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In RANS simulations for turbulent scalar transport, it is common that using an eddy-viscosity (EV) model to close the Reynolds stress yields reasonable mean flow predictions but large errors in scalar transfer results regardless of scalar flux model inadequacies. This failure mode of EV models is generally related to the fact that the transport of momentum and scalar depends on different Reynolds stress components. The present work addresses two common issues relevant to such failures in turbulent scalar transport around obstacles. The first issue is the general overprediction of scalar transfer near the upwind surfaces, which is primarily attributed to the absence of wall-blocking mechanism in conventional EV models. We accordingly propose a Shear-Preserving-Wall-Blocking (SPWB) method to analytically correct the overpredicted wall-normal stress under the realizability constraint. The second issue is the general underprediction of scalar transfer in the downstream large separation regions, which is essentially attributed to the presence of vortex shedding invalidating the scaling ground in conventional EV models' dissipation closures. We accordingly apply the recently proposed Double-Scale Double-Linear-EV (DSDL) model to scalar transport predictions. Consequently, a hybrid model SPWB-DSDL is developed. The model is then applied to two test cases, of which the first features a bluff obstacle with an upstream impingement flow and a downstream two-dimensional separation and the second a streamlined obstacle with an upstream concave surface flow and a downstream three-dimensional separation. In the two cases, the SPWB-DSDL model is capable of simultaneously yielding reasonable results of mean flow field, turbulence energy and stress, and scalar transfer in both upstream and downstream regions, thus demonstrating significant improvement upon a classical EV model.