A self-consistent model of a DC glow discharge with dust particles based on orbital motion limited theory, collision enhanced collection approximation, and a fluid approach extended by energy conservation equation is presented. The model indicates the influence of dust particles on radical distributions of plasma parameters in positive columns. Dust particles are embedded in the positive column with the density profile prescribed as a given step function. It is shown that with the increase in dust particle density, electron density and the radical electric field decrease in the dust region. For high dust density, especially when the loss of ions and electrons on the dust surface exceeds their production in ionization collisions in the dust region, a local minimum of electron density forms in the discharge axis and the radical electric field obtained from the Poisson equation becomes non-monotonous. The addition of dust increases the longitudinal electric field and electron temperature simultaneously to compensate the electron and ion loss on dust particles and preserve the discharge.