Numerical study of third‐grade nanofluid flow with motile microorganisms under the mixed convection regime over a stretching cylinder

The investigation of mixed convective flow involving microorganisms in nanofluid has garnered considerable interest in recent times owing to its extensive applicability in the biomedical domain. However, there has been a lack of study investigating a comprehensive parameter analysis for the flow of a third‐grade nanofluid around a cylinder in the presence of microorganisms. This study focuses on numerically investigating the flow of nanofluid around a stretched cylinder in the presence of motile microorganisms. The study also considers convective boundary conditions. Moreover, this study explores the nanofluid qualities related to Brownian motion and thermophoresis diffusion characteristics. The variable parameters include the Prandtl number (Pr), Peclet number (Pe), buoyancy ratio parameter (Nr), mixed convection parameter (), bioconvection Lewis number (Lb), Biot number (Bi), and Marangoni number (Ma). The bvp4c issue solver tool in MATLAB is used to numerically solve the nonlinear governing differential equations. The numerical model has been validated using prior papers. Graphical representations are created to depict several important measurements, such as velocity streamlines, velocity profiles, temperature distributions, nanoparticle concentrations, densities of gyrotactic motile microorganisms, local Nusselt numbers, skin friction, and Sherwood numbers. The link between the Nusselt number and the parameters Nt and Rd suggests that as Nt falls and Rd increases, the Nusselt number increases. The skin friction value is directly proportional to the values of Nr and Nc. There is a positive correlation between the rise in the local mass transfer rate and the values of Rd and Nt. The population of mobile microorganisms grows as the values of Lb and Pe decrease.