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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.

The present article aims to investigate the squeeze effects on hematite suspension-based curved annular plates with Rosensweig’s viscosity and Kozeny–Carman’s porous structure under the variable strong magnetic field and slip in the Shliomis model. The variable magnetic field is utilised to retain all magnetic elements within the model. The aforementioned mechanism would have the benefit of generating a maximal field at the system’s required active contact zone.

The Kozeny–Carman globular sphere model is used for porous facing. Rosensweig’s extension of Einstein’s viscosity is taken into consideration to enhance the fluid’s viscosity, and Beavers and Joseph’s slip boundary conditions are employed to assess the slip effect.

The pressure and lifting force under squeezing are computed through modification of the Reynolds equation with the addition of Kozeny–Carman’s model-based porosity, Rosensweig’s viscosity, slip and varying magnetic field. The obtained results for the lifting force are very encouraging and have been compared with Einstein’s viscosity-based model.

Researchers so far have carried out problems on lubrication of various sliders considering Einstein’s viscosity only, whereas in our problem, Rosensweig’s viscosity has been taken along with Kozeny–Carman’s porous structure model.

This study aims to undertake a comprehensive examination of heat transfer by convection in porous systems with top and bottom walls insulated and differently heated vertical walls under a magnetic field. For a specific nanofluid, the study aims to bring out the effects of different segmental heating arrangements.

An existing in-house code based on the finite volume method has provided the numerical solution of the coupled nondimensional transport equations. Following a validation study, different explorations include the variations of Darcy–Rayleigh number (Ra_m = 10–10⁴), Darcy number (Da = 10^–5–10^–1) segmented arrangements of heaters of identical total length, porosity index (ε = 0.1–1) and aspect ratio of the cavity (AR = 0.25–2) under Hartmann number (Ha = 10–70) and volume fraction of φ = 0.1% for the nanoparticles. In the analysis, there are major roles of the streamlines, isotherms and heatlines on the vertical mid-plane of the cavity and the profiles of the flow velocity and temperature on the central line of the section.

The finding of a monotonic rise in the heat transfer rate with an increase in Ra_m from 10 to 10⁴ has prompted a further comparison of the rate at Ra_m equal to 10⁴ with the total length of the heaters kept constant in all the cases. With respect to uniform heating of one entire wall, the study reveals a significant advantage of 246% rate enhancement from two equal heater segments placed centrally on opposite walls. This rate has emerged higher by 82% and 249%, respectively, with both the segments placed at the top and one at the bottom and one at the top. An increase in the number of centrally arranged heaters on each wall from one to five has yielded 286% rate enhancement. Changes in the ratio of the cavity height-to-length from 1.0 to 0.2 and 2 cause the rate to decrease by 50% and increase by 21%, respectively.

Further research with additional parameters, geometries and configurations will consolidate the understanding. Experimental validation can complement the numerical simulations presented in this study.

This research contributes to the field by integrating segmented heating, magnetic fields and hybrid nanofluid in a porous flow domain, addressing existing research gaps. The findings provide valuable insights for enhancing thermal performance, and controlling heat transfer locally, and have implications for medical treatments, thermal management systems and related fields. The research opens up new possibilities for precise thermal management and offers directions for future investigations.

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.

This study aims to delve into the coupled mixed convective heat transport process within a grooved channel cavity using CuO-water nanofluid and an inclined magnetic field. The cavity undergoes isothermal heating from the bottom, with variations in the positions of heated walls across the grooved channel. The aim is to assess the impact of heater positions on thermal performance and identify the most effective configuration.

Numerical solutions to the evolved transport equations are obtained using a finite volume method-based indigenous solver. The dimensionless parameters of Reynolds number (1 ≤ Re ≤ 500), Richardson number (0.1 ≤ Ri ≤ 100), Hartmann number (0 ≤ Ha ≤ 70) and magnetic field inclination angle (0° ≤ γ ≤ 180°) are considered. The solved variables generate both local and global variables after discretization using the semi-implicit method for pressure linked equations algorithm on nonuniform grids.

The study reveals that optimal heat transfer occurs when the heater is positioned at the right corner of the grooved cavity. Heat transfer augmentation ranges from 0.5% to 168.53% for Re = 50 to 300 compared to the bottom-heated case. The magnetic field’s orientation significantly influences the average heat transfer, initially rising and then declining with increasing inclination angle. Overall, this analysis underscores the effectiveness of heater positions in achieving superior thermal performance in a grooved channel cavity.

This concept can be extended to explore enhanced thermal performance under various thermal boundary conditions, considering wall curvature effects, different geometry orientations and the presence of porous structures, either numerically or experimentally.

The findings are applicable across diverse fields, including biomedical systems, heat exchanging devices, electronic cooling systems, food processing, drying processes, crystallization, mixing processes and beyond.

This work provides a novel exploration of CuO-water nanofluid flow in mixed convection within a grooved channel cavity under the influence of an inclined magnetic field. The influence of different heater positions on thermomagnetic convection in such a cavity has not been extensively investigated before, contributing to the originality and value of this research.

The purpose of this study is to investigate the interaction between magnetotactic bacteria and Fe₃O₄–water nanofluid (NF) in a wavy enclosure in the presence of 2D natural convection flow.

Uniform magnetic field (MF), Brownian and thermophoresis effects are also contemplated. The dimensionless, time-dependent equations are governed by stream function, vorticity, energy, nanoparticle concentration and number of bacteria. Radial basis function-based finite difference method for the space derivatives and the second-order backward differentiation formula for the time derivatives are performed. Numerical outputs in view of isolines as well as average Nusselt number, average Sherwood number and flux density of microorganisms are presented.

Convective mass transfer rises if any of Lewis number, Peclet number, Rayleigh number, bioconvection Rayleigh number and Brownian motion parameter increases, and the flux density of microorganisms is an increasing function of Rayleigh number, bioconvection Rayleigh number, Peclet number, Brownian and thermophoresis parameters. The rise in buoyancy ratio parameter between 0.1 and 1 and the rise in Hartmann number between 0 and 50 reduce all outputs average Nusselt, average Sherwood numbers and flux density of microorganisms.

This study implies the importance of the presence of magnetotactic bacteria and magnetite nanoparticles inside a host fluid in view of heat transfer and fluid flow. The limitation is to check the efficiency on numerical aspect. Experimental observations would be more effective.

In practical point of view, in a heat transfer and fluid flow system involving magnetite nanoparticles, the inclusion of magnetotactic bacteria and MF effect provide control over fluid flow and heat transfer.

This is a scientific study. However, this idea may be extended to sustainable energy or biofuel studies, too. This means that a better world may create better social environment between people.

The presence of magnetotactic bacteria inside a Fe₃O₄–water NF under the effect of a MF is a good controller on fluid flow and heat transfer. Since the magnetotactic bacteria is fed by nanoparticles Fe₃O₄ which has strong magnetic property, varying nanoparticle concentration and Brownian and thermophoresis effects are first considered.

This work aims to concentrate on the mixed convection of the stagnation point flow of ternary hybrid nanofluids towards vertical Riga plate. Aluminum trioxide (Al₂O₃), silicon dioxide (SiO₂) and titanium dioxide (TiO₂) are regarded as nanoparticles, with water serving as the base fluid. The mathematical model incorporates momentum boundary layer and energy equations. The Grinberg term for the viscous dissipation and the wall parallel Lorentz force coming from the Riga plate are taken into consideration in the context of the energy equation.

Through the use of appropriate nonsimilar transformations, the governing system is transformed into nonlinear nondimensional partial differential equations (PDEs). The numerical method bvp4c (built-in package for MATLAB) is used in this study to simulate governing equations using the local non-similarity (LNS) approach up to the second truncation level.

Numerous graphs and numerical tables expound on the physical properties of the nanofluid temperature and velocity profiles. The local Nusselt correlations and the drag coefficient for pertinent parameters have been computed in tabular form. Additionally, the temperature profile drops while the velocity profile increases when the mixed convection parameter is included to oppose the flow.

The fundamental goal of this work is to comprehend how ternary nanofluids move towards a vertical Riga plate in a mixed convective domain with stagnation point flow.

A novel type of heat transfer fluid known as hybrid nanofluids is used to improve the efficiency of heat exchangers. It is observed from literature evidence that hybrid nanofluids outperform single nanofluids in terms of thermal performance. This study aims to address the stagnation point flow induced by Williamson hybrid nanofluids across a vertical plate. This fluid is drenched under the influence of mixed convection in a Darcy–Forchheimer porous medium with heat source/sink and entropy generation.

By applying the proper similarity transformation, the partial differential equations that represent the leading model of the flow problem are reduced to ordinary differential equations. For the boundary value problem of the fourth-order code (bvp4c), a built-in MATLAB finite difference code is used to tackle the flow problem and carry out the dual numerical solutions.

The shear stress decreases, but the rate of heat transfer increases because of their greater influence on the permeability parameter and Weissenberg number for both solutions. The ability of hybrid nanofluids to strengthen heat transfer with the incorporation of a porous medium is demonstrated in this study.

The findings may be highly beneficial in raising the energy efficiency of thermal systems.

The originality of the research lies in the investigation of the Darcy–Forchheimer stagnation point flow of a Williamson hybrid nanofluid across a vertical plate, considering buoyancy forces, which introduces another layer of complexity to the flow problem. This aspect has not been extensively studied before. The results are verified and offer a very favorable balance with the acknowledged papers.

Inclination angle has been reported to have an enhancing effect on the thermal-hydraulic characteristics and entropy of some thermal systems. Therefore, this paper aims to numerically investigate the effects of inclination angle, volume concentration and Reynolds number on the thermal and hydraulic characteristics and entropy generation rates of water-based Al₂O₃ nanofluids through a smooth circular aluminum pipe in a turbulent flow.

A constant heat flux of 2,000 Watts is applied to the circular surface of the tube. Reynolds number is varied between 4,000 and 20,000 for different volume concentrations of alumina nanoparticles of 0.5%, 1.0% and 2.0% for tube inclination angles of ±90o, ±60o, ±45o, ±30o and 0o, respectively. The simulation is performed in an ANSYS Fluent environment using the realizable kinetic energy–epsilon turbulent model.

Results show that +45o tube orientation possesses the largest thermal deviations of 0.006% for 0.5% and 1.0% vol. concentrations for Reynolds numbers 4,000 and 12,000. −45o gives a maximum pressure deviation of −0.06% for the same condition. The heat transfer coefficient and pressure drop give maximum deviations of −0.35% and −0.39%, respectively, for 2.0% vol. concentration for Reynolds number of 20,000 and angle ±90o. A 95%–99.8% and 95%–98% increase in the heat transfer and total entropy generation rates, respectively, is observed for 2.0% volume concentration as tube orientation changes from the horizontal position upward or downward.

Research investigating the effect of inclination angle on thermal-hydraulic performance and entropy generation rates in-tube turbulent flow of nanofluid is very scarce in the literature.

This paper aims to investigate the thermal performance of equivalent square and circular thermal systems and compare the heat transport and irreversibility of magnetohydrodynamic (MHD) nanofluid flow within these systems.

The research uses a constraint-based approach to analyze the impact of geometric shapes on heat transfer and irreversibility. Two equivalent systems, a square cavity and a circular cavity, are examined, considering identical heating/cooling lengths and fluid flow volume. The analysis includes parameters such as magnetic field strength, nanoparticle concentration and accompanying irreversibility.

This study reveals that circular geometry outperforms square geometry in terms of heat flow, fluid flow and heat transfer. The equivalent circular thermal system is more efficient, with heat transfer enhancements of approximately 17.7%. The corresponding irreversibility production rate is also higher, which is up to 17.6%. The total irreversibility production increases with Ra and decreases with a rise in Ha. However, the effect of magnetic field orientation (γ) on total EG is minor.

Further research can explore additional geometric shapes, orientations and boundary conditions to expand the understanding of thermal performance in different configurations. Experimental validation can also complement the numerical analysis presented in this study.

This research introduces a constraint-based approach for evaluating heat transport and irreversibility in MHD nanofluid flow within square and circular thermal systems. The comparison of equivalent geometries and the consideration of constraint-based analysis contribute to the originality and value of this work. The findings provide insights for designing optimal thermal systems and advancing MHD nanofluid flow control mechanisms, offering potential for improved efficiency in various applications.