modified Buongiorno– type model incorporates Brownian motion, thermophoresis, magnetophoresis, and Darcy resistance. The resulting eigenvalue problem is solved via a Chebyshev pseudospectral–QZ algorithm under rigid–rigid (RR), rigid–free (RF), and free–free (FF) boundary conditions for both water–based (Wb) and ester–based (Eb) MNFs. Results show that magnetic and solutal effects lower the critical Rayleigh number (Rac) from the classical Darcy–Bénard limit of ≈39.48 to as low as ≈23.8, indicating enhanced instability. In contrast, increasing the FDV coefficient (δ), Langevin parameter (αL), and nanoparticle concentration difference (�φ) raises Rac, stabilizing the system. Eb–MNFs exhibit consistently higher Rac values—by 15%–20% compared to Wb–MNFs, due to greater viscosity and lower thermal diffusivity. These findings clarify the interplay of magnetoviscous damping and solutal buoyancy, offering predictive insights for the design of magnetically tunable porous heat exchangers and thermal management systems.

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