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In this study, the Homotopy Analysis Method (HAM) is employed to investigate the flow of a Ferro-hydrodynamic bio-nanofluid over a co-axial rotating disks with Stefan blowing, magnetic dipole, and hall effects. The heat transport mechanism is modeled by using the Brownian movement and thermophoresis. The governing equations are derived and transformed into nondimensional form using appropriate similarity transformations. The resulting equations are solved analytically using the Homotopy Analysis Method. The obtained results are compared with the existing literature and are found to be in excellent agreement. The effects of various parameters such as Hartmann number ( Ha ), Ferro-hydrodynamic interaction parameter ( B ), Stefan blowing effectPeclet ( Pe ), and bio-convection Lewis number ( Lb ) are examined  via  graphical representation. Moreover, the bio-nanofluid radial velocity field is enhanced by improving the values of hall and Ferro-hydrodynamic interaction parameter (FHD). The temperature profile is diminished due to increasing the values of hall parameter, while the opposite behavior is observed when rising the values of FHD parameter. Increasing the Hartmann number (Ha) lead to decline the radial and tangential velocity, whereas the temperature profile is enhanced. The motile microorganisms filed is significantly affected by bio-Lewis and Peclet numbers. The significance of Stefan blowing is discussed on the hydrodynamic, heat, and mass transport aspects for the instances off w= 0, andrespectively. Also, the drag coefficient, heat and mass transport, motile microorganisms rates are discussed  via  tables.

Homotopy analysis approach to Ferro-hydrodynamic bio-nanofluid flow over a co-axial rotating discs with Stefan blowing and magnetic dipole