The blood is a complex fluid that contains, in addition to water, cells, macro-molecules and a large number of smaller molecules. The physical properties of the blood are therefore the result of non-linear interactions of its constituents, which are influenced by the local flow field conditions. Hence, the local blood viscosity is a function of the local concentration of the blood constituents and the local flow field itself. This study considers the flow of blood-like fluids in generalised 90-degree bifurcating pipes and patient-specific arterial bifurcations relevant to the large aortic branches in humans. It is shown that the Red Blood Cell (RBC) distribution in the region of bifurcations may lead to large changes in the viscosity, with implications on the concentrations of the various cells in the blood plasma. This in turn implies that the flow in the near wall regions is more difficult to estimate and predict than that under the assumption of a homogeneous fluid. The rheological properties of blood are complex and are difficult to measure, since the results depend on the measuring equipment and the inherent flow conditions. We attempt to model the viscosity of water containing different volume fractions of non-deforming RBC-like particles in tubes. The apparent viscosities of the mixtures obtained from these model experiments have been compared to the predictions of the different rheological models found in the literature. The same rheological models have also been used in the different simulations, where the local RBC concentration and local shear rate are used in the viscosity models. The flow simulations account for the non-linearity due to coupling between the flow and fluid rheology. Furthermore, from a physiological perspective, it is shown that oscillatory wall shear stresses are affected by changes in RBC concentration in the regions of the bifurcation associated with atherogenesis. The intrinsic shear thinning rheological property of the blood, in conjunction with stagnation in separated flows, may be responsible for elevated temporal wall shear stress gradients (TWSSG) influencing endothelial cell behaviour, which has been postulated to play a role in the development of atherosclerosis. The blood-like fluid properties along with variations in the RBC concentration could also lead to variations in the developing flow structures in the larger arteries that could influence the work the heart has to bear.