Impact of new similarity transformations on heat transfer analysis of Casson tri-hybrid nanofluid in blood with thermal radiation through a stretching sheet: a homotopy perturbation Sumudu transformation approach

The investigation of nonlinearly stretching surface has been conducted using the Casson model, focusing on a unique mixture known as a ternary nanofluid. This specific nanofluid comprises a combination of blood with suspended aluminum alloys, namely AA7072and AA7075, as well as Al2O3 oxide. The nanoparticles dispersed in the underlying fluid are envisioned to possess a sphere-like structure, thereby ensuring optimal contact between the nanoparticle's extensive surface area and the base fluid. Consequently, this design enables enhanced heat absorption from the surface. Additionally, the unique combination of the nanoparticles facilitates swift mobility within the nanofluid, expediting their movement. We derived a novel set of similarity transformations, in which the similarity variable is dimensionless and appears in the formulation as a function of all independent variables. The Runge-Kutta Fehlberg 4-5th methodology was used to solve the modified equations numerically. In previous research papers, the Homotopy perturbation Sumudu transform method (HPSTM) was employed to derive the analytical solution solely for the momentum equation. However, in this current study, the Homotopy perturbation Sumudu transform method (HPSTM), is applied to solve the coupled momentum and heat equations of trihybrid nanofluid, resulting in an innovative analytical solution that has not been previously explored. The comparison with the numerical results demonstrates the precision of the present work. The repercussions of unique components on thermal and velocity plots are explained in graphical records for each case of nanofluid, hybrid nanofluid and trihybrid nanofluid separately. This study encourages the application of Homotopy perturbation Sumudu transform technique in more fluid flow problems.