Revealing the dynamic response of Prandtl–Eyring's ternary hybrid nanofluidic flow with Arrhenius activation energy: A model incorporating correlation coefficients and probable errors

The study of ternary hybrid nanofluids is a fascinating area of research that explores the unique properties and potential applications of combining three distinct solid components within a conventional fluid to enhance thermal efficiency. These nanofluids hold immense potential for improving heat transfer properties for various industrial applications. Their enhanced cooling abilities, coupled with their suitability for energy storage systems, make them a valuable tool for industries seeking to improve their cooling systems, save energy, and enhance cooling mechanisms. The effects of the nanoparticle shape factor on the steady two-dimensional hydrothermal flow of an incompressible MHD Prandtl–Eyring ternary hybrid nanofluid are examined in this research. All aspects of the process are considered during the computation, including activation energy effects and binary chemical reactions. Our governing equations have been turned into ordinary differential equations (ODEs) using similarity transformations, which we can solve numerically by using the Runge–Kutta–Fehlberg method. The investigation was carried out using graphs, charts, streamlines, and contour diagrams to illustrate the significant findings. To ascertain the flow factors related to velocity, temperature, and concentration, a parametric estimate method was employed. Utilized statistical analyses include regression, correlation, and probable error. Several amazing correlation coefficients are observed, and there is a strong association between the parameters and the physical features. The concentration field grows with a surge in activation energy, while the concentration of nanoparticles drops with an increase in chemical reaction. The selection of ternary hybrid nanofluids can significantly impact the performance of systems involved in steam generation, cooling, and heating due to their enhanced thermal properties. This study bridges a critical gap in understanding the interplay of non-Newtonian behaviors and advanced nanofluid systems, providing a robust framework for future technological advancements in fluid dynamics and thermal sciences.