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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 purpose of this paper is to study haemodynamic flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, magnetohydrodynamic (MHD) flow and aneurysm conditions. The findings of this study offer significant insights into the intricate interplay encompassing electro-osmosis, MHD flow, microorganisms, Joule heating and the ternary hybrid nanofluid.

The governing equations are first non-dimensionalised, and subsequently, a coordinate transformation is used to regularise the irregular boundaries. The discretisation of the governing equations is accomplished by using the Crank–Nicolson scheme. Furthermore, the tri-diagonal matrix algorithm is applied to solve the resulting matrix arising from the discretisation.

The investigation reveals that the velocity profile experiences enhancement with an increase in the Debye–Hückel parameter, whereas the magnetic field parameter exhibits the opposite effect, reducing the velocity profile. A comparative study demonstrates the velocity distribution in Au-CuO hybrid nanofluid and Au-CuO-GO ternary hybrid nanofluid. The results indicate a notable enhancement in velocity for the ternary hybrid nanofluid compared to the hybrid nanofluids. Moreover, an increase in the Brinkmann number results in an augmentation in entropy generation.

This study investigates the flow characteristics and entropy analysis in a bifurcated artery system subjected to stenosis, MHD flow and aneurysm conditions. The governing equations are non-dimensionalised, and a coordinate transformation is applied to regularise the irregular boundaries. The Crank–Nicolson scheme is used to model blood flow in the presence of a ternary hybrid nanofluid (Au-CuO-GO/blood) within the arterial domain. The findings shed light on the complex interactions involving stenosis, MHD flow, aneurysms, Joule heating and the ternary hybrid nanofluid. The results indicate a decrease in the wall shear stress (WSS) profile with increasing stenosis size. The MHD effects are observed to influence the velocity distribution, as the velocity profile exhibits a declining nature with an increase in the Hartmann number. In addition, entropy generation increases with an enhancement in the Brinkmann number. This research contributes to understanding fluid dynamics and heat transfer mechanisms in bifurcated arteries, providing valuable insights for diagnosing and treating cardiovascular diseases.

This study aims to analyze the impact of fractional derivatives on heat transfer and entropy generation during transient free convection inside various complex porous enclosures, such as triangle, L-shape and square-containing wavy surfaces. These porous enclosures are saturated with Cu-water nanofluid and subjected to the influence of a uniform magnetic field.

In the present study, Darcy’s model is used for the momentum transport equation in the porous matrix. Additionally, the Caputo time fractional derivative is introduced in the energy equation to assess the heat transfer phenomenon. Furthermore, the total entropy generation has been computed by combining the entropy generation due to fluid friction (S_ff), heat transfer (S_ht) and magnetic field (S_mf). The complete mathematical model is further simulated using the penalty finite element method, and the Caputo time derivative term is approximated using the L1 scheme. The study is conducted for various ranges of the Rayleigh number (102≤Ra≤104), Hartmann number (0≤Ha≤20) and fractional order parameter (0<α<1) with respect to time.

It has been observed that the fractional order parameter α governs the characteristics of entropy generation and heat transfer within the selected range of parameters. The Bejan number associated with heat transfer (Be_ht), fluid friction (Be_ff) and magnetic field (Be_mf) further demonstrate the dominance of flow irreversibilities. It becomes evident that the initial evolution state of streamlines, isotherms and local entropy varies according to the choice of α. Additionally, increasing Ra values from 10² to 10⁴ shows that the heat transfer rate increases by 123.8% for a square wavy enclosure, 7.4% for a triangle enclosure and 69.6% for an L-shape enclosure. Moreover, an increase in the value of Ha leads to a reduction in heat transfer rates and entropy generation. In this case, Bemf→1 shows the dominance of the magnetic field irreversibility in the total entropy generation.

Recently, fractional-order models have been widely used to express numerous physical phenomena, such as anomalous diffusion and dispersion in complex viscoelastic porous media. These models offer a more accurate representation of physical reality that classical models fail to capture; this is why they find a broad range of applications in science and engineering.

The fractional derivative model is used to illustrate the flow pattern, heat transfer and entropy-generating characteristics under the influence of a magnetic field. Furthermore, to the best of the author’s knowledge, a fractional-derivative-based mathematical model for the entropy generation phenomenon in complex porous enclosures has not been previously developed or studied.

This study aims to numerically scrutinize the entropy generation minimization and mixed convective heat transfer of multi-walled carbon nanotubes–Fe₃O₄/water hybrid nanofluid flow in a lid-driven square enclosure with heat generation in the presence of a porous layer on inner surfaces, considering local thermal non-equilibrium (LTNE) approach and the non-Darcy flow model.

The dimensionless governing equations for hybrid nanofluid and solid phases are solved by applying the finite volume method and semi-implicit method for pressure-linked equations algorithm.

The roles of the internal heat generation in the porous layer, LTNE model and nanoparticles volume fraction on mixed convection phenomenon and entropy generation are introduced for lid-driven cavity hybrid nanofluid flow. Based on the investigation of entropy generation and heat transfer, the minimum total entropy generation and average Nusselt numbers are found at 1 ≤ Ri ≤ 10 where the effect of the forced and free convection flow directions being opposite each other is very significant. When considering various nanoparticle volume fractions, it becomes evident that the minimum entropy generation occurs in the case of φ = 0.1%. The outcomes of LTNE number reveal the operating parameters in which thermal equilibrium occurs between hybrid nanofluid and solid phases.

The analysis of entropy generation under various shear and buoyancy forces plays a significant role in the suitable thermal design and optimization of mixed convective heat transfer applications. This research significantly contributes to the optimization of design and the advancement of innovative solutions across diverse engineering disciplines, such as packed-bed thermal energy storage and thermal insulation.

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.

Thermo-magnetic convective flow analysis under the impact of thermal radiation for heat and entropy generation phenomena is an active research field for understanding the efficiency of thermodynamic systems in various engineering sectors. This study aims to examine the characteristics of convective heat transport and entropy generation within an inverted T-shaped porous enclosure saturated with a hybrid nanofluid under the influence of thermal radiation and magnetic field.

The mathematical model incorporates the Darcy-Forchheimer-Brinkmann model and considers thermal radiation in the energy balance equation. The complete mathematical model has been numerically simulated through the penalty finite element approach at varying values of flow parameters, such as Rayleigh number (Ra), Hartmann number (Ha), Darcy number (Da), radiation parameter (Rd) and porosity value (e). Furthermore, the graphical results for energy variation have been monitored through the energy-flux vector, whereas the entropy generation along with its individual components, namely, entropy generation due to heat transfer, fluid friction and magnetic field, are also presented. Furthermore, the results of the Bejan number for each component are also discussed in detail. Additionally, the concept of ecological coefficient of performance (ECOP) has also been included to analyse the thermal efficiency of the model.

The graphical analysis of results indicates that higher values of Ra, Da, e and Rd enhance the convective heat transport and entropy generation phenomena more rapidly. However, increasing Ha values have a detrimental effect due to the increasing impact of magnetic forces. Furthermore, the ECOP result suggests that the rising value of Da, e and Rd at smaller Ra show a maximum thermal efficiency of the mathematical model, which further declines as the Ra increases. Conversely, the thermal efficiency of the model improves with increasing Ha value, showing an opposite trend in ECOP.

Such complex porous enclosures have practical applications in engineering and science, including areas like solar power collectors, heat exchangers and electronic equipment. Furthermore, the present study of entropy generation would play a vital role in optimizing system performance, improving energy efficiency and promoting sustainable engineering practices during the natural convection process.

To the best of the authors’ knowledge, this study is the first ever attempted detailed investigation of heat transfer and entropy generation phenomena flow parameter ranges in an inverted T-shaped porous enclosure under a uniform magnetic field and thermal radiation.

The purpose of this study is to determine the impact of two-phase power law nanofluid on a curved arterial blood flow under the presence of ovelapped stenosis. Over the past couple of decades, the percentage of deaths associated with blood vessel diseases has risen sharply to nearly one third of all fatalities. For vascular disease to be stopped in its tracks, it is essential to understand the vascular geometry and blood flow within the artery. In recent scenarios, because of higher thermal properties and the ability to move across stenosis and tumor cells, nanoparticles are becoming a more common and effective approach in treating cardiovascular diseases and cancer cells.

The present mathematical study investigates the blood flow behavior in the overlapped stenosed curved artery with cylinder shape catheter. The induced magnetic field and entropy generation for blood flow in the presence of a heat source, magnetic field and nanoparticle (Fe₃O₄) have been analyzed numerically. Blood is considered in artery as two-phases: core and plasma region. Power-law fluid has been considered for core region fluid, whereas Newtonian fluid is considered in the plasma region. Strongly implicit Stone’s method has been considered to solve the system of nonlinear partial differential equations (PDE’s) with 10–6 tolerance error.

The influence of various parameters has been discussed graphically. This study concludes that arterial curvature increases the probability of atherosclerosis deposition, while using an external heating source flow temperature and entropy production. In addition, if the thermal treatment procedure is carried out inside a magnetic field, it will aid in controlling blood flow velocity.

The findings of this computational analysis hold great significance for clinical researchers and biologists, as they offer the ability to anticipate the occurrence of endothelial cell injury and plaque accumulation in curved arteries with specific wall shear stress patterns. Consequently, these insights may contribute to the potential alleviation of the severity of these illnesses. Furthermore, the application of nanoparticles and external heat sources in the discipline of blood circulation has potential in the medically healing of illness conditions such as stenosis, cancer cells and muscular discomfort through the usage of beneficial effects.

The purpose of this study is to carry out a comprehensive analysis of magneto-hydrodynamics (MHD), nanofluidic flow dynamics and heat transfer as well as thermodynamic irreversibility, within a novel butterfly-shaped cavity. Gaining a thorough understanding of these phenomena will help to facilitate the design and optimization of thermal systems with complex geometries under magnetic fields in diverse applications.

To achieve the objective, the finite element method is used to solve the governing equations of the problem. The effects of various controlling parameters such as butterfly-shaped triangle vertex angle (T), Rayleigh number (Ra), Hartmann number (Ha) and magnetic field inclination angle (γ ) on the hydrothermal performance are analyzed meticulously. By investigating the effects of these parameters, the authors contribute to the existing knowledge by shedding light on their influence on heat and fluid transport within butterfly-shaped cavities.

The major findings of this study reveal that the geometrical shape significantly alters fluid motion, heat transfer and irreversibility production. Maximum heat transfer, as well as entropy generation, occurs when the Rayleigh number reaches its maximum, the Hartmann number is minimized and the angle of the magnetic field is set to 30° or 150°, while the butterfly wings angle or vertex angle is kept at a maximum of 120°. The intensity of the magnetic field significantly controls the heat flow dynamics, with higher magnetic field strength causing a reduction in the flow strength as well as heat transfer. This configuration optimizes the heat transfer characteristics in the system.

Further research can be expanded on this study by examining thermal performance under different curvature effects, orientations, boundary conditions and additional factors. This can be accomplished through numerical simulations or experimental investigations under various multiphysical scenarios.

The geometric configurations explored in this research have practical applications in various engineering fields, including heat exchangers, crystallization processes, microelectronic devices, energy storage systems, mixing processes, food processing, air-conditioning, filtration and more.

This study brings value by exploring a novel geometric configuration comprising the nanofluidic flow, and MHD effect, providing insights and potential innovations in the field of thermal fluid dynamics. The findings contribute a lot toward maximizing thermal performance in diverse fields of applications. The comparison of different hydrothermal behavior and thermodynamic entropy production under the varying geometric configuration adds novelty to this study.

Ferrofluid seals are known for their low friction torque and high tightness. However, they have some limitation due to the allowable rotational speed. The work presented here analyzes the performance of newly designed seals which are a combination of a ferrofluid and a centrifugal seal. The new seals can operate at high speeds. The purpose of this study is to theoretically predict the performance of combined seals.

Three seals were designed and selected for analysis. A version of the seals with a nonmagnetic insert is also considered, the purpose of which is to facilitate the installation and return of ferrofluid during low rotational speeds. The analyses were based on combining the results of numerical simulation of magnetic field distribution with mathematical models.

A combination of ferrofluid sealing and centrifugal sealing is possible. Analyses showed that the combined seal could hold a minimum pressure of 190 kPa in the velocity range of 0–100 m/s. The problem with this type of seal is the temperature.

New seal designs are presented. Key parameters that affect the seal operation are discussed. A methodology that can be used in the design of such seals is presented.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-07-2023-0221/.

This paper aims to examine the thermal transmission and entropy generation of hybrid nanofluid filled containers with solid body inside. The solid body is seen as being both isothermal and capable of producing heat. A time-dependent non-linear partial differential equation is used to represent the transfer of heat through a solid body. The current study’s objective is to investigate the key properties of nanoparticles, external forces and particular attention paid to the impact of hybrid nanoparticles on entropy formation. This investigation is useful for researchers studying in the area of cavity flows to know features of the flow structures and nature of hybrid nanofluid characteristics. In addition, a detailed entropy generation analysis has been performed to highlight possible regimes with minimal entropy generation rates. Hybrid nanofluid has been proven to have useful qualities, making it an attractive coolant for an electrical device. The findings would help scientists and engineers better understand how to analyse convective heat transmission and how to forecast better heat transfer rates in cutting-edge technological systems used in industries such as heat transportation, power generation, chemical production and passive cooling systems for electronic devices.

Thermal transmission and entropy generation of hybrid nanofluid are analysed within the enclosure. The domain of interest is a square chamber of size L, including a square solid block. The solid body is considered to be isothermal and generating heat. The flow driven by temperature gradient in the cavity is two-dimensional. The governing equations, formulated in dimensionless primitive variables with corresponding initial and boundary conditions, are worked out by using the finite volume technique with the SIMPLE algorithm on a uniformly staggered mesh. QUICK and central difference schemes were used to handle convective and diffusive elements. In-house code is developed using FORTRAN programming to visualize the isotherms, streamlines, heatlines and entropy contours, which are handled by Tecplot software. The influence of nanoparticles volume fraction, heat generation factor, external magnetic forces and an irreversibility ratio on energy transport and flow patterns is examined.

The results show that the hybrid nanoparticles concentration augments the thermal transmission and the entropy production increases also while the augmentation of temperature difference results in a diminution of entropy production. Finally, magnetic force has the significant impact on heat transfer, isotherms, streamlines and entropy. It has been observed that the external magnetic force plays a good role in thermal regulations.

Hybrid nanofluid is a desirable coolant for an electrical device. Various nanoparticles and their combinations can be analysed. Ferro-copper hybrid nanofluid considered with the help of prevailing literature review. The research would benefit scientists and engineers by improving their comprehension of how to analyses convective heat transmission and forecast more accurate heat transfer rates in various fields.

Due to its helpful characteristics, ferrous-copper hybrid nanofluid is a desirable coolant for an electrical device. The research would benefit scientists and engineers by improving their comprehension of how to analyse convective heat transmission and forecast more accurate heat transfer rates in cutting-edge technological systems used in sectors like thermal transportation, cooling systems for electronic devices, etc.

Entropy generation is used for an evaluation of the system’s performance, which is an indicator of optimal design. Hence, in recent times, it does a good engineering sense to draw attention to irreversibility under magnetic force, and it has an indispensable impact on investigation of electronic devices.

An efficient numerical technique has been developed to solve this problem. The originality of this work is to analyse convective energy transport and entropy generation in a chamber with internal block, which is capable of maintaining heat and producing heat. Effects of irreversibility ratio are scrutinized for the first time. Analysis of convective heat transfer and entropy production in an enclosure with internal isothermal/heat generating blocks gives the way to predict enhanced heat transfer rate and avoid the failure of advanced technical systems in industrial sectors.