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This paper aims to study numerically the flow, heat transfer, and entropy generation of aqueous copper oxide-silver hybrid nanofluid over a down-pointing rotating vertical cone, with linear surface temperature (LST) and linear surface heat flux (LSHF), in the presence of a cross-magnetic field. In industrial applications, such as oil and gas plants, food industries, steel factories and nuclear packages, the real bodies may contain nonorthogonal walls and variable cross-section three-dimensional forms which this issue can clarify the importance of selective geometry in the present research.

The mass-based scheme is accomplished for the simulation, and the entropy generation and Bejan number will be analyzed in conjunction with the aforementioned model. It has been hypothesized that two types of boundary conditions (LST and LSHF) as well as five nanoparticle shapes (sphere, brick, cylinder, platelet and disk) present a collection of crucial results. The overseeing PDEs are changed over completely to the dimensionless ODEs, and these are solved by Runge–Kutta–Fehlberg approach combined with a shooting methodology for certain values of physical parameters.

Subsequent to the fantastic compromise of the computational outcomes with past reports, the outcomes are introduced to conduct the investigation of the hydrodynamics/thermal boundary layers, the skin friction and the Nusselt number, as well as entropy generation and Bejan number. A state of hybrid nanofluid, which exhibits a remarkable increase in heat transfer in comparison to the states of mono-nanofluid and regular fluid, has been found to have the highest Nusselt number; however, the skin friction values should always be taken into account and managed. The entropy generation improves with the mass of the second nanoparticle (silver), while the opposite pattern is exhibited for the Bejan number. Furthermore, the lowest value of entropy generation number belongs to the cylindrical shape of nanoparticles in the LST case. In final, a significant accomplishment of the current study is the accurate output of the mass-based scheme for an entropy analysis problem.

To the best of the authors’ knowledge, for the first time, in this study, a new development of natural convective flow of a hybrid nanofluid about the warmed (LST and LSHF) and down-pointing rotating vertical cone by the mass-based algorithm has been presented. The applied methodology considers the masses of base fluid (water) and nanoparticles (Ag and CuO) as an alternative to the first and second nanoparticles volume fraction. Indeed, the combination use of the Tiwari–Das nanofluid model and the mass-based hybridity algorithm for the entropy generation analysis can be the main novelty of this work.

This paper aims to study a non-Newtonian micropolar fluid flow over a bidirectional flexible surface for multiple exact solutions of momentum boundary layer and thermal transport phenomenon subject to wall mass flux, second-order slip and thermal jump conditions.

The coupled equations are transformed into ordinary differential equations using similarity variables. Analytical and numerical techniques are used to solve the coupled equations for single, dual or multiple solutions.

The results show that the stretching flow, shrinking flow, the wall drag, thermal profile and temperature gradient manifest large changes when treated for special effects of the standard parameters. The role of critical numbers is definitive in locating the domains for the existence of exact solutions. The nondimensional parameters, such as mass transfer parameter, bidirectional moving parameter, plate deformation strength parameter, velocity slips, material parameter, thermal jump and Prandtl number, are considered, and their physical effects are presented graphically. The presence of governing parameters exhibits special effects on the flow, microrotation and temperature distributions, and various exact solutions are obtained for the special parametric cases.

The originality and value of this work lie in its exploration of non-Newtonian micropolar fluid flow over a bidirectional flexible surface, highlighting the multiple exact solutions for momentum boundary layers and thermal transport under various physical conditions. The study provides insights into the effects of key parameters on flow and thermal behavior, contributing to the understanding of complex fluid dynamics.

Several graphs, streamlines, isotherms and 3D plots are illustrated to enlighten the noteworthy fallouts of the investigation. Embedding flow factors for velocity, induced magnetic field and temperature have been determined using parametric analysis.

Ternary hybrid nanofluids has outstanding hydrothermal performance compared to classical mono nanofluids and hybrid nanofluids owing to the presence of triple tiny metallic particles. Ternary hybrid nanofluids are considered as most promising candidates in solar energy, heat exchangers, electronics cooling, automotive cooling, nuclear reactors, automobile, aerospace, biomedical devices, food processing etc. In this work, a ternary hybrid nanofluid flow that contains metallic nanoparticles over a wedge under the prevalence of solar radiating heat, induced magnetic field and the shape factor of nanoparticles is considered. A ternary hybrid nanofluid is synthesized by dispersing iron oxide (Fe3O4), silver (Ag) and magnesium oxide (MgO) nanoparticles in a water (H₂O) base fluid. By employing similarity transformations, we can convert the governing equations into ordinary differential equations and then solve numerically by using the Runge–Kutta–Fehlberg approach.

There is no fund for the research work.

This kind of study may be used to improve the performance of solar collectors, solar energy and solar cells.

This investigation unfolds the hydrothermal changes of radiative water-based Fe₃O₄-Ag-MgO-H₂O ternary hybrid nanofluidic transport past a static and moving wedge in the presence of solar radiating heating and induced magnetic fields. The shape factor of nanoparticles has been considered in this study.

This study investigates the flow and heat transfer in a magnetohydrodynamic (MHD) ternary hybrid nanofluid (HNF), considering the effects of viscous dissipation and radiation.

The transport equations are transformed into nondimensional partial differential equations. The local nonsimilarity (LNS) technique is implemented to truncate nonsimilar dimensionless system. The LNS truncated equation can be treated as ordinary differential equations. The numerical results of the equation are accomplished through the implementation of the bvp4c solver, which leverages the fourth-order three-stage Lobatto IIIa formula as a finite difference scheme.

The findings of a comparative investigation carried out under diverse physical limitations demonstrate that ternary HNFs exhibit remarkably elevated thermal efficiency in contrast to conventional nanofluids.

The LNS approach (Mahesh et al., 2023; Khan et al., 20223; Farooq et al., 2023) that we have proposed is not currently being used to clarify the dynamical issue of HNF via porous media. The LNS method, in conjunction with the bvp4c up to its second truncation level, yields numerical solutions to nonlinear-coupled PDEs. Relevant results of the topic at hand, obtained by adjusting the appropriate parameters, are explained and shown visually via tables and diagrams.

This study aims to analyze the two-dimensional ferrofluid flow in porous media. The effects of changes in parameters such as permeability parameter, buoyancy parameter, Reynolds and Prandtl numbers, radiation parameter, velocity slip parameter, energy dissipation parameter and viscosity parameter on the velocity and temperature profile are displayed numerically and graphically.

By using simplification, nonlinear differential equations are converted into ordinary nonlinear equations. Modeling is done in the Cartesian coordinate system. The finite element method (FEM) and the Akbari-Ganji method (AGM) are used to solve the present problem. The finite element model determines each parameter’s effect on the fluid’s velocity and temperature.

The results show that if the viscosity parameter increases, the temperature of the fluid increases, but the velocity of the fluid decreases. As can be seen in the figures, by increasing the permeability parameter, a reduction in velocity and an enhancement in fluid temperature are observed. When the Reynolds number increases, an increase in fluid velocity and temperature is observed. If the speed slip parameter increases, the speed decreases, and as the energy dissipation parameter increases, the temperature also increases.

When considering factors like thermal conductivity and variable viscosity in this context, they can significantly impact velocity slippage conditions. The primary objective of the present study is to assess the influence of thermal conductivity parameters and variable viscosity within a porous medium on ferrofluid behavior. This particular flow configuration is chosen due to the essential role of ferrofluids and their extensive use in engineering, industry and medicine.