Finite element analysis of nanolayer thermal conductivity in Boger nanofluid flow with radius of nanoparticle and motile microorganisms under time-dependent conditions

This study investigates the effect of the single-walled carbon nanotube (SWCNT) nanoparticle radius on the mixed convection and nanolayer thermal conductivity flow of a Boger nanofluid over a stretching disk. Due to their elastic and non-Newtonian properties, Boger fluids are applicable in fields like polymer processing, rheological studies, enhanced oil recovery, and industries such as biomedical, food, and cosmetics, where simulating complex fluid flow behaviors is crucial. The research further explores the heat and mass transfer of the Boger fluid, considering factors such as viscous dissipation, Joule heating, magnetic field influence, porous medium permeability, and activation energy, while focusing on the flow behavior of motile microorganisms. The partial differential equations (PDEs) governing the system are reformulated in dimensionless form using appropriate non-dimensional variables. The finite element method (FEM) is used to solve these nonlinear and complex flow equations through an iterative approach, generating both numerical solutions and graphical representations of the nonlinear system via MATLAB programming. To ensure the reliability and accuracy of the numerical solution, convergence criteria are assessed, and results are compared with established reference solutions. The impact of various dimensionless variables on different flow profiles is analyzed through 2D and 3D graphical representations, as well as numerical analysis of key physical quantities. The study finds that expanding the nanoparticle radius increases skin friction, while the Nusselt number decreases in the porous disk, with optimal results occurring at τ∗=0.1. The velocity profile improves with a higher solvent fraction, but diminishes as the relaxation time ratio increases at η∗=0.7 and τ∗=1.96. Increasing nanolayer thickness enhances temperature distribution, whereas a larger particle diameter reduces the heat transfer rate in nanofluid flow. Higher values of dimensional activation energy enhance the concentration profile, while an increase in temperature difference and dimensional reaction rate parameters reduces the mass transfer rate with variations in τ∗ and η∗. Additionally, higher values of the bioconvection Lewis and Peclet number parameters have opposite effects on microorganism distribution for different values of τ∗ and η∗, with the Sherwood number decreasing with larger dimensional activation energy values, and larger values of the motile Schmidt number enhancing the flow of motile microorganisms.