bioconvection phenomenon for the boundary layer flow of magnetohydrodynamic carreau liquid over a heated disk

A numerical examination is conducted for the magnetohydrodynamics steady carreau fluid flow on the transport of thermal energy and mass specie comprising nanoparticles with gyrotactic microorganisms through heated disk. the role of thermophoresis and brownian motion are added in this flow problem. governing equations are achieved by using the boundary layer theory in view of a coupled system of pdes involving boundary conditions. the highly non-linear system of odes is generated using the concept of the transformation approach. since the system of transformed equations is highly nonlinear, so, an approximate solution is estimated via optimal homotopy method. the role of prominent parameters on velocity, thermal energy, mass specie and motile density microorganisms examined graphically. additionally, graphical observations regarding mass specie, thermal energy and velocities are discussed briefly. it has estimated that the motion of fluid particles is diminished because of the intensity of the magnetic field while mass specie and fluid temperature rise versus enhancement the values of the magnetic field.