Homotopy perturbation method solution of magneto-polymer nanofluid containing gyrotactic microorganisms over the permeable sheet with Cattaneo–Christov heat and mass flux model

Many non-Newtonian materials behave as a polymeric solution and this type of materials is used in various industrial and physical applications such as polymer extraction, manufacturing processes, various geophysical systems, and glass production. Especially the gyrotactic microorganisms have widely used for the production of biodiesel, hydrogen, an essential sustainable energy source and in water treatment plants. This study intends to examine the impacts of magnetic field, convective boundary state on bioconvection of a tangent hyperbolic nanofluid in the presence of gyrotactic microorganisms over a porous stretching surface with a Cattaneo–Christov heat and mass flux model. Appropriate self-similarity variables are implemented to transform the fluid transport equations into ordinary differential equations that have been resolved using the homotopy perturbation method. The influences of effective parameters on transport properties of the fluid are represented with graphs and tables. This model forecast the shear-thinning attitude significantly and exactly describes the flow of fluids. It is noted from the obtained results that the velocity profile declines with raising the Weissenberg number and buoyancy ratio parameter. It also observed that the temperature profile rises with a growth in the radiation and thermal relaxation parameters. The higher values of the stagnation parameter increase the rate of heat transfer while it is opposite nature in the mixed convection parameter. Microorganisms density uplifts with an increase in Peclet number, while it decreases for the microorganism concentration difference. Microorganisms density increases with an enlargement in bioconvection Schmidt number.