This article proposes a mathematical investigation of unsteady flow and heat transfer in the presence of Joule Heating over a radially stretching sheet using a nanofluid of Cu-Ethylene glycol. With an extensive numerical study, we reveal the novel interaction between the shape factors of nanoparticles and surface deformations brought about by stretching. As opposed to earlier studies that have mostly concentrated on traditional nanoparticle forms, our investigation methodically looks at the unique behaviors of Cu-EG nanoparticles on stretching surfaces. The research findings offer great potential for numerous practical applications, in addition to providing insight into basic concepts related to fluid dynamics and heat transfer. The solution to this issue is significant for enhancing thermal management in manufacturing environments, such as cooling systems used in aerospace and electronics. Therefore, our work establishes a foundation for novel methods of creating materials with customized qualities, opening the door for the creation of next-generation technologies that are more sustainable and functional. A numerical solution of the highly non-linear ordinary differential equation is attained with suitable boundary conditions by applying BVP4C in MATLAB. Impact of pertinent parameters on Cu-Ethylene glycol nanofluid Joule Heating concentration, as well as Eckert, Prandtl, and Biot-number on flow and heat transport, are studied. Important results show that the Joule Heating effect raises the total heat transfer rate by roughly 15 %, and the addition of Cu nanoparticles improves thermal conductivity by around 22 %. The findings show that the combined influences of Joule Heating and nanoparticle concentration greatly increase the heat transfer efficiency, offering important new information for the optimization of cooling systems in a range of industrial applications. Finding of the current study is that the shape factor of platelets effectively transfers heat and flow, with sphere forms convey the least amount of heat.