A comparative study of two-phase flow of an infusion of gyrotactic microorganisms and dust particles in trihybrid nanofluid with melting phenomena and Soret–Dufour effects

Background: This investigation's main goal is to examine the impacts of Soret and Dufour on Marangoni convective flow of dusty trihybrid nanofluid over a Plate containing gyrotactic microorganisms, heat generation, and melting processes. A trihybrid nanofluid containing nanoparticles of Magnesium oxide MgO, Titanium dioxide TiO2, and Silver Ag in a water-based fluid. This proposed model is used to contrast the activity of dual well-known trihybrid nanofluid models for thermal conductivity, the Hamilton–Crosser model and the Yamada-Ota model. Methods: An appropriate similarity variable is utilized to reduce governing partial differential equations to couple nonlinear ordinary differential equations. After that the system of equations is numerically solved using the effective Bvp4c Method. Applications: Especially in high-performance cooling applications like electronics and aeronautical engineering, this comprehensive study could be very helpful in enhancing thermal management systems. With regard to the introduction of bio-convection brought about by the presence of gyrotactic bacteria, this model can be applied to advanced bio-engineering applications such as bioreactors and medical equipment. Understanding the behavior of these complex fluids under gradients in concentration and Soret–Dufour effects may also lead to improvements in the production and processing of materials, where precise temperature and concentration controls are critical. Results: The temperature and velocity distributions of the dusty ternary hybrid nanofluid are shown to be predominant with higher melting parameters; while, the concentration and microorganism distributions show the opposite pattern.