The primary objective of the existing framework is to examine the significance of gold nanoparticles immersed in human blood when magnetohydrodynamics (MHD) flow occurs within a stenotic artery. Gold nanoparticles are employed as nanomaterials for medication delivery primarily because of their potential for drug transport and imaging. The blood's warmth and velocity gradually decrease as the size of the gold nanoparticles increases. In addition, the effects of thermal radiation and heat source-sink are taken into account. Using a technique of appropriate similarity transformations, the partial differential equations (PDEs) were transformed into dimensionless ordinary differential equations (ODEs). Then, the ODEs were solved numerically and graphically using the bvp4c built-in solver in the mathematical program MAPLE. Then, using a shooting technique, higher order ordinary differential equations (ODEs) were solved. Graphs elaborate on the physical regulating parameters' results, such as temperature and velocity profiles. As the Biot number and thermal radiation parameter increase, the Biot number is estimated more highly, and the Nusselt number rises, but when the suction or injection parameter is used, it decreases. For the delivery of drugs, the gold nanoparticles are highly helpful, and the thermal distribution profile exhibits an increasing behavior. The current method has the potential to be very helpful in effective blood medication delivery.