Transport phenomena with fluid flow, heat, mass, nanoparticle species and microorganism transferexternal to a needle in a porous medium have many biomedical engineering applications (e. g.hypodermic needles used in hemotology). It is also used to design many biomedical engineeringequipments and coating flows with bio-inspired nanomaterials. Coating flows featuringcombinations of nanoparticles and motile micro-organisms also constitute an important applicationarea. A mathematical model for convective external boundary layer flow of a power-law nanofluidcontaining gyrotactic micro-organisms past a needle immersed in a Darcy porous medium isdeveloped. Multiple slips boundary conditions and Stefan blowing effects at the needle boundaryare taken into account. The model features a reduced form of the conservation of mass, momentum,energy, nanoparticle species and motile micro-organism equations with appropriate coupledboundary conditions. The governing nonlinear partial differential equations (NPDEs) areconverted to dimensionless form and appropriate invariant transformations are applied to obtainsimilarity ordinary differential equations (SODE). The transformed equations have been solvednumerically using the in-built Matlab bvp4c function. The influence of the emerging parameterson the dimensionless velocity, temperature, nanoparticle concentration, motile micro-organismdensity functions, skin friction, heat, mass, and micro-organism transfers) are discussed in detail.It is found that velocity decreases whilst temperature, concentration, and density of motile microorganism increase with an increase in blowing parameter for shear thinning (pseudoplastic),Newtonian, and shear thickening (dilatant) fluids. It is also found that skin friction, Nusselt number(dimensionless heat transfer rate), Sherwood number (dimensionless nanoparticle mass transferrate) and motile micro-organism wall density gradient decrease with increasing blowing, Darcy,power law and needle size parameters. Comparison with the earlier published results is alsoincluded and an excellent agreement is obtained
