Nanofluids are incredibly helpful to researchers because of their higher rates of heat transfer that have huge industrial usages. We discuss blood flow via a tiny artery with a stenosis in the appearance of heat and mass transfer in the existing critique. The non-Newtonian blood flow in narrow artery is mathematically investigated by depicting the blood as Oldroyd-B fluid. The major intention of this investigation is to investigate the impact of MHD in Oldroyd-B nanoliquid flow with gold (Au) nanoparticles (NPs) on stenosis arteries. The properties of heat transfer with joule dissipation are being examined. The base fluid for nanoparticles is blood. Appropriate transformations are exploited to convert the nonlinear PDEs that govern the system into nonlinear ODEs. The numerical results of these ODEs are determined using the Homotopy analysis method (HAM). Flow anticipates for every physical quantity is also investigated. Physical explanations are utilized to illustrate the physical effects of flow limitations versus assumed fluid flow. The results show that as the volume fraction, flow, and relaxation parameters increase, so does the velocity contour. The nanofluid temperature is decreased for the volume fraction and Prandtl number. In addition, the drag force and heat transfer explanations for blood flow dynamics are being investigated. As the flow parameter values increase, the Nusselt number decreases and the drag force increases. The modelling and numerical solution serves an essential role in trying to predict the cause of atherosclerosis.