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In this paper, the influence of velocity slip and the Newtonian heating parameters on Williamson Nanofluid across a variable stretching sheet is studied. The basic fluid flow equations are turned into a system of coupled ordinary differential equations with appropriate conditions, which are solved numerically with the Keller-box approach. The outcomes show that, increasing Williamson parameter, due to the viscosity velocity of the fluid slowdown. As a result, it is noticed that the velocity slip parameter reduces Williamson Nanofluid velocity, while increasing shear stress, according to the results. Furthermore, it has been discovered that unlike velocity profiles, the slip influence is more pronounced on temperature and concentration profiles. Furthermore, the Newtonian heating parameter may be shown to have rising functions for velocity and dimensionless temperature. Newtonian heating has uses in the petroleum industry, heat exchangers, conjugate heat transfer around fins and solar radiation. It is discovered that the Joule heating parameter improves the thermal boundary layer thickness and slows down the velocity of the fluid, which aids in maintaining system temperature. Additionally, it has been found that the temperature profile exhibits a stronger slip effect compared with the velocity profile. To prepare toffee, chocolate and other delicacies as efficiently as possible, it is crucial to investigate the flow of Williamson fluids (such as drilling muds, clay coatings, various suspensions and some lubricating oils, thermoplastic melts, and a variety of colloids) in the incidence of heat transfer. The novelty of this paper is the effect of joule heating, Newtonian heating parameter and velocity slip on Williamson fluid velocity and temperature gradient. Furthermore, the heat and mass transfer rates are calculated for various parameters numerically and shown in tabular form. [ABSTRACT FROM AUTHOR]

Hybrid nanofluids (HNF) are the advanced form of nanofluids used for improved heat transfer purposes. Taking this point in mind, the objective of the presented endeavor is to examine the Yamada–Ota HNF flow model comprising (gold–silver/engine oil) over a stretched cylindrical surface and a sheet (as a limiting case) in a permeable medium. The novelty of this research is the consideration of the surface-catalyzed reaction along with the homogeneous–heterogeneous reactions to accelerate the chemical reactions in the shortest possible time. The heat transport phenomenon is strengthened with the support of Joule heating, heat absorption/generation, and the convective heat boundary condition at the surface of the cylinder. The obtained ordinary differential equations are reduced from the partial differential equations using boundary layer theory and are numerically computed using the Keller box method. It is witnessed that for varied estimates of the magnetic parameter, the thermal profile enhances while the velocity field reduces. It is also noted that the fluid concentration is reduced when the surface-catalyzed parameter is enhanced. The validation of the envisioned model in a limiting case is also added to this investigation. [ABSTRACT FROM AUTHOR]

The objective of this work is to explore the flow features and thermal radiation properties of the 2-D Magnetohydrodynamic (MHD) Carreau nanofluid model over an impenetrable stretching surface by utilizing the supervised learning strength of Levenberg–Marquardt backpropagation neural networking technique (LMBNNT). The mathematical formulation for MHD Carreau nanofluid flow model (MHDCNFM) in terms of partial differential equations (PDEs) is transformed into equivalent nonlinear ordinary differential equations (ODEs) by utilizing the similarity transformation and dimensional parameters. A reference dataset of proposed LMBNNT is made for Carreau nanofluid flow model exploiting the strength of Lobatto IIIA technique through the variations of different parameters against the velocity, temperature profile and concentration. These reference datasets are placed for validation, training and testing by LMBNNT and obtained outcomes are compared with reference results to check the accuracy of the designed methodology. The validation of the proposed solution methodology is obtained through the mean square error (MSE), error histogram error profile, regression p lot and fitness plot. MSE values' accuracy is upto 1 0 − 1 0 which establish the reliability of the LMBNNT. Moreover, due to an increase in Weissenberg number, fluid velocity decays in case of shear thinning liquid and higher values of Biot number enhance the temperature profile and improves the rate of heat transfer. Moreover, the increment in Hartman number reduces the surface drag force and large values of Prandtl number reduce the heat transfer process. These results of all these parameters are expressed in well-organized numerical and graphical forms. [ABSTRACT FROM AUTHOR]