Numerical study for bioconvection in Marangoni convective flow of Cross nanofluid with convective boundary conditions

The current study investigates incompressible, MHD flow of Cross nanofluid containing of gyrotactic microorganisms and thermophoretic particle deposition over a sheet with activation energy and variable thermal conductivity. The variable characteristic of thermal conductivity is considered as a linear function of temperature. The present study's insights can optimize the design of nanofluid-based systems, enhance drug delivery methods, improve environmental monitoring, refine materials engineering, advance microfluidics for diagnostics, boost renewable energy technologies, and upgrade electronics cooling solutions. Moreover, this study contribution to scientific understanding will catalyze further research across disciplines, fostering innovation and progress. Cross nanofluid containing iron oxide (Fe3O4) nanoparticles, and based fluid ethylene glycol (C2H6O2) is used. In the current study, distributions of concentration, temperature, mass, microorganisms, and flow are examined in the presence of nanofluid while also accounting for thermophoretic particle deposition and a heat source. The proposed flow equations are transmuted into ODEs by employing the suitable similarity variables. RKF-45th approach is used to evaluate the reduced equations. Graphs are used to determine the effects of important factors on thermal, microorganism, concentration, and flow profiles. With a rise in the Marangoni ratio parameter, the velocity distribution is enhanced, whereas the temperature distribution exhibit inverse behavior.