Entropy modeling in bioconvective stratified magnetohydrodynamic cross hybrid nanofluid flow with thermal radiation

Hybrid nanofluids(HNF) with microorganisms are significant for improving the efficiency and control of systems that rely on biological processes. These could include biotechnology, environmental treatment, biomedical engineering, and energy systems, where enhanced heat transfer and nanoparticle functionality can offer performance advantages. The aim of the current study is to scrutinize the entropy generation(EG) stratified cross hybrid nanomaterial flow by a stretchable cylinder in the presence of gyrotactic microorganisms. Hybrid nanofluid is developed by suspending rigid nanoparticles of titanium dioxide $\left({\text{TiO}}_2\right)$ and silver $\left(\text{Ag}\right)$ into water $\left(H_{2}O\right)$ based Cross fluid. Momentum equation is formulated accounting the features of Darcy-Forchheimer and permeability of the surface. Joule heating and thermal radiation impacts are considered in the thermal energy equation. Thermal, mass concentration and density stratifications are considered at the edge of the surface. The flow governing model is obtained by implementing boundary layer assumptions. To obtain the numerical solution, transformations are utilized to yield the corresponding system of ODE's. Mathematica software is availed to execute the code for the Runge-Kutta Fehlberg (RKF-45). Graphical investigation is carried out to examine the impact of diverse physical variables on the temperature, entropy rate, velocity, gyrotactic microorganism, Bejan number, and concentration profiles. In addition, against each involved physical parameter, the numerical results have been analyzed for surface drag force, mass, heat, and motile density transfer rates. The results show that higher stratification decays the thermal, solutal, and density profiles of the bioconvective hybrid nanofluid field. Heat transfer rate boosts versus Hartmann number and radiation parameter. Hybrid fluid velocity and mass concentration fields increase with rising curvature parameters, while thermal and motile density fields decrease. Furthermore, entropy rate and Bejan quantities accelerates through Brinkman, Hartman and radiation variables.