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This study aims to understand the difference between irreversibility in heat and work transfer processes. It also aims to explain that Helmholtz or Gibbs energy does not represent “free” energy but is a measure of loss of Carnot (reversible) work opportunity.

The entropy of mass is described as the net temperature-standardised heat transfer to mass under ideal conditions measured from a datum value. An expression for the “irreversibility” is derived in terms of work loss (W_loss) in a work transfer process, unaccounted heat dissipation (Q_loss) in a heat transfer process and loss of net Carnot work (CW_net) opportunity resulting from spontaneous heat transfer across a finite temperature difference during the process. The thermal irreversibility is attributed to not exploiting the capability for extracting work by interposing a combination of Carnot engine(s) and/or Carnot heat pump(s) that exchanges heat with the surrounding and operates across the finite temperature difference.

It is shown, with an example, how the contribution of thermal irreversibility, in estimating reversible input work, amounts to a loss of an opportunity to generate the net work output. The opportunity is created by exchanging heat with surroundings whilst transferring the same amount of heat across finite temperature difference. An entropy change is determined with a numerical simulation, including calculation of local entropy generation values, and results are compared with estimates based on an analytical expression.

A new interpretation of entropy combined with an enhanced mental image of a combination of Carnot engine(s) and/or Carnot heat pump(s) is used to quantify thermal irreversibility.

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.

This study aims to present the numerical analysis of exergy transfer and irreversibility through the discrete filling of high-porosity aluminum metal foams inside the horizontal pipe.

In this study, the heater is embedded on the pipe’s circumference and is assigned with known heat input. To enhance the heat transfer, metal foam of 10 pores per inch with porosity 0.95 is filled into the pipe. In filling, two kinds of arrangements are made, in the first arrangement, the metal foam is filled adjacent to the inner wall of the pipe [Model (1)–(3)], and in the second arrangement, the foam is located at the center of the pipe [Models (4)–(6)]. So, six different models are examined in this research for a fluid velocity ranging from 0.7 to7 m/s under turbulent flow conditions. Darcy Extended Forchheimer is combined with local thermal non-equilibrium models for forecasting the flow and heat transfer features via metal foams.

The numerical methodology implemented in this study is confirmed by comparing the outcomes with the experimental outcomes accessible in the literature and found a fairly good agreement between them. The application of the second law of thermodynamics via metal foams is the novelty of current investigation. The evaluation of thermodynamic performance includes the parameters such as mean exergy-based Nusselt number (Nu_e), rate of irreversibility, irreversibility distribution ratio (I_DR), merit function (MF) and non-dimensional exergy destruction (I^*). In all the phases, Models (1)–(3) exhibit better performance than Models (4)–(6).

The present study helps to enhance the heat transfer performance with the introduction of metal foams and reveals the importance of available energy (exergy) in the system which helps in arriving at optimum design criteria for the thermal system.

The uniqueness of this study is to analyze the impact of discrete metal foam filling on exergy and irreversibility in a pipe under turbulent flow conditions.

The purpose of this paper is to analyze the natural convection heat transfer and irreversibility characteristics in a quadrantal porous cavity subjected to uniform temperature heating from the bottom wall.

Brinkmann-extended Darcy model is used to simulate the momentum transfer in the porous medium. The Boussinesq approximation is invoked to account for the variation in density arising out of the temperature differential for the porous quadrantal enclosure subjected to uniform heating on the bottom wall. The governing transport equations are solved using the finite element method. A parametric study is carried out for the Rayleigh number (Ra) in the range of 10³ to 10⁶ and Darcy number (Da) in the range of 10⁻⁵-10⁻².

A complex interaction between the buoyant and viscous forces that govern the transport of heat and entropy generation and the permeability of the porous medium plays a significant role on the same. The effect of Da is almost insignificant in dictating the heat transfer for low values of Ra (10³, 10⁴), while there is a significant alteration in Nusselt number for Ra ≥10⁵ and moreover, the change is more intense for larger values of Da. For lower values of Ra (≤10⁴), the main contributor of irreversibility is the thermal irreversibility irrespective of all values of Da. However, the fluid friction irreversibility is the dominant player at higher values of Ra (=10⁶) and Da (=10⁻²).

From an industrial point of view, the present study will have applications in micro-electronic devices, building systems with complex geometries, solar collectors, electric machinery and lubrication systems.

This research examines numerically the buoyancy driven heat transfer irreversibility in a quadrantal porous enclosure that is subjected to uniform temperature heating from the bottom wall, that was not investigated in the literature before.

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.

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 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.

The study aims to assess the heater and cooler positional impacts systematically using four different quadrantal cavities filled with hybrid nanofluid, keeping the curved surface adiabatic under the orientated magnetic fields. Both heat transfer and entropy generation analyses are performed for a hybrid nanofluid flow in a quarter circular cavity considering different orientations of magnetic fields. The investigation is focused to assess the heater and cooler positional impacts systematically using four different quadrantal cavities (first to fourth quadrantal cavities), keeping the curved surface always adiabatic. The impacts of pertinent variables like Rayleigh number, Hartmann number and volumetric concentration of hybrid nanofluid on heat transfer characteristics are in consideration with the second law of thermodynamics. The analysis includes the thermal, viscous and magnetic aspects of entropy generation.

After validating against the experimental results, the present work explores numerically following the Galerkin weighted finite element technique. The solution is obtained through an iterative process satisfying the convergence limit of 10⁻⁸ and 10⁻¹⁰ for the maximum residuals and the mass defect, respectively.

It revealed that the mutual exchange of heater-cooler positions on the adjacent straight edges of the quadrant cavity does not have any impact on the flow direction. Although the magnitude of flow velocity enhances, the sidewall plays a decision-making role in the formation of a single circulation vortex. It also shows that thermal entropy production is the main cause behind thermodynamic irreversibility. The second or third quadrantal arrangement could have been opted as the best configuration of the heater-cooler position for achieving superior heat transfer. The Lorentz force plays a great role to moderate the heat transfer process. The maximum entropy generation is located, as expected, at the heating-cooling junction point.

There are plenty of prospects for extension of the present research concept numerically or experimentally, adopting three-dimensional analysis, working fluids, boundary conditions, etc. In fact, the study could be carried out for unsteady or turbulent fluid flow.

As the position of the heated source and cold sink on the enclosure geometry can significantly alter the thermo-fluid phenomena, this kind of analysis is of utmost relevance for the further development of efficient heating/cooling arrangements and proper management of the devices subjected to magnetic field applications. This original contribution could be a potentially valuable source for future research and exploration pertaining to a thermal system or device, like heat exchangers, solar collectors, thermal storage, electronic cooling, food and drying technologies and others.

In the literature, an inadequate number of works have focused on a quadrantal cavity, mostly considering the first quadrant of the circle. However, during practical applications, it is possible that the cavity can take the shape of the other three quadrants too, and the corresponding knowledge on relative performance is still missing. Furthermore, the present investigation includes the existence of magnetic fields at various orientations. The impact analysis of this field-induced Lorentz force on the nanofluid thermal performance is another major contribution from the present work that would enrich the domain knowledge and could be useful for thermal system engineers.

The purpose of this paper is to investigate the effects of Ha and the Nanoparticles (NP) volume fraction over the irreversibility and heat transport in Darcy–Forchheimer nanofluid saturated lid-driven porous medium.

The present paper highlights entropy generation because of mixed convection for a lid-driven porous enclosure filled through a nanoliquid and submitted to a uniform magnetic field. The analysis is achieved using Darcy–Brinkman–Forchheimer technique. The set of partial differential equations governing the considered system was numerically solved using the finite element method.

The main observations are as follows. The results indicate that the movement of horizontal wall is an important factor for the entropy generation inside the porous cavity filled through Cu–water nanoliquid. The variation of the thermal entropy generation is linear through NPs volume fraction. The total entropy generation reduces when the Darcy, Hartmann and the nanoparticle volume fraction increase. The porous media and magnetic field effects reduce the total entropy generation.

Interest in studying thermal interactions by convective flow within a saturating porous medium has many fundamental considerations and has received extensive consideration in the literature because of its usefulness in a large variety of engineering applications, such as the energy storage and solar collectors, crystal growth, food processing, nuclear reactors and cooling of electronic devices, etc.

By examining the literature, the authors found that little attention has been paid to entropy generation encountered during convection of nanofluids. Hence, this work aims to numerically study entropy generation and heat transport in a lid-driven porous enclosure filled with a nanoliquid.

To amend the efficiency of engineering processes and electronic devices, it is very urgent to assess the irreversibility in the term entropy generation (EG). The efficiency of energy transportation in a system can be improved by minimization of the rate of EG. In this context, the aim of the present study is to estimate irreversible losses of an unsteady magnetohydrodynamic (MHD) flow of a viscous incompressible electrically conducting non-Newtonian molybdenum disulfide-polyethylene glycol Casson nanofluid past a moving vertical plate with slip condition under the influence of Hall current, thermal radiation, internal heat generation/absorption and first-order chemical reaction. Molybdenum disulfide (MoS₂) nanoparticles are dispersed in the base fluid polyethylene glycol (PEG) to make Casson nanofluid. Casson fluid model is considered to characterize the rheology of the non-Newtonian fluid, whereas Rosseland approximation is adopted to simulate the thermal radiative heat flux in the energy equation.

The closed-form solutions are obtained for the model equations by using the Laplace transform method (LTM). Graphs and tables are prepared to examine the impact of pertinent flow parameters on the pertinent flow characteristics. The energy efficiency of the system via the Bejan number is studied extensively.

Analysis reveals that Hall current has diminishing behavior on entropy production of the thermal system. Strengthening of the magnetic field declines the velocity components and prop-ups the rate of EG. Adding nanoparticles into the base fluid reduces the EG, whereas there are an optimum volume fraction of nanoparticles for which the EG is minimized. Further, the rate of decay of EG is prominent in molybdenum disulfide-polyethylene glycol in comparison to PEG.

The results of this study would benefit the industrial sector in achieving the maximum heat transfer at the cost of minimum irreversibilities with an optimal choice of embedded thermophysical parameters. In view of this agenda, this study would be adjuvant in powder technology, polymer dynamics, metallurgical process, manufacturing dynamics of nano-polymers, petroleum industries, chemical industries, magnetic field control of material processing, synthesis of smart polymers, etc.

The novelty of this study is to encompass the analytical solution by using the LTM. Such an exact solution of non-Newtonian fluid flow is rare in the literature. Limited research articles are available in the field of EG analysis during the flow of non-Newtonian nanoliquid subject to a strong magnetic field.