An investigation into a non-linearly stretching surface was conducted, focusing on a unique combination known as a shape-dependent hybrid nanofluid. The nanofluid consisted of a mixture of ethylene glycol and water, with dispersed multi-walled carbon nanotubes (MWCNT) and silver (Ag) particles of various shapes, including spherical, columnar, and lamellar. Many fluid flow problems require the use of similarity transformations to simplify the problem. However, it is crucial to derive an appropriate set of similarity transformations for each specific flow problem. Unfortunately, many researchers have overlooked this step or used inappropriate similarity transformations borrowed from other works, leading to erroneous results. This paper aimed to address this issue by deriving the correct set of similarity transformations for a specific flow problem, ensuring that the similarity variable was dimensionless and dependent on all independent variables in the formulation. Additionally, the stretching velocity was appropriately dimensioned. The semi-analytical solution for the modified differential equations was obtained using the Hermite wavelet transformation method, while the numerical solution for the coupled differential equations was solved using the 4th – 5th order Runge–Kutta-Felhberg method. A 64.5% increase in the Prandtl number leads to a 53.49% decrease in temperature. An 800% increase in the radiation parameter results in a 105.76% rise in temperature. Additionally, a 100% increase in the Eckert number causes the temperature to increase by 71.82%. This work emphasizes the importance of deriving appropriate similarity transformations for specific flow problems.
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