Hemodynamic data on the roles of physiologically critical blood particulates are needed to better understand cardiovascular diseases. The blood flow patterns and particulate buildup were numerically simulated using the multiphase non-Newtonian theory of dense suspension hemodynamics in a realistic right coronary artery (RCA) having various cross sections. The local hemodynamic factors, such as wall shear stress (WSS), red blood cell (RBC) buildup, viscosity, and velocity, varied with the spatially nonuniform vessel structures and temporal cardiac cycles. The model generally predicted higher RBC buildup on the inside radius of curvature. A low WSS region was found in the high RBC buildup region, in particular, on the area of maximum curvature of a realistic human RCA. The complex recirculation patterns, the oscillatory flow with flow reversal, and vessel geometry resulted in RBC buildup due to the prolonged particulate residence time, specifically, at the end of the diastole cycle. The increase of the initial plasma viscosity caused the lower WSS. These predictions have significant implications for understanding the local hemodynamic phenomena that may contribute to the earliest stage of atherosclerosis, as clinically observed on the inside curvatures and torsion of coronary arteries.