The captivating realm of bio-convection has garnered significant attention due to its wide array of applications spanning medicine, cancer treatment, advanced aircraft manufacturing, water distillation, enhanced electronic instruments, efficient batteries, cosmetics production, and modern defense equipment. Recognizing this multifaceted significance, a numerical investigation focused on buoyancy-driven flow, encompassing thermal and diffusion processes within a saturated Darcy medium. This study accounted for thermal radiation, Brownian motion, gyrotactic organisms, and thermophoresis, elucidating their effects under two pivotal scenarios: flow around a cone and a paraboloid. The governing physical system initially manifested as nonlinear partial differential equations. Through appropriate transformations, this system was converted into an ordinary differential system, facilitating analysis. Employing the numerical prowess of the Runge-Kutta method, these equations were solved. The culmination of this endeavor unveiled graphical solutions portraying the intricacies of two distinct revolutions—cone and paraboloid. These graphical representations, accompanied by tables, elucidated various physical attributes of the system. Notably, they detailed thermal and diffusion distributions, along with rates of heat and mass transfers. An intriguing observation surfaced: the presence of micro-organisms significantly elevated the mass transfer rate compared to scenarios without micro-organisms.