Comparative thermal analysis of Nickel and Tantalum based hybrid nanofluid using constant proportional Caputo and Atangana–Baleanu operators with time-controlled condition

The main purpose of this research work is to examine how the immersion of nickel and tantalum nanoparticles in water affects the flow and thermal properties of water, with the aim of anticipating potential enhancements. The investigation pertains to the flow behavior of a hybrid nanofluid over an extensively elongated vertical surface under the influence of a condition that varies with time. The phenomenon of heat transfer transpires due to the combined effects of natural convection and thermal radiation. An in-depth comprehension of flow patterns and heat transfer over a vertical surface is essential for optimizing heat exchange processes, designing efficient cooling systems, and enhancing overall energy efficiency. It also helps in climate modeling, weather prediction, and the improvement of the performance of solar thermal systems. The basic model is generalized using Atangana–Baleanu (AB) and constant proportional Caputo (CPC) operators. This generalization leads to the development of two different fractional settings for which separate mathematical analyses are performed. With the help of some new unit-independent quantities, exact solutions for both fractional frameworks are computed using the Laplace transform. For the elucidation of changes in velocity and thermal fields due to different physical effects, several graphical and tabular representations are produced. The outcomes illustrate that the incorporation of uniform concentrations of nickel and tantalum nanoparticles in water leads to raising its thermal efficacy up to 40.39%. The nanoparticles consisting of lamina shapes are observed to produce the maximum amelioration in thermal features. The CPC model based profiles of flow and temperature fields are lower than those procured via the AB model. As a result of nanoparticles’ intrinsic characteristics, the insignificant heat transfer capability of water is greatly amplified, leading to a notable boost in its thermal performance. Thus, the examined hybrid nanofluid can be used as a viable alternative to water in various engineering applications.