A new fractional mathematical model of extraction nanofluids using clay nanoparticles for different based fluids

In this paper, the heat transfer analysis of viscous (clay water-based) nanofluid over an exponentially moving vertical plate is discussed. When clay nanoparticles are mixed to water-based fluids, the thermal conductivity, thickness stages, and danger level of the fluid increase, which deliver hardy to extraordinary temperatures and controller the fluid charge. Clay nanoparticles show a vigorous rule in the drilling techniques of oils and gases from stuns and acreage. More accurately, clay nanoparticles are suspended in three different based fluids (water, kerosene, and engine oil). The governing PDE of nanofluids has been modeled by appealing ABC fractional derivative. The dimensionless temperature and velocity fields are attained as the solutions of the governing equations by Laplace transformation technique. The reported results are expressed in terms of ML function. To validate the results, the impact of several flow parameters and some comparison with the exiting results from the literature are made using Mathcad and designed in different figures. In some cases, our outputs are reduced to the results obtained in the literature. In comparison, we found that our results decay better than the classical approach proposed in existing research works. We also have compared the presents results based on ABC derivative, Caputo and CF derivatives. As a consequence, we have implied that ABC derivative decays better than C and CF derivatives and velocity of engine oil-based fluid decays near the plate in comparison with other based fluids.