Intensification of thermal performance in heat transfer systems is an emerging area of research. The present exploration focuses on the development of intrinsic irreversibility and thermal characteristics of Williamson hybrid nanofluid flow. Here, it analyzes the influence of hybrid nanoparticle such as copper oxide \((CuO)\) and titanium oxide \((Ti{O}_{2})\) as well as the effect of the magnetic field in such flows, it fills certain unexplored gaps and aids in optimizing more advanced thermal systems and energy-efficient technologies. The impact of buoyant force with suction/injection at the walls is considered. Also accounting for thermal and exponentially dependent heat sources/sinks in a natural convection scenario. The governing equations are modeled and translated to dimensionless form; it is further solved by utilizing the Hermite wavelet method. The outcome of the pertinent flow parameter and physical features are presented graphically. A notable enhancement of velocity profile and thermal profile is attained in sphere-shaped nanoparticles, followed by hexahedron, tetrahedron, column, and lamina-shaped nanoparticles. The temperature profile diminishes by enhancing the magnetic parameter and Biot number. The sphere-shaped nanoparticles exhibit higher entropy than lamina-shaped nanoparticles, that is \(N{s}_{Sphere}>N{s}_{Tetrahedron}>N{s}_{Hexahedron}>N{s}_{Column}>N{s}_{Lamina}.\) The findings of this work highlight the potential of using hybrid nanofluids within the Williamson model, leveraging an advanced mathematical approach to enhance thermal performance.
