This paper undertakes a thorough study to examine heat and mass transfer of two-layer hybrid nanofluid flow in a vertical channel. Casson fluid model is used to investigate the non-Newtonian nature of blood flow (base fluid) in this study. The problem is formulated which includes laminar, incompressible flow with additional viscous dissipation effects. Titanium dioxide and Graphene nanoparticles are employed in this study for the hybrid notion. At the interface, it is considered that the velocity and temperature remain continuous. A group of non-dimensional transformations are used to non-dimensionalized the set of ordinary differential equations and those non-linear differential equations are then solved using an analytical method known as homotopy analysis method (HAM). The behavior of physical parameters on velocity and temperature are presented graphically. Variation of Nusselt number against emerging parameters are tabulated to provide numerical data for validation. The findings of present study can provide insight into the behavior of blood flow in diseased conditions atherosclerosis, thrombosis, and other cardiovascular diseases. This study can also help in designing more effective drug delivery systems for targeted therapies.