Exploring assisting and opposing flow characteristics in a saturated darcy medium with non-uniform heat source or sink and suspended microbes

Aim of the studyIn this study, I investigated buoyancy-driven convection involving suspended microorganisms in a saturated Darcy porous medium, considering the effects of thermal radiation, Brownian motion, thermophoresis, and non-uniform heat source/sink. I focused on slender geometries, specifically a cone and a cylinder, under both assisting and opposing flow conditions, to better understand their impact on heat and mass transfer behavior. Significance and novelty:Bio-convection has wide-ranging applications in drug delivery, cancer therapy, electronics cooling, microbial fuel cells, water purification, and cosmetic formulations. Unlike other researchers, I uniquely integrated the effects of non-uniform thermal conditions, gyrotactic microorganism dynamics, and slender body geometry. The inclusion of a multilinear regression model added an analytical layer for interpreting parameter sensitivity, which enhanced the model's utility in engineering design. MethodologyThe governing nonlinear partial differential equations were transformed into a system of ordinary differential equations using similarity transformations. These equations were solved numerically using the fourth-order Runge-Kutta method coupled with a shooting technique. To further analyze parametric trends, multilinear regression was applied to the simulation data. Results and insightsThe presence of gyrotactic microorganisms significantly enhanced mass transfer rates compared to microbe-free scenarios. An increase in thermophoresis led to higher temperature distributions but reduced both concentration and microorganism density. Fluid velocity increased under assisting flows due to stronger buoyancy forces. These trends were demonstrated through detailed stream function and temperature plots and numerical findings for important flow and heat transfer parameters in tabular form for the flow dynamics. ConclusionThis study provides meaningful insights into the role of microorganisms in enhancing mass and heat transfer in porous media. The model serves as a strong foundation for future extensions involving experimental validation, time-dependent simulations, turbulent bio-convection, and more complex geometrical configurations for industrial and biomedical applications.