Ecological Coefficient Of Performance Research Articles

Transition to chaotic flow, bifurcation, and entropy generation analysis inside a stratified trapezoidal enclosure for varying aspect ratio

In this numerical study, we investigate the effect of aspect ratio (AR) on the natural convection (NC) flow and entropy generation (Sgen) in a stratified fluid confined inside a trapezoidal enclosure with thermally stratified side walls. The bottom of the enclosure is heated, and top of the enclosure is cooled. We use the Finite Volume Method (FVM) for simulating unsteady flows. We consider a Prandtl number (Pr = 0.71 for air) and explore AR of 0.2, 0.5, and 1.0, covering a wide range of Grashof numbers (Gr) from 10 to 108. The outcomes are presented for Grashof numbers and the effect of the AR on fluid flow, rates of heat transfer (HT), and Sgen inside the enclosure. Critical Grashof numbers are identified, marking the shift in flow behavior from being influenced by baroclinic to Rayleigh–Bénard instability, and from a steady to an unsteady state for various AR. In the context of this transition to chaotic flow, several supercritical bifurcations are observed, including a Pitchfork bifurcation from symmetric to asymmetric states and a Hopf bifurcation from a steady state to an unsteady state. Additionally, we analyze the discrepancies in average entropy generation (Savg) and average Bejan number (Beavg) across the entire enclosure, considering various AR and Gr values. It is observed that for enclosures with Gr ≥ 105, Savg increases as AR decreases, indicating an enhancement in HT rate with decreasing AR. Furthermore, a quantitative relationship between Savg, HT, AR, and Gr is presented. The study concludes that, as AR increases, the ecological coefficient of performance (ECOP) decreases, signifying a reduction in thermodynamics efficiency.

Energy and exergo-environmental analysis of a refrigerator-Stirling/Photovoltaic system for cold production

The Stirling refrigerator is a device capable of using green energies such as solar power. In this work, a refrigerator-Stirling/photovoltaic system is proposed to harness solar energy for cold production. The system consists of photovoltaic (PV) panels that capture solar energy and convert it into electricity, and a transmission belt linking the motor to the Stirling beta refrigerator to use the electricity for cooling purposes. The system is modeled on the basis of finite-dimensional thermodynamics, taking into account the refrigerator's internal and external irreversibilities. In addition, the wiring loss, dust coverage and shading of the photovoltaic system and the mechanical power loss of the Stirling refrigerator are taken into account in this model. Power equality has been considered as a system constraint. Finally, the effects of operational and design parameters on system performance are investigated. A numerical code is written in Matlab. The effects of PV module efficiency, Stirling regenerator efficiency and PV derating factor on system performance are quantified, also the optimum operating parameters obtained. The refrigerator-Stirling/photovoltaic has a high COP and a low cooling capacity, in contrast to the refrigerator-Stirling/Dish-Stirling. The optimum solar electric COP and maximum cooling rate are 0.7063 and 1413 W respectively at an optimum panel area of 2 m2. Optimum exergy efficiency is 38.5 % at fv = 0.1, ecological coefficient of performance (ECOP) is 20.3 % at N = 48 rot.s−1, optimum exergy destroyed is 33.31 W at K1 = 21.5 W.K−1. This system can be used to preserve vaccines in hospitals.

Heat transfer augmentation and entropy generation minimization by employing synergistic aspects of hybrid (Fe3O4 + MWNTs) nanoliquid in star shaped enclosure with thermally conductive cylinder and inclined magnetic field aspects

This article aims to simulate optimum thermal convection and minimization in entropy generation in viscous hybrid nanofluid (Fe3O4-MWNTs/H2O) flow in thermally cold star shaped enclosure and containing heated cylinder. Shape effect of cylinder in managing associated hydrothermal attributes is also interrogated. Physical aspect of magnetic field making angle of inclination with domain is accounted. Formulation of transport equations is expressed in the form of dimensionless partial differential setup containing the thermophysical relations of induced hybrid nanoparticles. The constructed flow issue has been simulated by using Galerkin finite element method (G-FEM) with appliance of COMSOL Multiphysics®software computer package.Results and grid convergence assessment tests are also executed in the study. Significant impact of flow controlling parameters on velocity, temperature and entropy generation profiles has been presented in graphical and tabular manner. Variation is three different types of entropies namely, viscous, thermal and magnetic are estimated. Quantities of interest like, total entropy, average Nusselt and Bejan numbers are also calculated against the sundry parameters. Ecological coefficient of performance which measures the efficiency of physical systems is interrogated which is important physical quantity in practical problems. It is inferred from the outcomes that induction of hybrid nanoparticles (Fe3O4 − MWCNT) produces considerable augmentation of thermal attributes of base fluid. Moreover, it is depicted that average Nusselt number exceeds up to 26.5 % for star shaped inner cylinder in comparison to the square cylinder. Increment up to 6 % in average Nusselt number and 2.19 % decrease in entropy is depicted when hybrid nanoparticles are added in the base fluid (ϕ≠0) in comparison to the situation when nanoparticles are not induced (ϕ=0).

Numerical simulation of entropy generation in thermo-magnetic convection in an inverted T-shaped porous enclosure under thermal radiation

PurposeThermo-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.Design/methodology/approachThe 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.FindingsThe 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.Practical implicationsSuch 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.Originality/valueTo 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.

Multi objective ecological optimization of an irreversible Stirling cryogenic refrigerator cycle

The primary objective of the current study is to demonstrate the multi-objective, ecological optimization of an irreversible Stirling cycle-based cryogenic refrigerator. The novelty of the work lies in the ecological optimization of the system, where irreversibilities are considered during the study and the thermal reservoirs have finite energy. The heat source and heat sink exchange energy with the working fluid and respective thermodynamic processes are carried out. The aim is to maximize the ecological objective function and the ecological coefficient of performance, and the effect of design variables on the objective function is investigated. The heat sink capacitance rate, temperature ratio, heat source, and sink capacitance rates, and effectiveness of the hot and cold side heat exchangers are regarded as the design variables. A heat transfer search algorithm is used to optimize the objective functions, and multiple optimal solutions are presented using the Pareto optimal curve. The multi-criteria decision technique TOPSIS is employed to select the ideal solution. For an ideal point selected through TOPSIS, the system works at an optimum ECF and ECOP of 787 W and 5.9, respectively. The ECOP of the system for the current study is 1.81 times and 4.03 times higher than the existing literature. However, the maximum ECF of 1797 W or maximum ECOP of 17.2 can be obtained for the given constraints of design variables.

Design and multi-scenario optimization of a hybrid power system based on a working gas turbine: Energy, Exergy, Exergoeconomic and Environmental evaluation

The rising demand for electricity, along with the need to minimize carbon footprints, has motivated academics to investigate the flexible and efficient integration of energy conversion technologies. A novel hybrid power generation system based on environmentally friendly and cost-effective technologies to recover the waste heat of a working gas turbine is designed and assessed in different scenarios of multi-objective optimization from energy, exergy, exergoeconomic, and environmental (4E) perspectives. In the proposed system, a steam methane reformer and a water gas shift reactor are utilized for hydrogen production, while a polymer electrolyte membrane fuel cell (PEMFC) and steam/organic Rankine cycles are run for generating additional power. Aspen Plus, in conjunction with Fortran, Microsoft Excel, and MATLAB, is used to model and simulate the designed plant. The response surface methodology (RSM) is utilized to determine accurate surrogate models to describe the evaluation criteria, and the Non-dominated Sorting Genetic Algorithm II technique is employed to seek the optimal conditions. Moreover, TOPSIS and LINMAP decision-making approaches are used to find the best final solution among Pareto frontiers. The analysis of variance (ANOVA) and sensitivity analysis are also applied to evaluate the importance of the design variables. In this regard, three single-objective optimizations and four multi-objective optimization scenarios based on the maximization of the ecological coefficient of performance (ECOP) and the minimization of CO2 emissions and total system product cost (Ċp) are carried out. It is demonstrated that the system’s evaluation criteria have the highest and lowest sensitivity to the variation of reformer temperature and ORC pressure, respectively. From the triple-objective optimization procedure, the decision variables including reformer temperature, ORC pressure, Rankine cycle I pressure, and Rankine cycle II pressure are 544 °C, 4.35 bar, 158.12 bar, and 52.82 bar, respectively. At these conditions, the total hybrid system’s energy efficiency, exergy efficiency, exergy destruction, net generated power, and total investment cost rate are 45.96%, 46.83%, 215.72 MW, 203.67 MW, and 9791 $/h, respectively. The findings of this paper conclude that it is necessary to address all objective functions simultaneously in the system’s ultimate optimum design. Furthermore, the objective of this paper becomes even more apparent when there is no choice but to cut greenhouse gas emissions while also addressing the rising global energy demand.

Finite Time Thermodynamic Modeling and Performance Analysis of High-Temperature Proton Exchange Membrane Fuel Cells.

In order to improve the output performance of high-temperature proton exchange membrane fuel cells (HT-PEMFC), a finite time thermodynamic (FTT) model for HT-PEMFC was established. Several finite time thermodynamic indexes including power density, thermodynamic efficiency, exergy efficiency, exergetic performance efficient (EPC), entropy production rate and ecological coefficient of performance (ECOP) were derived. The energetic performance, exergetic performance and ecological performance of the HT-PEMFC were analyzed under different parameters. Results showed that operating temperature, doping level and thickness of membrane had a significant effect on the performance of HT-PEMFC and the power density increased by 58%, 31.1% and 44.9%, respectively. When the doping level reached 8, the output performance of HT-PEMFC wa optimal. The operating pressure and relative humidity had little influence on the HT-PEMFC and the power density increased by 8.7%% and 17.6%, respectively.

Performance investigation and evaluation of an engine operating on a modified dual cycle

In this study, a novel high-performance engine cycle composed of 5 processes and including constant temperature process has been developed by using novel numerical methods and compared with the classical dual cycle. The results of the classical thermodynamic model demonstrated that the proposed cycle which has a constant temperature process is better in terms of thermal efficiency and dimensionless net work compared to the classical dual cycle. After the validation of superiority of the developed cycle over the classical dual cycle, performance investigations of the novel cycle engine have been carried out in terms of power, power density, destructed exergy, thermal efficiency, ecological coefficient of performance, effective ecological power density by developing a novel fuel-air cycle model. The influences of design and operational parameters such as cut-off ratio, compression ratio, cycle temperature ratio, equivalence ratio, engine speed, stroke length, cylinder bore, cylinder wall temperature, air intake temperature, pressure ratio, on the performance specifications have been numerically derived.

Energetic, Exergetic, Environmental, and Economic Assessment of a Cascade Refrigeration System Operating with Four Different Ecological Refrigerant Pairs

In this work, a cascade refrigeration system operating with four different ecological refrigerant pairs was modeled. This system uses R744 (Carbon dioxide) in the low-temperature cycle and operates with R290 (propane), R1234yf (2,3,3,3-tetrafluoropropene), R152a (1,1-difluorethane), and R717 (ammonia) in the high-temperature cycle. Energetic, exergetic, environmental, and economic performance of the cascade system was investigated to determine the most appropriate ecological refrigerant couple. The parameters used in each mentioned performance were COP (Coefficient of Performance), [Formula: see text] (Exergy Efficiency), TEWI (Total Equivalent Warming Impact), ECOP (Ecological coefficient of performance), and [Formula: see text] (Total plant cost rate), respectively. The results showed that the cascade refrigeration system operating with R744/R717 provided the best performance for the thermodynamic conditions analyzed, presenting a COP of 2.10, [Formula: see text] of 56.9%, [Formula: see text] of 24 334 USD/year, ECOP of 4.86, and TEWI of 25.67 tons of CO2. Finally, evaluating the total plant cost rate of this cascade system, it was noted that the capital and maintenance cost rate [Formula: see text] corresponds to 89.1% of the [Formula: see text] value, the operational cost rate [Formula: see text] corresponds to 10.27% of the [Formula: see text] value and the environmental cost rate [Formula: see text] corresponds to 0.63% of [Formula: see text].

Overall and component basis performance evaluations for turbojet engines under various optimal operating conditions

An evaluation using various operating conditions such as the maximums of: power, power density, ECOP and ECOL optimization functions for the analysis of turbojet engines is reported. Although, these well-known optimization functions were applied for various cycle types by researchers, the application of these methods for aircraft turbojet engines have not been explored. To this effect, a Brayton cycle including diffuser and nozzle together with the compressor, combustion chamber and turbine with various irreversibilities was considered. Engine irreversibilities are taken into account through appropriate efficiencies for each component. Different parameters influencing the cycle performance are examined such as compressor pressure ratio, cycle temperature ratio, compressor and turbine efficiencies, altitude and flight Mach number. The cycle performance was assessed utilizing the maximum power (MP), power density (MPD), Ecological Coefficient of Performance (ECOP) and Ecological Function (ECOL) conditions. In addition, the size variation of individual engine components and their contribution to the overall performance was also assessed under maximum power, power density, ECOP and ECOL conditions. The comparisons show that the design parameters at the maximum ECOL and maximum ECOP conditions may lead to smaller, more efficient and lower fuel consumption for turbojet engines than those at maximum power and maximum power density. However, on a component basis (compressor, combustion chamber, turbine and nozzle) the engine power, thrust, thermal efficiency, size and TSFC can be enhanced when utilizing the MP, MPD, ECOP and ECOL optimization functions.

Ecological Performance Optimization of a High Temperature Proton Exchange Membrane Fuel Cell

According to finite-time thermodynamics, an irreversible high temperature proton exchange membrane fuel cell (HT-PEMFC) model is established, and the mathematical expressions of the output power, energy efficiency, exergy efficiency and ecological coefficient of performance (ECOP) of HT-PEMFC are deduced. The ECOP is a step forward in optimizing the relationship between power and power dissipation, which is more in line with the principle of ecology. Based on the established HT-PEMFC model, the maximum power density is obtained under different parameters that include operating temperature, operating pressure, phosphoric acid doping level and relative humidity. At the same time, the energy efficiency, exergy efficiency and ECOP corresponding to the maximum power density are acquired so as to determine the optimal value of each index under the maximum power density. The results show that the higher the operating temperature and the doping level, the better the performance of HT-PEMFC is. However, the increase of operating pressure and relative humidity has little effect on HT-PEMFC performance.

Exergetic optimisation of a four-temperature-level absorption heat pump based on finite-time thermodynamics

ABSTRACT A finite-time thermodynamics study and an exergetic optimisation for a four-temperature-level absorption heat pump have been performed. The maximum of the exergetic-performance coefficient (EPC) and the corresponding optimal ecological coefficient of performance (ECOP), ecological objective function (E), exergetic efficiency (ex), coefficient of performance (COP), specific entropy generation rate and heating load have been obtained. The effects of internal irreversibilities, external irreversibilities, heat leakages, ratio of the rejected heat of the absorber to the condenser and the heat-transfer coefficients of different components on the system performance have been analysed and discussed. It was noticed a greater harmful impact of heat losses in the generator-absorber assembly. Comparisons of EPC criterion with ECOP, COP, E and ex criteria have been provided. The results demonstrate that the four-temperature-level absorption heat pump working at maximum EPC conditions has a significant advantage in terms of entropy generation rate and coefficient of performance.

Multi-Objective Optimization of Thermo-Ecological Criteria-Based Performance Parameters of Reheat and Regenerative Braysson Cycle

Abstract The reheat and regenerative Braysson cycle being an alternative for combined cycle power plants needs to be optimized for its efficient utilization of energy resources. Therefore, to obtain the best possible overall pressure ratio, regenerator effectiveness, and pressure ratio across multistage compression in order to simultaneously maximize exergy efficiency, nondimensional power density (NDPD), and ecological coefficient of performance (ECOP) for three different maximum temperature situations, multi-objective optimization of the above cycle is carried out using nondominated sorting genetic algorithm-II (NSGA-II). The optimal solutions given by the Pareto frontier are further assessed through widely used decision makers namely LINMAP, TOPSIS, and Bellman–Zadeh techniques. The optimal solutions attained by the decision-making process are further evaluated for their deviation from the nonideal and ideal solutions. The optimal solution obtained through TOPSIS possesses the minimum deviation index. Finally, the results are authenticated by performing an error analysis. Such optimal scenarios achieved for the three maximum temperatures are further analysed to achieve the final objective of the most optimal solution which happens to be at 1200 K. The simultaneous optimization of performance parameters which reflect the thermo-ecological criteria to be satisfied by a power plant has resulted in values of 0.479, 0.327, and 0.922 for exergy efficiency, nondimensional power density, and ecological coefficient of performance, respectively. These optimized performance parameters are obtained for an overall pressure ratio of 7.5, regenerator effectiveness of 0.947, and pressure ratio across multistage compression of 1.311.

THERMODYNAMIC ASSESSMENT OF WATER DIESEL EMULSIFIED FUEL USAGE IN A SINGLE CYLINDER DIESEL ENGINE

ABSTRACT In this study, 5% (W5), 10% (W10), and 15% (W15) of water-diesel emulsified fuels have been prepared using surfactants and obtained emulsifications were experimentally tested in a single-cylinder diesel engine on maximum torque and maximum power area at full load condition. In this way, theoretical analyses have been performed in order to evaluate the energy potential of a diesel engine fueled with emulsified fuel. According to results, thermal efficiency raises up to 9.4% with water amount increment since the reduction of work is smaller than the reduction of fuel energy rate. Fuel exergy rates increase up to 14.3% thanks to oxygen and hydrogen content of water but the destruction rate of exergy increased at the same time up to 25.2% and also exergetic efficiency reduces as up to 16.9% compared to neat diesel. Last of all, the ecological coefficient of performance (ECOP) criterion was obtained as 0.24 and 0.18 on maximum torque area and 0.28 and 0.21 on maximum power area for neat diesel and W15 as a disadvantage of water emulsified fuels.

Power, efficiency, ecological function and ecological coefficient of performance optimizations of irreversible Diesel cycle based on finite piston speed

By connecting the finite time thermodynamics and the finite speed thermodynamics, an irreversible reciprocating Diesel cycle model is established with considering the irreversibilities caused by finite piston speed, heat transfer, friction, and internal irreversible loss. Through numerical calculations, the relationships among net power output (P), thermal efficiency (η), ecological function (E), ecological coefficient of performance (ECOP) and compression ratio (γ), piston speed and piston speed ratio are analyzed. As it is shown in the results, the relation curves of P−γ, η−γ, E−γ, ECOP−γcharacteristics of the cycle are parabolic ones, and those of P−ηand E−ηcharacteristics of the cycle are loop-shaped ones. When piston speed ratio is a constant, the maximum net power output increases, the maximum ecological function first increases and then decreases, the maximum thermal efficiency and the maximum ecological coefficient of performance both decrease with the increase of piston speed. When piston speed is a constant, the maximum net power output and the maximum ecological function both first increase and then decrease, and the maximum thermal efficiency and maximum ecological coefficient of performance both decrease with the increase of piston speed ratio.

Multi-criteria performance analysis of dual miller cycle – Organic rankine cycle combined power plant

Performance improvement in power generation systems have been current issues in the recent years. Combined power plants including Organic Rankine Cycle are promising for performance improvement to generate efficient energy. This study has examined a way of optimum conditions for both efficiency and exhaust emissions by introducing a combined plant of Dual Miller Cycle-Organic Rankine Cycle focused on diesel engine applications. Three different types of working fluids with appropriate characters are used in the Organic Rankine Cycle. Effective efficiency, effective power, exergy destruction, effective power density, ecological coefficient of performance, exergetic efficiency and effective ecological power density are investigated for both Dual Miller Cycle and Dual Miller Cycle – Organic Rankine Cycle combined plant configurations. The impacts of engine design and working parameters such as cycle temperature ratio, cycle pressure ratio, engine speed, cylinder dimensions and equivalence ratio on the performance parameters are investigated. Octafluorocyclobutane and pentafluoropropane have been used as working fluids of Organic Rankine Cycle. The results showed that pentafluoropropane is the best suitable organic fluid. The effective efficiency, ecological coefficient of performance and exergy destruction have been found as 45.42%, 74.14% and 12.4 kW, respectively. The results of this examination have shown optimum values of the engine design and operating parameters in terms of thermo-ecological feasibility which also reduces harmful ship emissions like nitrous oxides.

On the entropy generation for a porous enclosure subject to a magnetic field: Different orientations of cardioid geometry

Natural or free convection is one mode of convection heat transfer where temperature changes leads to density variation. For example, free convection can happen in an enclosure that has two walls with different temperatures. In the present study, the heat transfer behavior of a cardioid shaped porous cavity is investigated. Regarding the situation of the inner cardioid, four modes can be considered for the problem that is called cases A, B, C and D. The Cu-water nanofluid has been selected as working fluid and the flow is affected by an external magnetic field. Non-dimensional governing equations (stream-vorticity functions) are solved numerically using the control volume finite element method (CVFEM). The ecological coefficient of performance (ECOP) as a criterion of cavity performance is evaluated. The effects of decision variables such as Darcy number, Hartmann number, Rayleigh number, and nanoparticle volume fraction on the entropy generation number, the ECOP and the average Nusselt number are studied. The results show that case C is better rather than other cases from the view point of the second law of thermodynamics.

Thermodynamic mapping of A321-200 in terms of performance parameters, sustainability indicators and thermo-ecological performance at various flight phases

In this paper, the performance parameters, sustainability indicators and thermo-ecological parameters are presented to the literature by modelling 140.56 kN propulsion turbofan engine of the A321-200 registered to the International Aero Engines manufacturer under type code 3IA008 and type name V2533-A5. In the study, firstly, exergy efficiency of each component is calculated by two different approaches, and then four different depletion ratios of each component are determined. In addition, the exergetic improvement potential ratios of components and systems are presented. Waste exergy ratio, recoverable exergy rate, exergy destruction factor, environmental effect factor and exergetic sustainability index has been selected as sustainability indicators. Finally, the ECOP (ecological coefficient of performance) function is calculated and comparatively evaluated in the specified flight phases as well as the flight phases are classified in terms of sustainability and environmental impacts. The element emphasizing the originality of this article is that the sustainability and environmental impacts in all flight phases are mapped.

Thermodynamic Assessment and Optimization of Performance of Irreversible Atkinson Cycle

Although various investigations of Atkinson cycle have been carried out, distinct output power and thermal efficiencies of the engine have been achieved. In this regard, thermal efficiency, Ecological Coefficient of Performance (ECOP), and Ecological function (ECF) are optimized with the help of NSGA-II method and thermodynamic study. The Pareto optimal frontier which provides an ultimate optimum solution is chosen utilizing various decision-making approaches, containing fuzzy Bellman-Zadeh, LINMAP, and TOPSIS. With the help of the results, interpreting the performances of Atkinson cycles and their optimization is enhanced. Error analysis has also been performed for verification of optimization and determining the deviation in the study.

Investigation of entropy generation in a square inclined cavity using control volume finite element method with aided quadratic Lagrange interpolation functions

One of the most concerned subjective in Mechanical science is natural convection study in a cavity. Furthermore, the investigation of entropy generation can be useful for better designing of the thermal systems. In the present study, natural convection flow and entropy generation are numerically investigated in the presence of a magnetic field in a square inclined cavity which known as the effect of magneto-hydrodynamic (MHD). Firstly, governing equations, including mass, momentum, and energy balance equations are applied to the problem. Then, governing equations are rewritten in dimensionless form using non-dimensional parameters, vorticity, and stream function. Furthermore, the entropy generation equation is written as a non-dimensional equation. Then, the contribution of the heat transfer entropy generation into the total entropy generation rate is determined using the Bejan number. A new measure for evaluation of the thermal performance of the cavity is presented that is the so-called ecological coefficient of performance (ECOP) based on the second law of thermodynamics. Flow and heat transfer characteristics are investigated for different values of the Rayleigh number, inclination angle, and Hartmann number. The new correlations of entropy generation as a function of Rayleigh number are obtained using the two-dimensional version of quadratic Lagrange interpolation functions (QLIFs). The obtained values for the average Nusselt number and the entropy generation number are compared with those of the literature and excellent agreement is observed. The results show that the entropy generation number rises with increasing of Hartmann number and whereas it has a maximum value for a specified inclination angle. Also, ECOP increases with increasing of Hartmann number for low values of Rayleigh number. The results discover that the optimum values of the inclination angle are 20°, 35° and 48°for Hartmann number 0, 25 and 75 at Ra = 105, respectively. Also, with increasing Ha from 25 to 75, the contribution of the Ngen due to magnetic field decreases from 23% to 9% for β = 0° and it decreases from 24% to 6% for β = 45°.