Mixed bio-convection analysis on MHD Casson hybrid nanofluid flow over a spinning cone/plate embedded in a variable porosity medium: a comparative study

The study of heat and mass transport in MHD flows through various geometries is vital for the design of heat exchangers and other devices. With this initiative, a mathematical framework has been proposed to explore the two-dimensional mixed convective, heat, and mass transport dynamics of the magneto-hydrodynamic Casson hybrid nanofluid flow comprised of Fe3O4/TiO across two distinct geometries, the cone and plate revolving in an upright position within a variable porosity medium. The influence of a heat source/sink, Brownian motion, thermophoresis, bio-convection of gyrotactic microorganisms, chemical reaction, and nanoparticle shape effects are substantial physical features of the investigation. The governing equations are partial differential equations that are subsequently transferred into an appropriate structure of coupled nonlinear ordinary differential equations using the requisite similarity variables. In order to compute the transformed non-dimensional governing equation and their relevant boundary conditions, the Range-Kutta fourth-order methodology is used in conjunction with the shooting procedure. With the aid of graphs and tables, the influence of non-dimensional quantities on momentum, energy, solutal, and motile microorganism profiles, along with friction drag, heat transfer rate, Sherwood, and motile density numbers, is discussed. The results showed that flow over a plate containing nanoparticles in the shape of a blade improves heat transfer rate. Also, it has been revealed that the heat and mass transmission efficiency of a revolving cone is substantially higher than that of a rotating plate. Furthermore, the present findings are compared to prior studies, which show significant agreement.