Application of EoEP principle with variable heat transfer coefficient in minimizing entropy production in heat exchangers

A more realistic application of the entropy minimization principle EoEP is presented. This principle dictates uniform local entropy generations along the heat exchanger in order to minimize the total entropy generation rate due only to heat transfer. For a certain heat duty and area of an existing exchanger, this is done by changing the temperatures of one fluid while the temperatures of the other fluid are held constant. Since the heat duty is fixed, the change in the temperatures of the fluid after the change, however, may sometimes cause a drastic change in its flow rate. This may cause considerable changes in the overall heat transfer coefficient (U) and, consequently, in the entropy generation rate. Depending on the choice of the fluid for changing, the new entropy generation rates may be higher or lower than those based on constant U as is the case in papers recently published. So, the classical application of the EoEP principle needs to be modified to achieve more realistic entropy generation rates. In this study, the principle of EoEP with variable U is applied to some cases of heat exchange, and a simple method is presented as a criterion for the proper choice of the fluid to be changed.     

Gibbs function continuation for the stable computation of chemical equilibrium

We consider the computation of the chemical equilibrium state of an ideal gas mixture of given elemental composition, with and without general linear constraints on the species present. While computer programs to solve these problems have been available for more than 30 years, it is found that they are not always successful in determining the chemical equilibrium state in the presence of constraints. We present here the new method of Gibbs function continuation, which is guaranteed to determine the chemical equilibrium state for all well-posed constrained and unconstrained problems.     

Entropy generation at the onset of natural convection

The entropy generation due to heat transfer and friction has been determined in transient state for laminar natural convection by solving numerically the mass, momentum and energy balance equations, using a control volume finite-element method. The variations of the total entropy generation as function of time for Rayleigh number and irreversibility distribution ratio set at 10³?Ra?10⁵ and 10⁻⁴???10⁻¹ were investigated. The evolution of the maximum of entropy generation with the Rayleigh number is studied. The effect of the irreversibility distribution ratio on the maximum entropy generation and the entropy generation in steady state are analyzed. The irreversibility maps for Rayleigh number set at 10³?Ra?10⁵ and irreversibility distribution ratio ?=10⁻⁴ are plotted.     

Entropy generation of turbulent double-diffusive natural convection in a rectangle cavity

Turbulent double-diffusive natural convection is of fundamental interest and practical importance. In the present work we investigate systematically the effects of thermal Rayleigh number (Ra), ratio of buoyancy forces (N) and aspect ratio (A) on entropy generation of turbulent double-diffusive natural convection in a rectangle cavity. Several conclusions are obtained: (1) The total entropy generation number (S_total) increases with Ra, and the relative total entropy generation rates are nearly insensitive to Ra when Ra ≤ 10⁹; (2) Since N > 1, S_total increases quickly and linearly with N and the relative total entropy generation rate due to diffusive irreversibility becomes the dominant irreversibility; and (3) S_total increases nearly linearly with A. The relative total entropy generation rate due to diffusive and thermal irreversibilities both are monotonic decreasing functions against A while that due to viscous irreversibility is a monotonic increasing function with A. More important, through the present work we observe a new phenomenon named as “spatial self-copy” in such convectional flow. The “spatial self-copy” phenomenon implies that large-scale regular patterns may emerge through small-scale irregular and stochastic distributions. But it is still an open question required further investigation to reveal the physical meanings hidden behind it.     

Numerical investigation on developing laminar forced convection and entropy generation in a wavy channel

The present paper investigates the developing laminar forced convection and entropy generation in a wavy channel with numerical methods. The effects of aspect ratio (W/H) and Reynolds number (Re) on entropy generation are the major concerns. The studied cases cover W/H = 1, 2 and 4, and Re range from 100 to 400. The flow features, including secondary flow motion and temperature distribution as well as the detailed distributions of local entropy generation due to frictional and heat transfer irreversibilities are reported. Through the evaluations of entropy generation in the whole flow field, the case of W/H = 1 is found to have the minimal entropy generation among all of the analyzed cases. Besides, the higher Re is found to be beneficial for obtaining the lower values of the total resultant entropy generation in the flow field. Accordingly, the case with W/H = 1 and higher Re is suggested to be used under the current flow conditions, so that the irreversibility resulted from the developing laminar forced convection in the wavy channel could be least and the best exergy utilization could be achieved.     

Entropy generation in impinging flow confined by planar opposing jets

In this paper, entropy generation in impinging flow confined by planar opposing jets is investigated systematically for the first time. Different from previous works on entropy generation for practical flows, in this study the lattice Boltzmann method, which is more suitable for massive parallel computing, is used to solve the governing equations for flow field as well as the entropy generation equation, instead of traditional numerical methods. The effects of the Reynolds number 10 ≤ Re ≤ 500 and the distance ratio between opposing jets 2/5 ≤ W/L ≤ 4/5 on entropy generation are revealed. It is found that the local entropy generation number is more sensitive to the variation of W/L than Re when Re > 50. The total entropy generation number increases exponentially with Re but decreases as a power function of W/L. In addition, the entropy generation will receive significant influence from the damping traveling pressure wave during the transient state and the maximum emerges when the gas ejected from the top and bottom jets begins meeting and impinging.     

Entropy generation due to natural convection in discretely heated porous square cavities

Optimization of industrial processes for higher energy efficiency may be effectively carried out based on the thermodynamic approach of entropy generation minimization (EGM). This approach provides the key insights on how the available energy (exergy) is being destroyed during the process and the ways to minimize its destruction. In this study, EGM approach is implemented for the analysis of optimal thermal mixing and temperature uniformity due to natural convection in square cavities filled with porous medium for the material processing applications. Effect of the permeability of the porous medium and the role of distributed heating in enhancing the thermal mixing, temperature uniformity and minimization of entropy generation is analyzed. It is found that at lower Darcy number (Da), the thermal mixing is low and the heat transfer irreversibility dominates the total entropy generation. In contrast, thermal mixing is improved due to enhanced convection at higher Da. Friction irreversibility is found to dominate the total entropy generation for higher Prandtl number (Pr) fluids at higher Da, whereas the heat transfer irreversibility dominates the total entropy generation for lower Pr fluids. Based on EGM analysis, it is established that larger thermal mixing at high Darcy number may not be always recommended as the total entropy production is quite large at high Darcy number. Overall, it is found that the distributed heating methodology with multiple heat sources may be an efficient strategy for the optimal thermal processing of materials.     

Entropy flow and generation in radiative transfer between surfaces

Entropy of radiation has been used to derive the laws of blackbody radiation and determine the maximum efficiency of solar energy conversion. Along with the advancement in thermophotovoltaic technologies and nanoscale heat radiation, there is an urgent need to determine the entropy flow and generation in radiative transfer between nonideal surfaces when multiple reflections are significant. This paper investigates entropy flow and generation when incoherent multiple reflections are included, without considering the effects of interference and photon tunneling. The concept of partial equilibrium is applied to interpret the monochromatic radiation temperature of thermal radiation, T_λ(λ, Ω), which is dependent on both wavelength λ and direction Ω. The entropy flux and generation can thus be evaluated for nonideal surfaces. It is shown that several approximate expressions found in the literature can result in significant errors in entropy analysis even for diffuse-gray surfaces. The present study advances the thermodynamics of nonequilibrium thermal radiation and will have a significant impact on the future development of thermophotovoltaic and other radiative energy conversion devices.     

Entropy generation in a hollow cylinder with temperature dependent thermal conductivity and internal heat generation with convective–radiative surface cooling

This article investigates entropy generation in an asymmetrically cooled hollow cylinder with temperature dependent thermal conductivity and internal heat generation. The inside surface of the cylinder is cooled by convection on its inside surface while the outside surface experiences simultaneous convective–radiative cooling. The thermal conductivity of the cylinder as well as the internal heat generation within the cylinder are linear functions of temperature, introducing two nonlinearities in the one-dimensional steady state heat conduction equation. A third nonlinearity arises due to radiative heat loss from the outside surface of the cylinder. The nonlinear system is solved analytically using the differential transformation method (DTM) to obtain the temperature distribution which is then used to compute local and total entropy generation rates in the cylinder. The accuracy of DTM is verified by comparing its predictions with the analytical solution for the case of constant thermal conductivity and constant internal heat generation. The local and total entropy generations depend on six dimensionless parameters: heat generation parameter Q, thermal conductivity parameter β, conduction–convection parameters Nc₁ and Nc₂, conduction–radiation parameter Nr, convection sink temperature δ and radiation sink temperature η.     

Effect of aspect ratio on entropy generation in a rectangular cavity with differentially heated vertical walls

In the present study, entropy generation in rectangular cavities with the same area but different aspect ratios is numerically investigated. The vertical walls of the cavities are at different constant temperatures while the horizontal walls are adiabatic. Heat transfer between vertical walls occurs by laminar natural convection. Based on the obtained dimensionless velocity and temperature values, the distributions of local entropy generation due to heat transfer and fluid friction, the local Bejan number and local entropy generation number are determined and related maps are plotted. The variation of the total entropy generation and average Bejan number for the whole cavity volume at different aspect ratios for different values of the Rayleigh number and irreversibility distribution ratio are also evaluated. It is found that for a cavity with high value of Rayleigh number (i.e., Ra = 10⁵), the total entropy generation due to fluid friction and total entropy generation number increase with increasing aspect ratio, attain a maximum and then decrease. The present results are compared with reported solutions and excellent agreement is observed. The study is performed for 10² < Ra < 10⁵, 10^− 4 < ? < 10^− 2, and Pr = 0.7.     

Entropy generation from hydrogen production of catalytic partial oxidation of methane with excess enthalpy recovery

Catalytic partial oxidation of methane (CPOM) is an important route for producing hydrogen and it is featured by autothermal reaction. To recognize the reaction characteristics of CPOM, H₂ production and entropy generation from CPOM in Swiss-roll reactors are studied numerically. The considered parameters affecting the performance of CPOM include the excess enthalpy recovery, gas hourly space velocity (GHSV), number of turns and atomic O/C ratio. The impact of chemical reactions, heat transfer and friction on entropy generation is also analyzed. The results indicate that preheating reactants through waste heat recovery as well as increasing GHSV or number of turns is conducive to enhancing H₂ yield, whereas the maximum H₂ yield develops at O/C = 1.2. A higher H₂ yield is always accompanied by a higher value of entropy generation, and chemical reactions are the main source of entropy generation, especially from steam methane reforming. In contrast, viscous dissipation almost plays no part on entropy generation, compared to heat transfer and chemical reactions. From the analysis of entropy generation, detailed mechanisms of H₂ production from CPOM can be figured out.     

Analysis of entropy generation using nanofluid flow through the circular microchannel and minichannel heat sink

In this paper, different types of entropy generations in the circular shaped microchannel and minichannel are discussed analytically using different types of nanoparticles and base fluids. In this analysis, Copper (Cu), alumina (Al₂O₃) as the nanoparticle and H₂O, ethylene glycol (EG) as the base fluids were used. The volume fractions of the nanoparticles were varied from 2% to 6%. In this paper, the irreversibility or entropy generation analysis as the function of entropy generation ratio, thermal entropy generation rate and fluid friction entropy generation rate for these types of nanofluids in turbulent flow condition have been analyzed using available correlations. Cu–H₂O nanofluid showed the highest decreasing entropy generation rate ratio (36%) compared to these nanofluids flow through the microchannel at 6 vol.%. The higher thermal conductivity of H₂O causes to generate much lower thermal entropy generation rate compared to the EG base fluid. The fluid friction entropy generation rate decreases fruitfully by the increasing of volume fraction of the nanoparticles. Cu–H₂O and Cu–EG nanofluid gave the maximum decreasing rates of the fluid friction entropy generation rate are 38% and 35% respectively at 6% volume fraction of the nanoparticles. Smaller diameter showed less entropy generation in case of all nanofluids.     

Comparative second-law analysis of internal combustion engine operation for methane,methanol, and dodecane fuels

A method for both combustion irreversibility and working medium availability computations in a high-speed, naturally-aspirated, four-stroke, internal combustion engine cylinder is presented. The results of the second-law analysis of engine operation with n-dodecane (n-C₁₂H₂₆) fuel are compared with the results of a similar analysis for cases where a light, gaseous (CH₄) and an oxygenated (CH₃OH) fuel is used. The rate of entropy production during combustion is analytically calculated as a function of the fuel reaction rate with the combined use of first- and second-law arguments and a chemical equilibrium hypothesis. It is shown theoretically that the decomposition of lighter molecules leads to less entropy generation compared to heavier fuels. This is verified computationally for the particular fuels and the corresponding decrease in combustion irreversibility is calculated. Special reference is made to the effect of the lower mixing entropy of the exhaust gas of an oxygenated fuel (CH₃OH) as a contribution to the discussion of the advantages and disadvantages of the use of such fuels.     

Analysis of entropy generation for distributed heating in processing of materials by thermal convection

Analysis of entropy generation has been carried out for square cavities with distributed heated sources filled with various materials involving wide range of Pr(=0.015, 0.7, 10, 1000) during the conduction and convection regime within Ra(=10³ ? 10⁵). Entropy generation terms involving thermal and velocity gradients are evaluated accurately based on elemental basis set via Galerkin finite element method. Local entropy maps are analyzed in detail for various cases and the dominance of thermal and frictional irreversibilities is studied via average Bejan number. The heat transfer irreversibility is found to dominate during conduction regime while the fluid friction irreversibility dominates the entropy generation in the convection regime, except for the low Pr fluid based on the heating configuration of the cavity. Further, the variation of total entropy generation has been observed to be similar for different heating configurations for higher Pr fluids (=10, 1000) whereas, the configuration of cavity has been found to have little effect on total entropy generation for fluids with Pr = 0.7 during both conduction and convection regimes. Thermal mixing and degree of temperature uniformity due to distributed heating in various cases are also reported and optimum cases for processing of various fluids are presented based on minimum entropy generation.     

Entropy generation analysis in a uniformly heated microchannel heat sink

Present investigation analyzes the issue of entropy generation in a uniformly heated microchannel heat sink (MCHS). Analytical approach used to solve forced convection problem across MCHS, is a porous medium model based on extended Darcy equation for fluid flow and two-equation model for heat transfer. Simultaneously, closed form velocity solution in a rectangular channel is employed to capture z-directional viscous effect diffusion and its pronounced effect on entropy generation through fluid flow. Subsequently, governing equations are cast into dimensionless form and solved analytically. Second law analysis of problem is then conducted on the basis of obtained velocity and temperature fields and expressions for local and average entropy generation rate are derived in dimensionless form. Average entropy generation rate is then utilized as a criterion for assessing the system performance. Finally, the effect of influential parameters such as, channel aspect ratio (α_S), group parameter (Br/Ω), thermal conductivity ratio (C) and porosity (ε) on thermal and total entropy generation is investigated. In order to examine the accuracy of the analysis, the results of thermal evaluation are compared to one of the previous investigations conducted for thermal optimization of MCHS.     

Entropy generation minimization in turbulent mixed convection flows

This paper reports the results of a numerical investigation of turbulent mixed convection from a symmetrically heated vertical channel, bathed by a steady upward flow of cold air. The computations have been performed using FLUENT 6.2 by employing the k–ε model for turbulence with enhanced wall treatment. The entropy generation rates due to (i) heat transfer across a finite temperature difference and (ii) irreversibility due to fluid friction have been calculated as post-processed quantities with the computed velocity and temperature profiles. Optimal inlet velocities at which the total entropy generation rate reaches a minimum value are found to exist, for every set of heat flux and aspect ratio. Further, this optimum velocity turns out to be independent of the aspect ratio and increases linearly with the heat flux. Simple and easy to use correlations for the optimum Reynolds number and the dimensionless average wall temperatures corresponding to the optima are developed. Plots of total entropy generation rate against the velocity clearly demonstrate that near the optimum conditions, buoyancy does not have a significant role to play in deciding the optimum. For the range of parameters considered in this study, it is seen that for optimum conditions, the ratio of the entropy generation due to fluid friction to total entropy generation rate, known in literature as the Bejan number, varies within a narrow band (0.14–0.22).     

Entropy generation in Casson nanofluid flow over a surface with nonlinear thermal radiation and binary chemical reaction

We introduce a model that precisely accounts the flow of fluid of Casson nanofluid over a stretched surface with activation energy and analyze entropy generation. The model is an attempt to investigate heat transfer and entropy generation in the laminar boundary layer near a stagnation point. The modified Arrhenius function for activation energy is used. Here, the flow of the fluid is subjected to nonlinear thermal radiation, viscous disipation, binary chemical reaction, and external magnetic field. The coupled nonlinear system is further validated using the spectral lineralization method. The method is found to be accurate and convergent. The results show that the Reynolds number and Casson parameter have a significant effect in entropy generation.     

Effect of entropy change of lithium intercalation in cathodes and anodes on Li-ion battery thermal management

The entropy changes (ΔS) in various cathode and anode materials, as well as in complete Li-ion batteries, were measured using an electrochemical thermodynamic measurement system (ETMS). LiCoO₂ has a much larger entropy change than electrodes based on LiNi_xCo_yMn_zO₂ and LiFePO₄, while lithium titanate based anodes have lower entropy change compared to graphite anodes. The reversible heat generation rate was found to be a significant portion of the total heat generation rate. The appropriate combinations of cathode and anode were investigated to minimize reversible heat generation rate across the 0-100% state of charge (SOC) range. In addition to screening for battery electrode materials with low reversible heat, the techniques described in this paper can be a useful engineering tool for battery thermal management in stationary and transportation applications.     

Entropy generation and thermodynamic optimization of fully developed laminar convection in a helical coil

The present paper analyses the entropy generation of the fully developed laminar convection in a helical coil with constant wall heat flux and presents the optimal design based on the minimum entropy generation principal. The important design parameters, including Reynolds number (Re), coil-to-tube radius ratio (δ) and nondimensional coil pitch (λ) are varied to investigate their influences on the entropy generation. The results presented in this paper cover Re range of 100–10,000, δ and λ range from 0.01 to 0.3. Compared with Re and δ, the coil pitch λ is found to have minor influence on the entropy generation. For a demonstrated case, the minimum entropy generation occurs in the range bounded by Re from 2271 to 4277 and δ from 0.17 to 0.3, within which the irreversibility of the system is lowest and the system performance would be optimum. The details show that there is an optimal Re for a helical coil with a fixed δ; meanwhile for a helical coil flow with a specified Re, the smaller δ should be selected when the Re is larger than 5000, and the larger δ should be selected when the Re is less than 5000. These results provide worthwhile information for heat exchanger designers to find the optimal helical coil design from the viewpoint of the thermodynamic second law.