The current study explores a three-dimensional swirling flow of titania–ethylene glycol-based nanofluid over a stretchable cylinder with torsional motion. The heat transfer process is explored subject to heat source/sink. Here, titania–ethylene glycol–water-based nanofluid is used. The Maxwell–Bruggeman models for thermal conductivity and modified Krieger–Dougherty models for viscosity are employed to scrutinize the impact of nanoparticle aggregation. A mathematical model based on partial differential equations (PDEs) is developed to solve the flow problem. Following that, a similarity transformation is performed to reduce the equations to ordinary differential equations (ODEs), which are then solved using the finite element method. It has been proven that nanoparticle aggregation significantly increases the temperature field. The results reveal that the rise in Reynolds number improves the heat transport rate, whereas an increase in the heat source/sink parameter value declines the heat transport rate. Swirling flows are commonly found in many industrial processes such as combustion, mixing, and fluidized bed reactors. Studying the behavior of nanofluids in these flows can lead to the development of more efficient and effective industrial processes.

The global energy need the development and functioning of heat exchangers and thermal systems for the use and resuscitation of thermal energy. Because of the heat transfer enrichment properties of nanoparticles, industries including nuclear reactors, biological sensing, gas sensing, solar synthesis, the chemical industry, and others have considered using nanoparticles in their respective fields to advance the thermal efficiency of normal liquids. In connection with this, we have envisioned a mathematical model that illustrates the flow and radiative heat transfer of a hybrid nanofluid over a curved stretching sheet with the injection/suction and Arrhenius activation energy. A numerical solution is attained using the Runge–Kutta–Fehlberg fourth, fifth-order and the shooting process. The solution is established through the graphs, which explain each profile in terms of involved parameters. Results reveal that the velocity of the liquid decreases as suction upsurges. The heat transfer enhances for rising values of radiation parameter and Biot number for injection and suction cases. The rate of mass transfer decreases for a rise in values of activation energy parameter, but the differing movement is detected for increasing values of chemical reaction rate parameter.

The investigation of thermal performance in the nanofluids for unsteady boundary layer flow by considering the impacts of suction/injection is a significant research area in the field of fluid dynamics. This flow situation is broadly used in aerodynamics and space sciences as well. The model is formulated for ND-H₂O and Ag-H₂O nanofluids and then tackled numerically and captured the dynamics of the nanofluids under the multiple flow parameters. From the results, it is investigated that both ND-H₂O and Ag-H₂O have high thermal performance characteristics. However, higher heat transfer performance is observed for Ag based nanofluid. Further, a graphical and tabular comparison under certain assumptions is provided to authenticate the analysis.

The present research examines the steady, one-dimensional thermal distribution and heat transfer of a wavy fin. This heat transfer analysis considers convective effects as well as temperature-dependent thermal conductivity. Furthermore, a novel implementation of a neural network with backpropagated Levenberg–Marquardt algorithm (NN-BLMA)-based machine learning intelligent strategies is provided to interpret the heat transfer analysis of a convective wavy fin. The non-linear ordinary differential equation (ODE) of the study problem is converted into its non-dimensional form using the similarity transformation technique. The dimensionless equation obtained is then numerically explored via the Runge–Kutta–Fehlberg scheme. A data set for varying the pertinent parameters is generated, and an artificial neural network model is designed to estimate the heat transfer behavior of the wavy fin. The effectiveness of the proposed NN-BLMA is subsequently endorsed by analyses using a regression model, mean square error, and histograms. The findings of comprehensive computational parametric studies illustrate that the presented technique, NN-BLMA is an effective convergent stochastic numerical solver employed for the heat transfer model of the convective wavy fin. The wavy fin’s temperature dispersion optimizes as the thermal conductivity parameter rises. Heat transfer rate is higher in wavy fin compared to rectangular fin.