Effects of Local Thermal Non-Equilibrium and Rotation on Thermo-Bioconvection in Porous Media Saturated with Gravitactic Microorganisms

This study investigates the onset of convective instabilities in a porous medium inhabited by gravitactic microorganisms, incorporating the effects of rotation and local thermal non-equilibrium. This system is confined between two horizontal parallel surfaces, heated from below. Microorganism behavior is modeled using Pedley’s framework, while fluid motion through the porous structure is described using the Darcy–Brinkman model. Density variations are incorporated through the Oberbeck–Boussinesq approximation. A linear stability analysis is carried out, yielding a system of ordinary differential equations obtained through normal mode analysis and addressed using the Galerkin method. Both stationary and oscillatory convection modes are examined to capture the full range of dynamic behavior. The results show that rotation and interphase heat transfer stabilize the system by suppressing buoyancy-driven motion, whereas permeability and microorganism motility promote instability by enhancing fluid transport and density variations. Additionally, oscillatory convection becomes significant under strong rotational effects, while boundary conditions play a key role in modulating the onset and nature of instability. Also, numerical results reveal that for free–free, rigid–rigid, and rigid–free boundaries, increasing the interphase heat transfer and rotation rate from 0 to 104 raises the critical Rayleigh–Darcy number by approximately 199%, 199%, 200%, and 382%, 143%, 28%, respectively. These findings highlight the strong stabilizing influence of interphase heat transfer and rotation on porous bioconvection, offering valuable insights for optimizing systems such as microbial fuel cells and bio-reactors.