One of the key issues of stellar evolution theory is the influence of the transport processes related to rotationally driven macroscopic motions on the internal structure and the evolution of stars. Turbulent mixing of chemical elements due to differential rotation in stellar radiative zones is currently taken into account in many stellar evolution codes through transport coefficients firstly derived by Zahn (1992, A&A, 265, 115). The purpose of our work is to constrain one of these coefficients, the radial diffusion coefficient driven by radial differential rotation through local direct numerical simulations of steady homogeneous stably stratified sheared turbulence, and to compare the results with phenomenological models. In particular, we have determined the dependence of the turbulent diffusion coefficient on thermal diffusivity and chemical stratification.