A force model leading to the usual quasilinear particle flux is developed for the equations of motion used in the transport equations of the multi-fluid transport code TASK/TX. The model precisely corresponds to a quasilinear flux consisting of diagonal, thermodiffusive and pure convective contributions, where the turbulent coefficients of the force model are externally provided by a model of the turbulent process. Our approach is consistent in that particle transport can be described through a change in radial particle flux by solving the continuity equation and the equations of motion self-consistently. Time-dependent simulations that vary the ratio of particle diffusivity to thermal diffusivity show that thermal neutrals as a particle source in the core region affect the formation of density profile in the limit of the smallness of the ratio, while an increase in the ratio rapidly decreases the effectiveness of the source effect.