ABSTRACT The study of the dynamics of Upper‐Convected‐Maxwell and Casson fluids conveying tiny particles significantly enhances our understanding of multiphase flows, with vital implications for biomedical, industrial, and environmental applications. Despite extensive research, the influence of Joule dissipation and thermal source/sink on the swimming of gyrotactic microorganisms in steady‐state Casson‐Maxwell nanofluid flow through a porous medium with radiation and Soret effects remains underexplored. This investigation, utilizing Buongiorno's bioconvection nanoliquid model, incorporates Brownian motion and thermophoresis to reveal critical features of gyrotactic microorganisms. The heat and mass transfer characteristics are described through two‐dimensional, coupled steady‐state differential equations. Dimensional complexity is reduced via appropriate scaling transformations. Results demonstrate that increasing the magnetic parameter significantly retards the Casson‐Maxwell nanofluid flow while enhancing the thermal profile. Increased Brownian motion and thermophoretic parameters accelerate heat diffusion. Notably, enhanced radiation, heat source/sink, and Eckert numbers further promote thermal diffusion, whereas a higher Peclet number diminishes the microorganism concentration field. These findings offer valuable insights for industrial and thermal engineering, particularly in optimizing machine efficiency and productivity. The Matlab‐based bvp4c numerical results show excellent agreement with existing solutions, reinforcing their validity and applicability. When Brownian number is minimal, the proportional to heat transfer rate decreases with thermophoretic number at the rate of −1.5532 but decreases with thermophoretic number at the rate of −0.0891 when Brownian number is sufficiently large.
Sharanayya et al. (Wed,) studied this question.