The effect of the uniform fluid properties approximation (Oberbeck-Boussinesq (OB)) in turbulent mixed convection is investigated via direct numerical simulation (DNS) of water flows with viscosity (μ) and thermal expansion coefficient (β) both independently and simultaneously varying with temperature (non-Oberbeck-Boussinesq conditions (NOB)). Mixed convection is analyzed for the prototypical case of Poiseuille-Rayleigh-Bénard (PRB) turbulent channel flow. In PRB flows, the combination of buoyancy driven (Rayleigh-Bénard) with pressure driven (Poiseuille) effects produce a complex flow structure, which depends on the relative intensity of the flow parameters (i.e., the Grashof number, Gr, and the shear Reynolds number, Reτ). In liquids, however, temperature variations induce local changes of fluid properties which influence the macroscopic flow field. We present results for different absolute values of the shear Richardson numbers () under constant temperature boundary conditions. As Riτ is increased buoyant thermal plumes are generated, which induce large scale thermal convection that increases momentum and heat transport efficiency. Analysis of friction factor (Cf) and Nusselt number (Nu) for NOB conditions shows that the effect of viscosity is negligible, whereas the effect of thermal expansion coefficient is significant. Statistics of mixing show that (i) mixing increases for increasing Riτ (and decreases for increasing Reτ) and (ii) the effect of thermal expansion coefficient on mixing increases for increasing Riτ (and decreases for increasing Reτ). A simplified phenomenological model to predict heat transfer rates in PRB flows has also been developed.