Entropy Generation Decreases Research Articles

Entropy generation analysis on Darcy-Forchheimer Maxwell nanofluid flow past a porous stretching sheet with threshold Non-Fourier heat flux model and Joule heating

This research paper inspects the flow characteristics of a magnetohydrodynamic (MHD) Maxwell nanofluid in the presence of a Darcy-Forchheimer (DF) model applied to a stretching sheet. Additionally, numerical analysis is performed to evaluate the findings, utilizing a nanofluid composed of copper (Cu) suspended in water. The energy equation in this study incorporates thermal radiation, viscous dissipation, the Cattaneo-Christov heat flux model, and joule heating. The entropy generation is then determined based on the obtained solutions for temperature and velocity, in compliance with the flow constraints. By applying suitable similarity transformations, the conservative equations of energy and momentum are transformed into nonlinear ordinary differential equations (ODEs). To solve these equations, a bvp4c method implemented through Matlab software is employed. By taking into account pertinent characteristics like the relaxation Prandtl number, magnetic parameter, time parameter, radiation parameter, and others, one can analyse the normalized shear stress at the wall, temperature profile, and rate of heat flux. For practical purposes, the local Nusselt and number of skin frictions are determined for various modified values of the physical constraints. This provides vital insights about the system's behavior under various settings. The graphical results indicate that the velocity profile exhibits a decrease as the volume fraction, magnetic parameter, Maxwell fluid parameter, and inertia coefficient parameter increase. The entropy generation demonstrates an increase with growing values of the Brinkman number and magnetic parameter. On the other hand, entropy generation declines with increasing values of the temperature ratio parameter. The Bejan number exhibits the opposite behavior of the entropy generation. Specifically, as the Bejan number increases, the entropy generation decreases, and vice versa.

Entropy analysis and mixed convection of nanofluid flow in a pillow plate heat exchanger in the presence of porous medium

A pillow plate heat exchanger (PPHE) is one of the types of heat exchangers that haven't received the attention they deserve despite their high efficiency and operational capability. A unique feature of PPHEs is their pillow-shaped structure, which is achieved through hydroforming. In light of this, scholars have been interested in analyzing and optimizing the thermo-hydraulic properties of PPHEs. In this study, the interior of the PPHE was occupied with a permeable substance with a high porosity percentage (0.9034 ≤ ɛ ≤ 0.9586 and 0.00015 ≤ dp ≤ 0.00065) and saturated with Ag-water (0 ≤ϕ ≤ 0.06) nanofluid, which has a profound influence on the heat transfer rate of PPHEs. In order to analyze the determinants affecting the heat transfer rate of PPHEs under these conditions, the governing equations were solved using the finite volume method and also the Brinkman-Forchheimer-extended Darcy equation. According to the results, heat transfer is enhanced in PPHE when using a permeable medium with high porosity and a small pore size. That is, PPHEs transfer heat more efficiently when they are placed in a denser porous medium because heat conduction is boosted. Moreover, due to the increased thermal conductivity of the nanoparticles, the application of nanoparticles to the base fluid also enhanced heat transfer and Nusselt number. However, decreases in friction factor and entropy generation were observed with increasing porosity, pore size, and Darcy number, due to reduced flow resistance. A decrease in Richardson number also results in a decrease in friction factor and entropy generation. At the wake region of welding spots, the velocity has reached its lowest values; consequently, this led to a reduction in the heat transfer rate. Nevertheless, within dense porous media, at the lower hydraulic diameter points, the conduction contributes to heat transfer improvement. The porous medium acts as a heat sink and absorbs the heat from the welding spot. This allows the heat to be dissipated away from the welding spot, which reduces the velocity and heat transfer rate. The nanofluid, on the other hand, helps to increase the thermal conductivity of the medium, resulting in more heat being transferred to the surrounding material. Consequently, the results demonstrated that PPHEs' thermal and thermodynamic performance could be significantly improved by using a porous medium saturated with nanofluid.

Numerical analysis of a helically corrugated tube using a novel combination of W/EG-based non-Newtonian hybrid nanofluid

In this study, the second law analysis of a non-Newtonian hybrid TiO2-SiO2 nanofluid based on water/ethylene glycol has been carried out. The influence of the corrugation-height ratio (e/dh) and volume fraction (φ) on the rates of entropy creation and exergy destruction are investigated using a helically corrugated tube. The model is simulated using ANSYS FLUENT 19.0 with the corrugated wall kept at a constant heat flux of 25 kW/m2 and a range of hybrid nanofluid volume flow rates from 15 to 25 lpm. As the corrugation height and particle volume percentage increases, the HCT's rates of entropy generation and exergy destruction decrease. Additionally, as the volume flow rate of the hybrid nanofluid increases within the abovementioned range, the Bejan number and entropy generation number also decrease. For volume fraction of 5%, the Bejan number decreases to 0.873 at 25 lpm. The total irreversibility is reduced by adding corrugation and employing hybrid nanofluids. Also, working with the combination of corrugation and hybrid nanofluid leads to a notable increase in exergetic efficiency, reaching a maximum value of 82.8%.

Hydrothermal characteristics, entropy and kinetic energy investigation in a sinusoidal cavity for variable wavelengths and solid volume fraction using Cu-water nanofluid

The use of thermofluids in a cavity under magnetohydrodynamics (MHD) with the natural convective flow has been extensively researched, with numerous attempts made by researchers. However, none have examined the role of nanofluid concentrations on a sinusoidal cavity with variable wavelengths at two walls using Cu-water nanofluid with MHD. Therefore, the present study evaluated nanofluid concentration impact in a sinusoidal cavity for three different wavelengths under magnetic field conditions and Rayleigh numbers using Cu-water nanofluid. Four different solid volume fractions (ϕ = 0.02, 0.04, 0.06, 0.08), three different wavelengths (λ = 2, 3, 4), three different Rayleigh numbers (Ra=103,104, 105) have been considered for the study using the finite element method. The LBB-stable element is used to approximate velocities, pressures, and temperatures. The numerical results have been validated from the past study. The variation of kinetic energy, average Nusselt number, viscous, thermal, magnetic, and total entropy generation for various wavelengths has been shown for varying the concentration of nanofluid and Hartmann number. Additionally, the effect of Rayleigh numbers on the entropy generations for three different wavelengths has been presented. The results revealed that the heat transfer rate, kinetic energy, and entropy generation rise with the decreased value of volume concentrations for most of the cases. It is also noticed that these parameters also negatively effect due to the magnetic field. Therefore, with the rise of the Hartmann number, the fluid flow, thermal parameters, and entropy generation decrease. Moreover, Ra has a notable role in entropy generation. Entropy generations have been found higher for Ra=105, and the lowest is found for the case of Ra=103.

Entropy Generation and Control: Criteria to Calculate Flow Optimization in Biological Systems

Living beings are composite thermodynamic systems in non-equilibrium conditions. Within this context, there are a number of thermodynamic potential differences (forces) between them and the surroundings, as well as internally. These forces lead to flows, which, ultimately, are essential to life itself, but, at the same time, are associated with entropy generation, i.e., a loss of useful work. The maintenance of homeostatic conditions, the tenet of physiology, demands the regulation of these flows by control of variables. However, due to the very nature of these systems, the regulation of flows and control of variables become entangled in closed loops. Here, we show how to combine entropy generation with respect to a process, and control of parameters (in such a process) in order to create a criterium of optimal ways to regulate changes in flows, the coefficient of flow-entropy (CJσ). We demonstrate the restricted possibility to obtain an increase in flow along with a decrease in entropy generation, and the more general situation of increases in flow along with increases in entropy generation of the process. In this scenario, the CJσ aims to identify the best way to combine the gain in flow and the associated loss of useful work. As an example, we analyze the impact of vaccination effort in the spreading of a contagious disease in a population, showing that the higher the vaccination effort the higher the control over the spreading and the lower the loss of useful work by the society.

Entropy generation analysis for mixed convection flow of nanofluid due to vertical plate with chemical reaction effects

The analysis have been presented to observe the optimized flow of Casson nanofluid conveying the applications of external heat generation and mixed convection features. The problem is further influenced by chemical reactive species with order one. The significant of Bejan number is evaluated. A vertically moving with convective heat phenomenon endorsed the flow. The modeled problem is reflected in terms PDE’s which are further simplifies with dimensionless form. The analytical outcomes have been established with implementation of Laplace technique. The graphical impact conveying the different parameters is assessed. The insight of skin friction and Nusselt number is observed via various curves. It is observed that entropy generation enhanced due to porosity parameter and magnetic number. With increasing Casson fluid parameter, the entropy generation decrease. Moreover, the Bejan number decreases for chemical reaction constant.

Investigation into the effects of hydrophobicity on thermohydraulic characteristics and entropy generation of hybrid nanofluid with the magnetic property in a micro-heat sink under a magnetic field

The cooling of devices is a big challenge in the electronics industry, and most process units (graphical are central process units) experience defects under harsh temperature conditions, so dissipating generated heat under various working conditions should be studied seriously. This study investigates the magnetohydrodynamics of hybrid ferro-nanofluids in the presence of hydrophobic surfaces in a micro-heat sink. To scrutinize this study, a finite volume method (FVM) is applied. The ferro-nanofluid includes water as a base fluid and multiwall carbon nanotubes (MWCNTs) and Fe3O4 as nanoadditives, which are used in three concentrations (0, 1, and 3%). Other parameters such as the Reynolds number (5–120), Hartmann number (magnitude of the magnetic field from 0 to 6), and hydrophobicity of surfaces are scrutinized for their impacts on heat transfer and hydraulic variables as well as entropy generation variables. The outcomes indicate that increasing the level of hydrophobicity in surfaces leads simultaneously to improved heat exchange and reduced pressure drop. Likewise, it decreases the frictional and thermal types of entropy generation. Intensifying the magnitude of the magnetic field enhances the heat exchange as much as the pressure drop. It can also decrease the thermal term in entropy generation equations for the fluid, but increase the frictional entropy generation and adds a new term, magnetic entropy generation. Incrementing the Reynolds number improves the convection heat transfer parameters, although it intensifies the pressure drop in the length of the channel. Also, the thermal entropy generation and frictional entropy generation decrease and increase with an increasing flow rate (Reynolds number).

Investigation of thermal characteristics and entropy generation in a solar collector including Fly Ash-Cu hybrid nanofluids: Numerical approach using mixture model

Heat transfer enhancement is one of the substantial challenges in solar energy conversion systems. By using two different working fluids, namely water and Fly Ash-Cu/water hybrid nanofluids (80:20 Vol.%), this numerical research aims to improve heat transfer by modeling the flat plate solar collector's (FPSC) tube in a zigzag shape instead of a common straight pipe. The innovation of the present study is to evaluate the second law of thermodynamics in a proposed solar collector including Fly Ash-Cu/water hybrid nanofluids and compare the second law of thermodynamics’ results with the Mixture model. Also, various thermal characteristics, such as the Nusselt number, convection heat transfer coefficient (HTC), friction factor, and outlet temperature, are examined at different nanoparticle concentrations, two inlet temperatures, and different mass flow rates. The system works under conjugated laminar mixed convection and constant solar irradiation, 800 W m-2. Results reveal that working fluid pumps with a higher flow rate increase Nusselt number, convection heat transfer coefficient, and friction entropy generation, about 33.33%, 41%, and 88%, respectively, while outlet temperature, friction factor, and thermal entropy generation decrease with increasing mass flow rate. Furthermore, using nanoparticles with a higher concentration considerably increase friction and thermal entropy generation.

Numerical Forced Convection Heat Transfer, Fluid Flow and Entropy Generation Analyses of Al2O3- Water Nanofluid in Elliptical Channels

This study investigates a three-dimensional elliptical microchannel heat sink for heat dissipation in laminar forced convection. The study seeks to improve thermal performance and overcome overheating associated with excessive temperature commonly experienced in heat-generating equipment, which is beyond the temperature usually specified by the manufacturer. The objective of the study is to evaluate the heat transfer, fluid flow, and entropy generation characteristics of Al2O3-water nanofluid in an elliptical cooling channel. The numerical analysis is investigated on the structure experiencing constant volumetric heat generation. The parameters considered are Reynolds number of 100 ≤ Re ≤ 500, nanoparticle concentration ϕ, from 0% to 4% with channel aspect ratio Ar from 1 to 3. The impacts of these parameters on the maximum temperature, heat transfer coefficient, friction factor, and volumetric entropy generation are reported. The study demonstrates that heat transfer is enhanced in the elliptical cooling channel at different aspect ratios, nanoparticle concentrations, and Reynold numbers. The results showed that as the nanoparticle concentration, channel aspect ratio, and Reynolds number (Re) increase, the maximum temperature, and total entropy generation decrease. As the channel aspect ratio increases at a specified Re = 200 and nanofluid concentration, ɸ = 3%, the maximum temperature, and total entropy generation decrease by up to 62% while the heat transfer coefficient increases by up to 78% and the friction factor increase by less than 2% with aspect ratio. However, the friction factor is not sensitive to the nanofluid concentration as a coolant.

Entropy generation analysis on thermo-hydraulic characteristics of microencapsulated phase change slurry in wavy microchannel with porous fins

• Combined design enables smaller temperature gradient and more uniform temperature. • Larger h m and lower ΔP can be concurrently gained in wavy MCHS with porous fins. • Thermal entropy is three orders of magnitude larger than the frictional entropy. • Thermal entropy increases with heat flux but the frictional entropy is opposite. • Lower irreversible losses can be achieved at the cost of higher power consumption. Recent advancement in micro/nano-scale electronic systems, the need for efficient heat dissipation has become more rigorous, and traditional thermal management solutions are facing enormous challenges. In this study, a novel combined design of wavy microchannel heat sink (MCHS) with porous fins and microencapsulated phase change material (MPCM) suspension is developed and numerically studied to achieve a balance between flow and heat transfer behaviors. The equivalent heat capacity method is adopted to deal with the phase change process of microcapsule particles in steady and laminar states, and the Brinkman–Darcy–Forchheimer model based on the volume-averaged method is employed to characterize the fluid flow in porous fins. A three-dimensional solid-fluid conjugate model is established based on the finite-volume method to investigate the effects of different coolant types (water and MPCM suspension), geometric parameters (wavy amplitude, wavelength, and channel width ratio), and working conditions (inlet flow velocity, heat flux, and slurry concentration) on the thermo-hydraulic properties and entropy generation of wavy MCHS. The results reveal that the combination of porous fins and MPCM suspension presents smaller temperature gradient and more uniform temperature distribution than conventional design. Larger heat transfer coefficient and lower pressure drop can be simultaneously obtained in wavy MCHS with porous fins than in solid fin configuration. The thermal entropy generation is three orders of magnitude larger than the frictional entropy generation, and the Bejan number is close to 1 for different microchannel configurations. Thermal entropy generation increases with increasing heat flux but the frictional entropy generation decreases. Lower irreversible losses can be achieved at the expense of greater pumping power consumption caused by increasing inlet velocity and suspension concentration. The superior effect of wavy MCHS with porous fins using MPCM suspension as coolant has been observed in all cases.

Investigation of a temperature-sensitive ferrofluid to predict heat transfer and irreversibilities in LS-3 solar collector under line dipole magnetic field and a rotary twisted tape

This article numerically studies the performance of the LS-3 parabolic trough collector. The parabolic trough solar system is equipped with an innovative rotary twisted tape. The absorber tube and twisted tape have the same length. Moreover, line dipole magnetic field is applied to improve the performance of solar collector. In addition, the characteristics of the irreversibilities are investigated. Commercial temperature-sensitive ferrofluid is selected for working fluid, and the nanoparticles along with the base fluid assumed to be uniform. The effect of rotational speed, twisted ratio, and line dipole magnetic field are compared with plain tube. The heat flux profile on absorber tube is ascertained by the Monte Carlo Ray Tracing method. Curve fitting method is used to obtain the mathematical function of the heat flux profile. To solve the equations including continuity, momentum, energy, and SST κ−ω model, the finite volume procedure is selected. The more convective heat transfer coefficient occurs by dipole magnetic field, the maximum enhancement reaches over 97% at B = 100 G. In addition, the twisted tape can increase heat transfer by 305% at twisted ratio = 2.5 and rotational speed = 200 rpm. Furthermore, if the twisted tape has rotational speed, the thermal entropy generation decreases.

The behavior of heat transfer and entropy in a thin layer of liquid under laser heating

Experimental studies of heat flux, Nusselt number, heat transfer coefficient and entropy generation under local laser heating in the range of water layer heights from 1.4 to 5 mm have been carried out. The laser heats a graphite spot on the glass wall, which warms up the liquid. To date, most studies in the fields of the velocity rotor and entropy generation have been carried out theoretically, and in the absence of surface Marangoni forces. There is extremely little experimental data on the measurement of these fields, especially at non-stationary three-dimensional heat exchange. The temperature field on the free surface of the liquid layer is strongly inhomogeneous and asymmetrical at a layer height of 1.4 mm. At a layer height of 4–5 mm, the symmetry of the temperature field increases. Using the optical method of Particle Image Velocimetry, instantaneous fields of velocity and vorticity have been studied. As the layer height increases, the characteristic size of vortex structures on the liquid surface rapidly decreases with a sharp decrease in the correlation function of the vortex flow. Local laser heating of the layer creates a spatially uneven heat exchange, which is formed during self-organization of various convective vortex structures. For the first time it is shown that the behavior of entropy generation during local heating of the layer differs from the case with uniform heating of the wall. The transition of a symmetric velocity field from two vortices to an asymmetric field with many vortices leads to a decrease in entropy generation with an increase in the Rayleigh and Marangoni numbers. The heat transfer coefficient in the liquid decreases with increasing layer height from 1.4 mm to 5 mm.

Effect of NP shapes on Fe3O4 – Ag/kerosene and Fe3O4 – Ag/water hybrid nanofluid flow in suction/injection process with nonlinear-thermal-radiation and slip condition; Hamilton and Crosser's model

This study examines the flow and thermal properties of water and kerosene hybrid nanofluids in a horizontal microchannel. The effects of nonlinear thermal radiation, heat source coefficient, convective and slip boundary conditions on nanofluids in a microchannel have been studied. The impact of different nanoparticle shape factors on the temperature of nanofluids has also been analysed. The governing partial differential equations have been transformed in to ordinary differential equations using dimensionless terms. In the next step, the corresponding ordinary differential equations have been cracked using the RKF45 numerical approach, and the particles shape factor on dimensionless velocity and energy fields for hybrid nanofluid then reported. The results revealed that the spherical and lamina shape factors for both water and kerosene hybrid nanofluid differ the most, the water-based hybrid nanofluid has a higher velocity than the kerosene-based hybrid nanofluid, the thermal energy of both water and kerosene-based hybrid nanofluid was higher in the lower channel plate than the upper channel plate, flow rate falls near the lower channel wall and increases towards the upper channel wall as Reynolds number increases. Thermal energy and entropy generation decrease as the temperature parameter rises.

Second law of thermodynamic analysis of 40:60% propylene glycol and water mixture based nanodiamond nanofluid under transition flow

Second law efficiency (exergy) was studied experimentally for transition flow in a tube of 40:60% (weight) p4ropylene glycol and water mixture based nanodiamond nanofluid. Prior to prepare the stable nano-diamond (ND) nanofluid, its soot was rinsed by strong chemicals. The experiments were carried out for several values of particle loading (0.2% to 1.0%) and of Reynolds number (2000 to 8000). The experimental analysis was also conducted for the heat transfer, friction factor and pumping power characteristics of the ND nanofluid. By increasing the values of particle concentration and Reynolds number, the results indicate an increase of heat transfer, Nusselt number, friction factor, pumping power and thermal performance factor, and a decrease of the thermal entropy generation. In comparison with the base fluid data, the heat transfer coefficient, Nusselt number, pressure drop, pumping power, friction factor and the thermal performance factor of the ND nanofluid augment by 36.83%, 24.16%, 15.38%, 13.18%, 19.9%, and 16.94%, respectively, and the thermal entropy generation decreases by 26.92% for 1.0 vol% and Reynolds number of 5321.16.

Performance evaluation of helical coils as a passive heat transfer enhancement technique under flow condensation by use of entropy generation analysis

Current research focuses on the performance of helically coiled tubes as a passive heat transfer enhancement technique for R134a flow condensation from an entropy generation perspective. Similar to other enhancement techniques, helical coils, are accompanied by pressure drop as a penalty, diminishing their performance, so that these coils are of lower performance compared to straight tubes where the increase in entropy generation due to pressure drop overcomes the decrease in entropy generation due to enhanced heat transfer. Unlike previous studies that have largely investigated heat transfer and pressure drop characteristics of helical coils regardless of their performance, this study employs entropy generation analysis as an effective method to distinguish flow and geometrical conditions at which helical coils are of lower entropy, i.e. higher performance, compared to straight tubes. The findings reveal that, for both helical and straight tubes, entropy generation is enhanced as tube diameter, mass velocity, vapor quality, and wall heat flux increase and saturation temperature decreases. Additionally, applying helical coils within wider ranges of mass velocities can be justified at lower values of tube (≤8.3 mm) and coil diameters (≤200 mm), saturation temperatures (≤40 °C), and vapor quality (≤0.6), and at higher values of wall heat flux (≥15 kW/m2). These results substantiate that employing helical coils in lieu of straight tubes is not justifiable always (for all flow and geometrical conditions) although they are of superior heat transfer performance compared to straight tubes.

Design of a Pulsing Flow Driven Turbine

Abstract There is widespread interest in using pressure gain combustion in gas turbine engines to increase gas turbine engine efficiency and reduce fuel consumption. However, the fluctuating turbine inlet conditions inherent with pressure gain combustion cause a decrease in turbine efficiency. Designing a turbine for pulsing flow would counteract these losses. An optimization of turbine geometry for pulsing flow was conducted with entropy generation as the objective function. A surrogate model was used for the optimizations based on data extracted from two-dimensional computational fluid dynamics simulations. Optimizations run for different pulsing amplitudes informed a revised turbine design. The new turbine geometry was validated with a periodic, time-accurate simulation, and a decrease in entropy generation of 35% was demonstrated. The design recommendations were to weight the design of the turbine toward the peak of the pressure pulse, to consider the range of inlet angles and decrease the camber near the leading edge, and to reduce the blade turning.

Analysis of entropy generation of ferrofluid flow in the microchannel with twisted porous ribs: The two-phase investigation with various porous layers

Heat sinks are always in the center of electronic cooling researchers' attention. Microchannels, due to their increased surface and better thermal performance than that of normal heat sinks were used in electronic cooling devices. In this numerical investigation, the first and second laws of the thermodynamic impact of twisted porous ribs on the microchannel were studied. The effects of the Reynolds number and volume fraction of nanoparticles were investigated. The range of Reynolds number was 250 to 1000. All types of the microchannel in this study consisted of a clear microchannel, a twisted porous ribbed microchannel with two and three layers of twisted porous ribs. The results show that by inserting porous ribs, the local cross-section decreases, and the local Reynolds number increases. Also, twisted porous ribs are the cause of nanofluid flow circulation and make the heat transfer coefficient greater. Increasing the porous layer from one layer to three layers has an increasing effect on the heat transfer coefficient, and the friction factor and increasing the φ is the reason for increasing the friction factor. Finally, the microchannel with triple layers of twisted porous ribs has better performance in total entropy generation, and by inserting twisted porous ribs, the entropy generation decreases.

MHD conjugate heat transfer and entropy generation analysis of MWCNT/water nanofluid in a partially heated divided medium

AbstractThe aim of this article is to conduct the lattice Boltzmann simulation of the magnetohydrodynamic (MHD) natural conjugate heat transfer in an apportioned cavity loaded with a multiwalled carbon nanotube/water nanofluid. The divided cavity is, to some extent, heated and cooled at the upright walls, whereas the horizontal walls are adiabatic. The nanofluid properties are evaluated on the basis of experimental correlations. The parameters ranges in the study are as follows: nanoparticles' volume fraction (%): 0 ≤ ϕ ≤ 0.5, temperature (°C): T = 27, Rayleigh number (Ra): 103 ≤ Ra ≤ 105, Hartmann number (Ha): 0 ≤ Ha ≤ 90, and the magnetic field inclination angle (γ): 0 ≤ γ ≤ π/2. The current outcomes are observed to be in great concurrence with the numerical results introduced in the literature. The impacts of the aforesaid parameters on local and average heat transfer, entropy generation, and Bejan number (Be) are explored and discussed. Indeed, the transfer of heat increases linearly with ϕ for a low Ra. As Ra increases, the average Nusselt number decreases for a high value of ϕ. The increase of nanoparticles' volume fraction leads to a reduction in the entropy generation and an increase in the Bejan number for a high Ra, but at low Ra, these functions remain constant. As the Ha increases, the transfer of heat and the entropy generation decreases, whereas there is an increase in Be. The transfer of heat, total entropy generation, and the Be depends strongly on the direction of the magnetic field. The increase of heater and cooler size has a great influence on the transfer of heat, entropy generation, and Be.

Optimization, Stability, and Entropy in Endoreversible Heat Engines.

The stability of endoreversible heat engines has been extensively studied in the literature. In this paper, an alternative dynamic equations system was obtained by using restitution forces that bring the system back to the stationary state. The departing point is the assumption that the system has a stationary fixed point, along with a Taylor expansion in the first order of the input/output heat fluxes, without further specifications regarding the properties of the working fluid or the heat device specifications. Specific cases of the Newton and the phenomenological heat transfer laws in a Carnot-like heat engine model were analyzed. It was shown that the evolution of the trajectories toward the stationary state have relevant consequences on the performance of the system. A major role was played by the symmetries/asymmetries of the conductance ratio of the heat transfer law associated with the input/output heat exchanges. Accordingly, three main behaviors were observed: (1) For small values, the thermodynamic trajectories evolved near the endoreversible limit, improving the efficiency and power output values with a decrease in entropy generation; (2) for large values, the thermodynamic trajectories evolved either near the Pareto front or near the endoreversible limit, and in both cases, they improved the efficiency and power values with a decrease in entropy generation; (3) for the symmetric case (), the trajectories evolved either with increasing entropy generation tending toward the Pareto front or with a decrease in entropy generation tending toward the endoreversible limit. Moreover, it was shown that the total entropy generation can define a time scale for both the operation cycle time and the relaxation characteristic time.

Magnetic field effects on natural convection and entropy generation of non-Newtonian fluids using multiple-relaxation-time lattice Boltzmann method

The magnetic field effect on natural convection flow of power-law (PL) non-Newtonian fluid has been studied numerically using the multiple-relaxation-time (MRT) lattice Boltzmann method (LBM). A two-dimensional rectangular enclosure with differentially heated at two vertical sides has been considered for the computational domain. Numerical simulations have been conducted for different pertinent parameters such as Hartmann number, [Formula: see text], Rayleigh number, [Formula: see text], PL indices, [Formula: see text]–1.4, Prandtl number, [Formula: see text], to study the flow physics and heat transfer phenomena inside the rectangular enclosure of aspect-ratio [Formula: see text]. Numerical results show that the heat transfer rate, quantified by the average Nusselt number, is attenuated with increasing the magnetic field, i.e. the Hartmann number (Ha). However, the average Nusselt number is increased by increasing the Rayleigh number, [Formula: see text] and decreasing the PL index, [Formula: see text]. Besides, the generation of entropy for non-Newtonian fluid flow under the magnetic field effect has been investigated in this study. Results show that in the absence of a magnetic field, [Formula: see text], fluid friction and heat transfer irreversibilities, the total entropy generation decreases and increases with increasing [Formula: see text] and [Formula: see text], respectively. In the presence of the magnetic field, [Formula: see text], the fluid friction irreversibility tends to decrease with increasing both the shear-thinning and shear thickening effect. It is noteworthy that strengthening the magnetic field leads to pulling down the total entropy generation and its corresponding components. All simulations have been performed on the Graphical Processing Unit (GPU) using NVIDIA CUDA and employing the High-Performance Computing (HPC) facility.