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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.

The purpose of this study is to analyse the magnetic field effect on Fe₃O₄/H₂O Ferrofluid flowing in a sudden expansion tube, which has specific behaviour in terms of rheology, with convex dimple fins. Because the investigation of flow separation is a prominent application in performance, the effect of magnetic field and convex dimple on the thermo-hydraulic performance of sudden expansion tube are examined, in detail.

During the solution of the boundary conditions of the sudden expansion tube, finite volume method was used. Analyses have been conducted considering the single-phase solution, steady-state, incompressible fluid and no-slip condition of the wall under forced convection conditions. In the analyses, it has been assumed that the flow was developing thermally and has been fully developed hydrodynamically.

The present study focuses on exploring the influence of the magnetic field, nanofluid concentration and convex dimple fins on the thermo-hydraulic performance of sudden expansion tube. The results indicate that the strength of the magnetic field, nanofluid concentration and convex dimple fins have a positive effect on the convective heat transfer in the system.

The authors conducted numerical studies, determining through a literature search that no one had yet investigated enhancing heat transfer on a sudden expansion tube using combinations of magnetic fields, nanofluids and convex dimple fins. The results of the numerical analyses provide valuable information about the improvement of heat transfer and system performance in electronic device cooling and heat exchangers.

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.

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 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.

In recent times, there has been a growing interest in buoyancy-induced heat transfer within confined enclosures due to its frequent occurrence in heat transfer processes across diverse engineering disciplines, including electronic cooling, solar technologies, nuclear reactor systems, heat exchangers and energy storage systems. Moreover, the reduction of entropy generation holds significant importance in engineering applications, as it contributes to enhancing thermal system performance. This study, a numerical investigation, aims to analyze entropy generation and natural convection flow in an inclined square enclosure filled with Ag–MgO/water and Ag–TiO2/water hybrid nanofluids under the influence of a magnetic field. The enclosure features heated slits along its bottom and left walls. Following the Boussinesq approximation, the convective flow arises from a horizontal temperature difference between the partially heated walls and the cold right wall.

The governing equations for laminar unsteady natural convection flow in a Newtonian, incompressible mixture is solved using a Marker-and-Cell-based finite difference method within a customized MATLAB code. The hybrid nanofluid’s effective thermal conductivity and viscosity are determined using spherical nanoparticle correlations.

The numerical investigations cover various parameters, including nanoparticle volume concentration, Hartmann number, Rayleigh number, heat source/sink effects and inclination angle. As the Hartmann and Rayleigh numbers increase, there is a significant enhancement in entropy generation. The average Nusselt number experiences a substantial increase at extremely high values of the Rayleigh number and inclination.

This numerical investigation explores advanced applications involving various combinations of influential parameters, different nanoparticles, enclosure inclinations and improved designs. The goal is to control fluid flow and enhance heat transfer rates to meet the demands of the Fourth Industrial Revolution.

In a 90° tilted enclosure, the addition of 5% hybrid nanoparticles to the base fluid resulted in a 17.139% increase in the heat transfer rate for Ag–MgO nanoparticles and a 16.4185% increase for Ag–TiO2 nanoparticles compared to the base fluid. It is observed that a 5% nanoparticle volume fraction results in an increased heat transfer rate, influenced by variations in both the Darcy and Rayleigh numbers. The study demonstrates that the Ag–MgO hybrid nanofluid exhibits superior heat transfer and fluid transport performance compared to the Ag–TiO2 hybrid nanofluid. The simulations pertain to the use of hybrid magnetic nanofluids in fuel cells, solar cavity receivers and the processing of electromagnetic nanomaterials in enclosed environments.

Intumescent coatings are nowadays a dominant passive system used to protect structural materials in case of fire. Due to their reactive swelling behaviour, intumescent coatings are particularly complex materials to be modelled and predicted, which can be extremely useful especially for performance-based fire safety designs. In addition, many parameters influence their performance, and this challenges the definition and quantification of their material properties. Several approaches and models of various complexities are proposed in the literature, and they are reviewed and analysed in a critical literature review.

Analytical, finite-difference and finite-element methods for modelling intumescent coatings are compared, followed by the definition and quantification of the main physical, thermal, and optical properties of intumescent coatings: swelled thickness, thermal conductivity and resistance, density, specific heat capacity, and emissivity/absorptivity.

The study highlights the scarce consideration of key influencing factors on the material properties, and the tendency to simplify the problem into effective thermo-physical properties, such as effective thermal conductivity. As a conclusion, the literature review underlines the lack of homogenisation of modelling approaches and material properties, as well as the need for a universal modelling method that can generally simulate the performance of intumescent coatings, combine the large amount of published experimental data, and reliably produce fire-safe performance-based designs.

Due to their limited applicability, high complexity and little comparability, the presented literature review does not focus on analysing and comparing different multi-component models, constituted of many model-specific input parameters. On the contrary, the presented literature review compares various approaches, models and thermo-physical properties which primarily focusses on solving the heat transfer problem through swelling intumescent systems.

The presented literature review analyses and discusses the various modelling approaches to describe and predict the behaviour of swelling intumescent coatings as fire protection for structural materials. Due to the vast variety of available commercial products and potential testing conditions, these data are rarely compared and combined to achieve an overall understanding on the response of intumescent coatings as fire protection measure. The study highlights the lack of information and homogenisation of various modelling approaches, and it underlines the research needs about several aspects related to the intumescent coating behaviour modelling, also providing some useful suggestions for future studies.

This study comprehensively examines entropy generation and thermosolutal performance of a ternary hybrid nanofluid in a partially active porous cabinet. The purpose of this study is to comprehend the intricate phenomena of double diffusion by investigating the dispersion behavior of Al₂O₃, CuO, and Ag nanoparticles in water.

The cabinet design consists of two horizontal walls and two curved walls with the lower border divided into a heated and concentrated region of length b and the remaining sections are adiabatic. The vertical borders are cold and low concentration, while the upper border is adiabatic. Two cavity configurations such as convex and concave are considered. A uniform porous medium is taken within the ternary hybrid nanofluid. This has been characterized by the Brinkman-extended Darcy model. Thermosolutal phenomena are governed by the Navier-Stokes equations and are solved by adopting a higher-order compact scheme.

The present study focuses on exploring the influence of several well-defined parameters, including Rayleigh number, Darcy number, Lewis number, Buoyancy ratio number, nanoparticle volume concentration and heater size. The results indicate that the ternary hybrid nanofluid outperforms both the mono and hybrid nanofluids in all considered aspects.

This study brings forth a significant contribution by uncovering novel flow features that have previously remained unexplored. By addressing a well-defined problem, the work provides valuable insights into the enhancement of thermal transport, with direct implications for diverse engineering devices such as solar collectors, heat exchangers and microelectronics.

The purpose of this study is to investigate the influence of enclosure shape on magnetohydrodynamic (MHD) nanofluidic flow, heat transfer and irreversibility in square, trapezoidal and triangular thermal systems under fluid volume constraints, with the aim of optimizing thermal behavior in diverse applications.

The study uses numerical simulations based on a finite element-based technique to analyze the effects of the Rayleigh number (Ra), Hartmann number (Ha), magnetic field orientation (γ) and nanoparticle concentration (ζ) on heat transfer characteristics and thermodynamic entropy production.

The key findings reveal that the geometrical design significantly influences fluid velocity, heat transfer and irreversibility. Trapezoidal thermal systems outperform square systems, while triangular systems achieve optimal enhancement. Nanoparticle concentration enhances heat transfer and flow strength at higher Rayleigh numbers. The magnetic field intensity has a significant impact on fluid flow and heat transport in natural convection, with higher Hartmann numbers resulting in reduced flow strength and heat transfer. The study also highlights the influence of various parameters on thermodynamic entropy production.

Further research can explore additional geometries, parameters and boundary conditions to expand the understanding of enclosure shape effects on MHD nanofluidic flow and heat transfer. Experimental validation can complement the numerical simulations presented in this study.

This study provides valuable insights into the impact of enclosure shape on heat transfer performance in MHD nanofluid flow systems. The findings contribute to the optimization of thermal behavior in applications such as electronics cooling and energy systems. The comparison of different enclosure shapes and the analysis of thermodynamic entropy production add novelty to the study.

This paper aims at studying numerically the entropy generation of nanofluid flowing over an inclined sheet in the presence of external magnetic field, heat source/sink, chemical reaction along with slip boundary conditions imposed on an impermeable wall.

A suitable similarity transformation technique has been used to convert the coupled nonlinear partial differential equations to ordinary differential equations (ODEs). The ODEs are then solved simultaneously using the finite difference method implemented through an in-house computer program. The effects of different controlling parameters such as magnetic parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, chemical reaction parameter, Reynolds number, Brinkmann number, Prandtl number, velocity slip parameter, temperature slip parameter and the concentration slip parameter on the entropy generation and Bejan number have been discussed comprehensively through the relevant physical insights for the first time.

The relative strengths of the irreversibilities due to heat transfer, fluid friction and the mass diffusion arising due to the change in each of the controlling variables have been delineated both in the near-wall and far-away-wall regions, which may be helpful for a better understanding of the thermo-fluid dynamics of nanofluid in boundary layer flows. The numerical results obtained from the present study have also been validated with results published in open literature.

The effects of different controlling parameters such as magnetic parameter, radiation parameter, Brownian motion parameter, thermophoresis parameter, chemical reaction parameter, Reynolds number, Brinkmann number, Prandtl number, velocity slip parameter, temperature slip parameter and the concentration slip parameter on the entropy generation and Bejan number have been discussed comprehensively through the relevant physical insights for the first time.