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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.

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 entropy and thermal behavior analyses of non-Newtonian nanofluid double-diffusive natural convection inside complex domains may captivate a bunch of scholars’ attention because of the potential utilizations that they possess in modern industries, for example, heat exchangers, solar energy collectors and cooling of electronic apparatuses. This study aims to investigate the second law and thermal behavior of non-Newtonian double-diffusive natural convection (DDNC) of Al₂O₃-H₂O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by a magnetic field.

For the governing equations of the complicated and practical system with all considered parameters to be solved via a formidable numerical approach, the finite element method acts as an approach to achieving the desired solution. This method allows us to gain a detailed solution to the studied geometry.

This investigation has been executed for the considered parameters of range, such as power-law index, baffle length, Lewis number, buoyancy ratio, Hartmann number and Rayleigh number. The main results reveal that isothermal and concentration lines are significantly more distorted, indicating intensified concentration and temperature distributions because of the growth of baffle length (L). Nu_ave decreases by 8.4% and 0.8% while it enhances by 49.86% and 33.87%, respectively, because of growth in the L from 0.1 to 0.2 and 0.2 to 0.3.

Such a comprehensive study on the second law and thermal behavior of DDNC of Al₂O₃-H₂O nanofluid within a C-shaped cavity emplacing two hot baffles and impacted by magnetic field has not yet been carried out.

A porous cavity flow field generates entropy owing to energy and momentum exchange within the fluid and at solid barriers. The heat transport and viscosity effects on fluid and solid walls irreversibly generate entropy. This numerical study aims to investigate convective heat transfer together with entropy generation in a partially heated wavy porous cavity filled with a hybrid nanofluid.

The governing equations are nondimensionalized and the domain is transformed into a unit square. A second-order finite difference method is used to have numerical solutions to nondimensional unknowns such as stream function and temperature. This numerical computation is conducted to explore a wide range of regulating parameters, e.g. hybrid nano-particle volume fraction (σ = 0.1%, 0.33%, 0.75%, 1%, 2%), Rayleigh–Darcy number (Ra = 10, 10², 10³), dimensionless length of the heat source (ϵ = 0.25, 0.50,1.0) and amplitude of the wave (a = 0.05, 0.10, 0.15) for a number of undulations (N = 1, 3) per unit length.

A thorough analysis is conducted to analyze the effect of multiple factors such as thermal convective forces, heat source, surface corrugation factors, nanofluid volume fraction and other parameters on entropy generation. The flow and temperature fields are studied through streamlines and isotherms. The average Bejan number suggested that entropy generation is entirely dominated by irreversibility due to heat transport at Ra = 10, and the irreversibility due to the viscosity effect is severe at Ra = 10³, but the increment in s augments irreversibility due to the viscosity effect over the heat transport at Ra = 10².

To the best of the authors’ knowledge, this numerical study, for the first time, analyzes the influence of surface corrugation on the entropy generation related to the cooling of a partial heat source by the convection of a hybrid nanofluid.

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.

This study aims to investigate the influence of wall curvature in a semicircular thermal annular system on magneto-nanofluidic flow, heat transfer and entropy generation. The analysis is conducted under constant cooling surface and fluid volume constraints.

The mathematical equations describing the thermo-fluid flow in the semicircular system are solved using the finite element technique. Four different heating wall configurations are considered, varying the undulation numbers of the heated wall. Parametric variations of bottom wall undulation (f), buoyancy force characterized by the Rayleigh number (Ra), magnetic field strength represented by the Hartmann number (Ha) and inclination of the magnetic field (γ) on the overall thermal performance are studied extensively.

This study reveals that the fluid circulation strength is maximum in the case of a flat bottom wall. The analysis shows that the bottom wall contour and other control parameters significantly influence fluid flow, entropy production and heat transfer. The modified heated wall with a single undulation exhibits the highest entropy production and thermal convection, leading to a heat transfer enhancement of up to 21.85% compared to a flat bottom. The magnetic field intensity and orientation have a significant effect on heat transfer and irreversibility production.

Further research can explore a wider range of parameter values, alternative heating wall profiles and boundary conditions to expand the understanding of magneto-nanofluidic flow in semicircular thermal systems.

This study introduces a constraint-based analysis of magneto-nanofluidic thermal behavior in a complex semicircular thermal system, providing insights into the impact of wall curvature on heat transfer performance. The findings contribute to the design and optimization of thermal systems in various applications.

The purpose of this study is to investigate the impact of varying baffle height and spacing distance on heat transfer and cooling performance of electronic components in a baffled horizontal channel, using a Cu-H₂O nanofluid under mixed convection and laminar flow.

The mathematical model is two-dimensional and comprises a system of four governing equations, such as the conservation of continuity, momentum and energy. To obtain numerical solutions for these equations, the finite volume method was used for discretization. A validation process was performed by comparing this study’s results with those of previously published studies. The comparison revealed a close agreement. The numerical study was performed for a wide range of key parameters: The baffle height (0 ≤ h ≤ 0.7), the spacing distance between baffle and blocks (0.25 ≤ w ≤ 3), the Grashof and Reynolds numbers are kept equal to 10⁴ and 75, respectively, the channel aspect ratio is L/H = 10, and the volume fraction of Cu nanoparticles is fixed at φ = 5%.

The results of the study reveal a significant improvement in heat transfer in terms of total Nusselt number of the top and bottom hot components, which exhibited an improvement of 16.89% and 17.23% when the baffle height increases from h = 0 to h = 0.7. Additionally, the study found that reducing the distance between the baffle and the electronic components up to a certain limit can improve the heat transfer rate. Therefore, the optimal height of the baffle was found to be no lower than 0.6, and the recommended distance between the heaters and the baffle was 0.5.

This study provides valuable insights into the optimization of the design of baffled channels for improved heat transfer performance. The findings of study can be used to improve heat exchangers and cooling systems in various applications. The use of Cu-H₂O nanofluid under mixed convection and laminar flow conditions in channel with baffle and electronic components is also unique, making this study an original contribution to the field.

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.

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.