Hybrid nanofluid, a unique type of operational fluid, has gained considerable recognition due to its exceptional thermal conductivity. This study focuses on the thermal analysis of a shifting fin when a hybrid nanofluid is present with a constant flow rate U. It is considered that the fin’s thickness changes as it grows longer. As a result, several fin identities, including convex, triangular, and rectangular shapes, have been taken into consideration. Two types of nanoparticles, namely graphene oxide \((Go)\) , and molybdenum disulphide \((Mo{S}_{2})\) , are used in a benzene-water solution \(({C}_{6}{H}_{6}{O}_{2}-{H}_{2} O)\) . The specified conditions resulted in the development of an ordinary differential equation for the fin model. The equation was then changed to a form without dimensions. The Hermite wavelet method was utilized for the first time to address the challenge of a mobile fin submerged in a hybrid nanofluid. To confirm the outcomes, the obtained results were compared systematically with numerical simulations. Three fins with various shapes have been compared and contrasted. It is discovered that the temperature decrease rate is speedier in the triangular and convex fin compared to that of the rectangular fin. This study not only highlights the potential of hybrid nanofluids but also pioneers the application of HWM in fin design, advancing the field of thermal management technologies. An increase of 400% in the convection parameter results in a temperature decrease of 4.926% for the rectangular fin, 5.339% for the convex fin, and 5.599% for the triangular fin. Conversely, when the Peclet number increases by 400%, the temperature distribution along the fin tip rises by 7.1346% for the rectangular profile, 11.428% for the convex profile, and 12.298% for the triangular profile.
