The effective thermal conductivity of nanosystems is known to be strongly depending on their characteristic sizes. In steady state situations, the Guyer-Krumhansl equations have shown to give theoretical predictions that are in good agreement with experimental data. Here we use a specific slip boundary condition to determine the effective thermal conductivity in Si nanowires. We obtain a new expression depending on the dimensionless Knudsen number, i.e., on the ratio of the phonon mean free path and characteristic size of the nanowire. For the validation we use values obtained recently by a collaborating research group. Both factors yield an improved accuracy of the theoretical predictions with respect to experimental data.