In this article modeling and theoretical analysis of magnetized Williamson nanomaterial flow by permeable
surface of cylinder is studied. The idea of self-propelled gyrotactic microorganisms is implemented to stabilize
the suspended nanoparticles in Williamson liquid. Darcy-Forchheimer together with porosity effects are
accounted in the flow. Energy relation is modeled in view of thermal radiation, variable thermal conductivity
and Joule heating. Activation energy linked with chemical reaction is executed at the surface. Furthermore,
Brownian dispersion and thermophoresis effects are also considered. Flow governing dimensional model is
acquired using boundary layer suppositions. Suitable transformations are used to alter the system of PDE’s
into non-dimensional. NDSolve code in Mathematica package is utilized to solve the model. Impacts of various
flow regulating variables on velocity, temperature, mass concentration and motile density are investigated by
plotting. Coefficient of skin friction, Sherwood number, motile density number and heat transfer rate are tabulated
and analyzed. It is observed that velocity field decays while temperature field enhances versus rising
dimensionless magnetic parameter. Moreover, due to magnetic field more Lorentz force is applied to the flow as
a result surface drag force enhances while heat transfer rate decays.