Heat flow may be improved using a new form of nanofluid known as ternary hybrid nanofluid. Magnetic field, mass suction, and heat source effects on the stagnation area of [ ]) ternary hybrid nanofluid toward convectively heated stretching/shrinking cylinder with cylindrical shape nanoparticles are studied in this work. There will be an equation modeled under the given assumptions. It is feasible, with the help of similarity transformation, to convert nonlinear partial differential equations that are not quite solvable into ordinary differential equations that can be resolved numerically. The prevailing role of heat transfer and the features of movement of ternary hybrid nanofluids have been found to be significantly affected by the combination of Runge–Kutta-IV and the shotting technique in Mathematica. Many variables, including suction, Reynold number, nanoparticle volume fraction, magnetic field, Biot number, heat source, and stretching/shrinking influenced temperature, velocity, skin friction, and the local heat transfer rate, as shown in the graphs in the study. When magnetic field, suction, and Reynold number are present velocity increases, but inverse is true for nanoparticle volume fraction and stretching/shrinking parameter. The greatest influence on the surface is shown by the ternary hybrid nanofluid. Additionally, the heat transfer rate of the ternary hybrid nanofluid is faster than that of the hybrid and regular nanofluids.

The growth of hybrid nanofluids can be connected to their enhanced thermal performance as pertains to the dynamics of automobile coolant among others. In addition to that, the thermal characteristics of water-based nanofluids carrying three different types of nanoparticles are incredible. Keeping in view this new idea, the current investigation explores ternary hybrid nanofluid flow over a stretching sheet. Joule heating and viscous dissipation are addressed in the heat equation. Three distinct kinds of nanoparticles, namely, magnesium oxide, copper, and MWCNTs, are suspended in water to form a ternary hybrid nanofluid with the combination MgO-Cu-MWCNTs-H₂O. To stabilize the flow of the ternary hybrid nanofluid, transverse magnetic and electric fields have been considered in the fluid model. The production of entropy has been analyzed for the modeled problem. A comparative study for ternary, hybrid, and traditional nanofluids has also been carried out by sketching statistical charts. The equations that govern the problem are shifted to dimension-free format by employing transformable variables, and then they are solved by the homotopy analysis method (HAM). It has been revealed in this work that the flow of fluid opposes by magnetic parameter and supports by electric field the volumetric fraction of ternary hybrid nanofluid, while thermal profiles are gained by the growing values of these parameters. Boosting values of the electric field, magnetic parameters, and Eckert number support the Bejan number and oppose the production of entropy. Statistically, it has been established in this work that a ternary hybrid nanofluid has a higher thermal conductivity than hybrid or traditional nanofluids.

A Casson fluid is the most suitable rheological model for blood and other non-Newtonian fluids. Casson fluids hold yield-stress and have great significance in biomechanics and polymer industries. In this analysis, a numerical simulation of non-coaxial rotation of a Casson fluid over a circular disc was estimated. The influence of thermal radiation, second-order chemical reactions, buoyancy, and heat source on a Casson fluid above a rotating frame was studied. The time evolution of secondary and primary velocities, solute particles, and energy contours were also examined. A magnetic flux of varying intensity was applied to the fluid flow. A nonlinear sequence of partial differential equations was used to describe the phenomenon. The modeled equations were reduced to a non-dimensional set of ordinary differential equations (ODEs) using similarity replacement. The obtained sets of ODEs were further simulated using the parametric continuation method (PCM). The impact of physical constraints on energy, concentration, and velocity profiles are presented through figures and tables. It should be noted that the effect of the Casson fluid coefficient, the Grashof number, and the magnetic field reduces the fluid’s primary velocity contour. The mass transfer field decreases with the action of constructive chemical reactions, but is augmented by the effects of destructive chemical reactions. The accelerating trend in Schmidt number lowers the mass profile, while it is enhanced by increasing values of activation energy and Soret number.

Various studies have been conducted on the topic of predicting the thermal conductivity of nanofluids. Here, the thermal conductivity of nanofluids is determined using artificial neural networks since this approach is rapid and accurate, as well as cost-effective. To forecast the thermal conductivity of magnetohydrodynamic Williamson nanofluids flow through a vertical sheet, a feed-forward neural network with various numbers of neurons has been evaluated, and the best network based on the performance is selected. The fluid model incorporates the effects of Joule heating, heat generation absorption, thermal radiation, and a chemical reaction (MHD-WNF-HGA). A combination of heat radiation and reactive species improves the energy and solute profiles. The magnetic Reynolds number is assumed to be so small; therefore, the generated magnetic field has no effect. A postulate of similarity variables is used to convert the physical model in the form of nonlinear partial differential equations to an ordinary differential equation system. A supervised Levenberg–Marquardt backpropagation algorithm possesses a multilayer perceptron that is used for training the network, which is one of the top algorithms in machine learning. The bvp4c numerical technique is adopted to build the datasets for the construction of continuous neural network mapping. Flow, energy, and concentration profiles of the fluidic flow are constructed by adjusting several physical quantities such as the Williamson parameter, thermal radiation parameter, magnetic parameter, Eckert number, Darcy number, Brownian motion, and thermophoresis parameter. Analytical techniques such as error histogram graphs and regression-based statistical graphs are used to examine the accuracy of a suggested method. It has been found that the Levenberg–Marquardt backpropagation neural network mappings’ derivation, convergence, authentication, and consistency have been proven. Furthermore, thermal radiation assists the energy distribution to increase smoothly. Fluid velocity drops with the Williamson parameter, whereas thermophoresis impact enhances the strength of the nanofluid density.

In this research, a new heat transfer model for ternary nanofluid (Al₂O₃-CuO-Fe₃O₄)/C₂H₆O₂ inside slippery converging/diverging channel is reported with innovative effects of dissipation function. This flow situation described by a coupled set of PDEs which reduced to ODEs via similarity and effective ternary nanofluid properties. Then, LSM is successfully coded for the model and achieved the desired results influenced by $ \alpha ,Re,{\gamma }_{1} $ and $ Ec $. It is examined that the fluid movement increases for $ Re $ in the physical range of 30–180 and it drops for diverging channel ($ \alpha > 0 $) when the slippery wall approaches to $ \alpha = {60}^{o} $. The fluid movement is very slow for increasing concentration factor $ {\varphi }_{i} $ for $ i = \mathrm{1,2},3 $ up to 10%. Further, ternary nanofluid temperature boosts rapidly due to inclusion of trinanoparticles thermal conductivity and dissipation factor ($ Ec = \mathrm{0.1,0.2,0.3,0.4,0.6} $) also contributes significantly. Moreover, the temperature is maximum about the center of the channel ($ \eta = 0 $) and slip effects ($ {\gamma }_{1} = \mathrm{0.1,0.2,0.3,0.4,0.5,0.6} $) on the channel walls lead to decrement in the temperature $ \beta \left(\eta \right) $.