In this work, the momentum and thermal boundary layers for power-law fluids over a thin needle have been investigated numerically under wide ranges of kinematic and physical conditions, The curvature effects are incorporated into the analysis whereas the pressure variation in the axial direction has been neglected, Extensive results on axial velocity and temperature profiles elucidating the complex interplay between the shear-thinning or shear-thickening characteristics of the fluid, size of the needle and the Reynolds number of flow are presented herein. The role of the two commonly used thermal boundary conditions (constant temperature and constant heat flux) has been illustrated by way of contrasting the resulting temperature profiles and the values of the Nusselt number. Overall, the results presented herein encompass the following ranges of the physical and kinematic variables: 0.2 less than or equal to n less than or equal to 1.6; Pr-L < 1000 and Re-L < 10(6).