Comparative Fractional Modeling of Casson Hybrid Nanofluid Flow in Transformer Oil Using Caputo-Fabrizio and Atangana–Baleanu Approaches

High voltage exchanging flow and high voltage direct momentum has enlivened various creators to focus on protection framework, that endure the ascending high voltage level; different analysts have done exploratory work to demonstrate strength and capacities of transformer oil. This is finished by adding different nanoparticles in the oil (Hybrid nanofluid) for various transformer applications. In this article Casson fluid is considered as transformer base oil and Tungsten trioxide (WO ₃ ) and Silver (Ag) nano particles were added collectively in form of hybrid nano fluid. It is observed that by adding WO ₃ and Ag nanoparticles in transformers-based oil thermal performance of the transformers have been improved up to 7% as compared to transformer oil with hybrid nanofluid. A comparative analysis of two well-known fractional derivatives Caputo-Fabrizio and Atangana-Baleanu has been made also, closed form solutions in the two cases (AB and CF) acquired by means of the Laplace and Hankel transforms. Because of AB and CF approach, the two different solutions are discussed graphically and the impact of appropriate parameters on velocity field is shown in plots and examined. It is discovered that for unit time, the velocity acquired by means of AB and CF are indistinguishable. Velocity for less than unit time demonstrates small difference and, for time more than 1, this difference increases.