Effect of Local Thermal Nonequilibrium on Thermobioconvection in Porous Media

Abstract Bioconvection in porous media significantly influences numerous practical systems, such as bio-engineering processes, microfluidic transport, wastewater management, and the optimization of microbial fuel cells and bioreactors. This study investigates the initiation of thermobioconvection in a porous layer containing the negative gravitactic micro-organisms when subjected to local thermal nonequilibrium, confined between two horizontal surfaces subjected to bottom heating. The micro-organisms mobility is modeled using Pedley's formulation, while fluid motion is governed by the Darcy–Brinkman framework. The governing equations are analyzed using a normal mode formulation, leading to an eigenvalue problem that is solved via the Galerkin method for free–free and rigid–rigid boundary conditions. The analysis reveals that the system exhibits only stationary convection, as the computed values of frequency remain negative under both types of boundary conditions. Increasing the interphase heat transfer coefficient stabilizes the system by raising the critical thresholds for the onset of thermal and bioconvective instabilities, although this effect gradually saturates beyond 103. In contrast, stronger micro-organism swimming and lower cell diffusivity promote earlier onset of instability. Higher permeability also facilitates convection by reducing resistance to fluid motion, advancing the onset of instability up to approximately 0.3, beyond which the effect becomes nearly constant. In addition, the local thermal nonequilibrium (LTNE) formulation predicts higher critical thresholds, indicating a stabilizing effect due to heat redistribution between the solid and fluid phases.