Mixed convective flow in a vertical channel filled by a bidisperse porous medium in the presence of exothermic reactions

Transport phenomena in fluid-saturated bidisperse porous media (BDPM) are relevant to numerous practical applications, including thermal insulation, porous catalysts, heat pipes, and energy storage systems. In these systems, heat generation associated with exothermic chemical reactions can lead to thermal runaway and potentially hazardous ignition or explosion, while the effects of such heat release in BDPM remain only marginally investigated. This study investigates mixed convective flow in a long vertical channel filled with a BDPM in the presence of heat generation due to an exothermic chemical reaction occurring in the microphase, with the main objective of determining the critical conditions leading to thermal ignition/explosion when heat transfer takes place between the micro- and macrophases. A mathematical model based on a two-temperature and two-velocity formulation is developed for the macro- and microphases of the BDPM. The resulting dimensionless equations are solved numerically using an algorithm implemented with MATLAB routines, and the influence of the main governing parameters, particularly the Frank–Kamenetskii parameter and the interphase heat-transfer parameters, on the flow and heat-transfer behavior is analyzed. For the parameter ranges investigated, the numerical results reveal dual solutions below a critical value of the Frank–Kamenetskii parameter, and the corresponding existence and stability characteristics are established. The results also demonstrate that the interphase heat-transfer parameters significantly affect the thermal behavior and the conditions for ignition/explosion. These findings indicate that modifying the characteristics of artificially engineered BDPM, including porosity and interphase heat transfer, may provide a means of influencing or potentially preventing thermal ignition/explosion in porous systems relevant to chemical reactors and energy storage applications.