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It has been found experimentally as well as theoretically that the lattice thermal conductivity can be largely reduced by the size confinement effect. The significant boundary scattering effect is one of the dominant factors. In most existing lattice thermal conductivity models, an empirical relation is used for this scattering rate. An unconfined or confined phonon distribution obtained based on the phonon Boltzmann equation and the relaxation time approximation is then employed to calculate the lattice thermal conductivity. In this work, we first attempt to derive an analytical form of the boundary scattering rate for phonon conduction in a semiconductor nanowire and then claim two reasonable ways to take it into account correctly. Consistent mathematical models in the sense that the effects of the size confinement on (i) the phonon dispersion relation, (ii) the phonon distribution, (iii) the phonon group and phase velocities, and (iv) the Debye temperature are finally proposed.