Onset of convection in an anisotropic bidispersive porous media saturated by hybrid nanofluid

This study investigates convective instability in an anisotropic bidispersive porous medium saturated with a hybrid nanofluid. While hybrid nanofluids and bidispersive porous media have each been widely investigated, their combined influence on the onset of convection has not yet been explored. This study focuses on examining the combined effect. The governing equations are formulated using Darcy's law for momentum balance, the conservation equations for nanoparticles for macro- and micro-phases and the energy conservation assuming thermal equilibrium between the fluid and solid phases. The governing equations are solved by applying normal mode analysis together with a one-term Galerkin method. Both bottom-heavy and top-heavy nanoparticle distributions are considered for stationary and oscillatory modes. The results show that in the bottom-heavy nanoparticle configuration, both stationary and oscillatory modes of instability exist, with oscillatory mode being dominant. In contrast, in the top-heavy configuration, only the stationary mode of instability is observed. The effects of horizontal isotropy in thermal conductivity and permeability within macro- and micro-pores are examined. It is found that anisotropy significantly influences the stability threshold of the system. In a bottom-heavy nanoparticle distribution, increasing the anisotropic permeability from 0.5 to 2 in macro-pores raises the critical Rayleigh number by approximately 39.6% in the stationary mode and 41.3% in the oscillatory mode. The present study provides insight into the combined role of anisotropy and hybrid nanoparticle effects on the stability behaviors of bidispersive porous media. The results are useful in applications such as geothermal energy systems, thermal insulation materials, enhanced oil recovery, underground heat storage, and advanced cooling systems.