Here, we report a Monte Carlo study of the critical behavior (scaling law) for a two-dimensional model of nanofluids consisting of randomly distributed conducting nanoparticles with different geometries (circular, square and fibers with different aspect ratios). We have explicitly investigated the influence of the geometrical shape of nanoparticles on the scaling behavior of the electrical conductivity in a composite material. Our results show an aspect ratio dependence of the critical exponent for sticklike particles with finite widths (fibers).