Computation of bio-nano-convection power law slip flow from a needle with blowing effects in a porous medium

Transport phenomena with fluid flow, heat, mass, nanoparticle species and microorganism transfer external to a needle in porous medium have many biomedical engineering applications (e.g. hypodermic needles used hemotology). It is also design equipment's coating flows bio-inspired nanomaterials. Coating featuring combinations of nanoparticles motile micro-organisms constitute an important application area. A model for convective flow power-law nanofluid containing gyrotactic past Darcy developed. Multiple slips Stefan blowing effects at the boundary are considered. The features reduced form conservation equations appropriate coupled conditions. governing converted similarity using invariant transformations. transformed been solved numerically in-built Matlab bvp4c function. influence emerging parameters on characteristics, friction, micro-organism transfers discussed detail. Note that velocity decreases whilst temperature, concentration, density increase parameter shear thinning, Newtonian, thickening fluids. All physical quantities decreasing increasing blowing, Darcy, power law size parameters.