Features of microorganism and two-phase nanofluid in a tangent hyperbolic Darcy-Forchhiemer flow induced by a stretching sheet with Lorentz forces

This work examines the two-dimensional tangent hyperbolic flow over a stretching sheet with a uniform magnetic field. The Buongiorno model is utilized to analyze and explain the spread of uneven coefficients in the presence of gyrotactic microorganisms. The concept of microorganisms and the resulting bioconvection enhance the stability of the nanoparticles. The impacts of thermal radiation, heat sources, convective heating, and chemical reactions are also evaluated. The suggested mathematical problem results in a nonlinear set of partial differential equations (PDEs), which are subsequently reduced to ordinary differential equations (ODEs) by applying the appropriate transformation. The resultant highly nonlinear ordinary differential equations (ODEs) are numerically solved using MATLAB's built-in package known as bvp4c. An in-depth investigation into the changes in the velocity field, the temperature profile, the concentration of nanoparticles profile, and the motile density profile is analyzed through graphs against various influencing parameters. Additionally, computations of engineering interest quantities such as skin friction, local Nusselt number, local Sherwood number, and molecular density are presented in both graphical and tabular formats for further examination. It has been explored that with greater values of the Weissenberg number, the fluid velocity upsurges when n < 1 , whereas the opposite behavior is noticed when n > 1 . It is also noted that an increment in the Peclet number decreases motile density for both dilatants n > 1 and pseudoplastic n < 1 fluids. The computed results are compared with existing literature in limiting cases and found good agreement.