Impact of appropriate similarity transformations on the heat transfer analysis of the Casson trihybrid shape-dependent nanofluid with suction\(/\)injection and thermal radiation through a stretching sheet

Abstract

Exploration of a non-linear stretching sheet has been conducted by utilising the Casson model, focussing on an exclusive mixture known as a ternary hybrid nanofluid. This particular nanofluid is a mixture of ethylene glycol hosting suspended graphene, carbon nanotubes and aluminium oxide. The nanoparticles scattered in the underlying liquid are anticipated to exhibit distinct formations like brick blades and lamina, ensuring an efficient connection between the expansive surface of the nanoparticles and the foundational fluid. As a result, this configuration allows for improved absorption of heat from the surface. Many fluid flow problems require the use of a similarity transformation to simplify the equations and make them more tractable. However, it is crucial to derive the correct similarity transformation for each specific problem. Unfortunately, many researchers overlook this step or employ inappropriate transformations, leading to erroneous results. This paper aims to address this issue by systematically deriving suitable similarity transformations for various flow problems, ensuring the accuracy and reliability of the solutions obtained. We derived an appropriate set of similarity transformations for a particular flow problem, in which the similarity variable is dimensionless and appears in the formulation as a function of all independent variables. The numerical solution of the modified equations was obtained using the Runge–Kutta Fehlberg 4–5th method. The study suggests that the temperature distribution is most significant with nanoparticles featuring brick–brick–lamina configurations, followed by brick–brick–blade and brick–brick–brick arrangements.

Graphical abstract