Entropy

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1 pages, 7 KiB

Open AccessEditorial

Special Issue on Entropy Generation in Thermal Systems and Processes

by Ibrahim Dincer

Entropy 2003, 5(5), 357; https://doi.org/10.3390/e5050357 - 31 Dec 2003

Cited by 1 | Viewed by 4815

Abstract

Thermodynamics is defined as the science of energy and entropy which are applicable to all fields of science and engineering.[...] Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

Research

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16 pages, 152 KiB

Open AccessArticle

The Effect of Thermal Radiation on Entropy Generation Due to Micro-Polar Fluid Flow Along a Wavy Surface

by Cha’o-Kuang Chen, Yue-Tzu Yang and Kuei-Hao Chang

Entropy 2011, 13(9), 1595-1610; https://doi.org/10.3390/e13091595 - 2 Sep 2011

Cited by 19 | Viewed by 7366

Abstract

In this study, the effect of thermal radiation on micro-polar fluid flow over a wavy surface is studied. The optically thick limit approximation for the radiation flux is assumed. Prandtl’s transposition theorem is used to stretch the ordinary coordinate system in certain directions. [...] Read more.

In this study, the effect of thermal radiation on micro-polar fluid flow over a wavy surface is studied. The optically thick limit approximation for the radiation flux is assumed. Prandtl’s transposition theorem is used to stretch the ordinary coordinate system in certain directions. The wavy surface can be transferred into a calculable plane coordinate system. The governing equations of micro-polar fluid along a wavy surface are derived from the complete Navier-Stokes equations. A simple transformation is proposed to transform the governing equations into boundary layer equations so they can be solved numerically by the cubic spline collocation method. A modified form for the entropy generation equation is derived. Effects of thermal radiation on the temperature and the vortex viscosity parameter and the effects of the wavy surface on the velocity are all included in the modified entropy generation equation. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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2 pages, 225 KiB

Open AccessArticle

RETRACTED: Effect of Heat Leak and Finite Thermal Capacity on the Optimal Configuration of a Two-Heat-Reservoir Heat Engine for Another Linear Heat Transfer Law

by Tong Zheng, Lingen Chen, Fengrui Sun and Chih Wu

Entropy 2003, 5(5), 519-530; https://doi.org/10.3390/e5050519 - 31 Dec 2003

Cited by 13 | Viewed by 6563 | Retraction

Abstract

Based on a model of a two-heat-reservoir heat engine with a finite high-temperature source and bypass heat leak, the optimal configuration of the cycle is found for the fixed cycle period with another linear heat transfer law . The finite thermal capacity source [...] Read more.

Based on a model of a two-heat-reservoir heat engine with a finite high-temperature source and bypass heat leak, the optimal configuration of the cycle is found for the fixed cycle period with another linear heat transfer law . The finite thermal capacity source without heat leak makes the configuration of the cycle to a class of generalized Carnot cycle. The configuration of the cycle with heat leak and finite thermal capacity source is different from others. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

13 pages, 321 KiB

Open AccessArticle

Entropy Generation During Fluid Flow Between Two Parallel Plates With Moving Bottom Plate

by Latife Berrin Erbay, Mehmet S. Ercan, Birsen Sülüs and M. Murat Yalçÿn

Entropy 2003, 5(5), 506-518; https://doi.org/10.3390/e5050506 - 31 Dec 2003

Cited by 52 | Viewed by 8475

Abstract

Two dimensional numerical analysis of entropy generation during transient convective heat transfer for laminar flow between two parallel plates has been investigated. The fluid is incompressible and Newtonian and the flow is the hydrodynamically and thermally developing. The plates are held at constant [...] Read more.

Two dimensional numerical analysis of entropy generation during transient convective heat transfer for laminar flow between two parallel plates has been investigated. The fluid is incompressible and Newtonian and the flow is the hydrodynamically and thermally developing. The plates are held at constant equal temperatures higher than that of the fluid. The bottom plate moves in either parallel or in inverse direction to the flow. The governing equations of the transient convective heat transfer are written in two-dimensional Cartesian coordinates and solved by the finite volume method with SIMPLE algorithm. The solutions are carried for Reynolds numbers of 10², 5x10² and 10³ and Prandtl number of 1. After the flow field and the temperature distributions are obtained, the entropy values and the sites initiating the entropy generation are investigated. The results have indicated that the number of the entropy generation has its highest value at the highest Reynolds and Br/Ω values, which is obtained at counter motion of the lower plate. The lowest average number of the entropy generation on the bottom plate is obtained in parallel motion. The corners of the channel plates at the entrance play the role of active sites where the generation of entropy is triggered. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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10 pages, 295 KiB

Open AccessArticle

An Analysis of The Entropy Generation in a Square Enclosure

by Latife Berrin Erbay, Zekeriya Altaç and Birsen Sülüs

Entropy 2003, 5(5), 496-505; https://doi.org/10.3390/e5050496 - 31 Dec 2003

Cited by 50 | Viewed by 8681

Abstract

The entropy generation during transient laminar natural convection in a square enclosure is numerically investigated. Two different cases are considered. The enclosure is heated either completely or partially from the left side wall and cooled from the opposite side wall. The bottom and [...] Read more.

The entropy generation during transient laminar natural convection in a square enclosure is numerically investigated. Two different cases are considered. The enclosure is heated either completely or partially from the left side wall and cooled from the opposite side wall. The bottom and the top of the enclosure are assumed as insulated. The Boussinesq approximation is used in the natural convection modelling. The solutions are obtained from quiescent conditions proceeded through the transient up to the steady-state. The calculations are made for the Prandtl numbers 0.01 and 1.0 and Rayleigh numbers between 10²-10⁸. The entropy generation and the active places triggering the entropy generation are obtained for each case after the flow and thermal characteristics are determined. It is found that the active sites in the completely heated case are at the left bottom corner of the heated wall and the right top corner of the cooled wall at the same magnitudes. In the case of partial heating, however, the active site is observed at the top corner of the heated section especially at lower Pr and Ra values. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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14 pages, 304 KiB

Open AccessArticle

Analytical Entropy Analysis of Recuperative Heat Exchangers

by Antun Galovic, Zdravko Virag and Marija Zivic

Entropy 2003, 5(5), 482-495; https://doi.org/10.3390/e5050482 - 31 Dec 2003

Cited by 8 | Viewed by 8457

Abstract

The analytical solutions for the temperature variation of two streams in parallel flow, counter flow and cross-flow heat exchangers and related entropy generation due to heat exchange between the streams are presented. The analysis of limiting cases for the relative entropy generation is [...] Read more.

The analytical solutions for the temperature variation of two streams in parallel flow, counter flow and cross-flow heat exchangers and related entropy generation due to heat exchange between the streams are presented. The analysis of limiting cases for the relative entropy generation is performed, and corresponding analytical expressions are given. The obtained results may be included in a more general procedure concerning optimal heat exchanger design. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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15 pages, 430 KiB

Open AccessArticle

Convective Heating of Solid Surface: Entropy Generation Due to Temperature Field and Thermal Displacement

by Yagoub Nassar Al-Nassar

Entropy 2003, 5(5), 467-481; https://doi.org/10.3390/e5050467 - 31 Dec 2003

Cited by 2 | Viewed by 7693

Abstract

Convective heating and cooling of the surfaces find application in process industry. During the heating or cooling cycle of the process, thermodynamic irreversibility which can be associated with the process parameters occurs. Moreover, thermodynamic irreversibility associated with the heating cycle can be quantified [...] Read more.

Convective heating and cooling of the surfaces find application in process industry. During the heating or cooling cycle of the process, thermodynamic irreversibility which can be associated with the process parameters occurs. Moreover, thermodynamic irreversibility associated with the heating cycle can be quantified through entropy analysis. In the present study, convective heating of the solid surface is considered. A mathematical formulation of the temperature rise and thermal stress development during the transient heating process is presented. Entropy generation due to temperature field and thermal displacement is also formulated. The simulation for temperature rise, thermal displacement, and entropy generation are carried out for steel substrate. It is found that thermal displacement does not exactly follow the temperature distribution inside the substrate material. The magnitude of entropy generation due to temperature field is considerably higher than that corresponding to the thermal displacement. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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16 pages, 198 KiB

Open AccessArticle

Statistical and Physical Analysis of the External Factors Perturbation on Solar Radiation Exergy

by Juan Carlos Moreno, Javier Cañada and José Vincente Boscà

Entropy 2003, 5(5), 452-466; https://doi.org/10.3390/e5050452 - 31 Dec 2003

Cited by 1 | Viewed by 7081

Abstract

The purpose of this paper is to analyze the external factor perturbations on solar radiation. Firstly, the influence on the photon distribution function in the space of frequencies is analyzed and, later, the modification generated in equations of internal energy, entropy, and radiation [...] Read more.

The purpose of this paper is to analyze the external factor perturbations on solar radiation. Firstly, the influence on the photon distribution function in the space of frequencies is analyzed and, later, the modification generated in equations of internal energy, entropy, and radiation is viewed in order to deduce an expression to calculate the spectral exergy of perturbed radiation. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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8 pages, 148 KiB

Open AccessArticle

Optimization of a Thermoacoustic Engine with a Complex Heat Transfer Exponent

by Feng Wu, Chih Wu, Fangzhong Guo, Qing Li and Lingen Chen

Entropy 2003, 5(5), 444-451; https://doi.org/10.3390/e5050444 - 31 Dec 2003

Cited by 23 | Viewed by 9858

Abstract

Heat transfer between a thermoacoustic engine and its surrounding heat reservoirs can be out of phase with oscillating working gas temperature. The paper presents a generalized heat transfer model using a complex heat transfer exponent. Both the real part and the imaginary part [...] Read more.

Heat transfer between a thermoacoustic engine and its surrounding heat reservoirs can be out of phase with oscillating working gas temperature. The paper presents a generalized heat transfer model using a complex heat transfer exponent. Both the real part and the imaginary part of the heat transfer exponent change the power versus efficiency relationship quantitatively. When the real part of the heat transfer exponent is fixed, the power output P decreases and the efficiency η increases along with increasing of the imaginary part. The Optimization zone on the performance of the thermoacoustic heat engine is obtained. The results obtained will be helpful for the further understanding and the selection of the optimal operating mode of the thermoacoustic heat engine. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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12 pages, 573 KiB

Open AccessArticle

Reduced Exergy Method for Heat-Electricity Cost Allocation in Combined Heat and Power Plants

by Xue-min Ye

Entropy 2003, 5(5), 432-443; https://doi.org/10.3390/e5050432 - 31 Dec 2003

Cited by 8 | Viewed by 8852

Abstract

Although the cost allocation method does not change the total benefits of CHP, the use of various cost allocation methods generally results in significant differences in costs allocated for CHP products. In order to overcome the inadequacy of existing cost allocating methods in [...] Read more.

Although the cost allocation method does not change the total benefits of CHP, the use of various cost allocation methods generally results in significant differences in costs allocated for CHP products. In order to overcome the inadequacy of existing cost allocating methods in theory and in practice, according to the different roles of anergy and exergy in heat supply process of CHP plant, the reduced exergy method for cost allocation is formulated by introducing the concepts of the available anergy and reduced exergy. The contribution of the available anergy is expressed with a user factor, which can reflect different utilization for different practical conditions. Some practical conditions for typical CHP units are computed and compared with existing methods. Calculations show that the cost allocation by using the reduced exergy model is more rational and practical than those by using existing models in terms of embodying the physical meaning. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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15 pages, 311 KiB

Open AccessArticle

Droplet Size Distribution in Sprays Based on Maximization of Entropy Generation

by Xianguo Li and Meishen Li

Entropy 2003, 5(5), 417-431; https://doi.org/10.3390/e5050417 - 31 Dec 2003

Cited by 16 | Viewed by 8566

Abstract

The maximum entropy principle (MEP), which has been popular in the modeling of droplet size and velocity distribution in sprays, is, strictly speaking, only applicable for isolated systems in thermodynamic equilibrium; whereas the spray formation processes are irreversible and non-isolated with interaction between [...] Read more.

The maximum entropy principle (MEP), which has been popular in the modeling of droplet size and velocity distribution in sprays, is, strictly speaking, only applicable for isolated systems in thermodynamic equilibrium; whereas the spray formation processes are irreversible and non-isolated with interaction between the atomizing liquid and its surrounding gas medium. In this study, a new model for the droplet size distribution has been developed based on the thermodynamically consistent concept - the maximization of entropy generation during the liquid atomization process. The model prediction compares favorably with the experimentally measured size distribution for droplets, near the liquid bulk breakup region, produced by an air-blast annular nozzle and a practical gas turbine nozzle. Therefore, the present model can be used to predict the initial droplet size distribution in sprays. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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13 pages, 444 KiB

Open AccessArticle

Entropy Generation in Laminar Fluid Flow through a Circular Pipe

by Ahmet Z. Sahin and Rached Ben-Mansour

Entropy 2003, 5(5), 404-416; https://doi.org/10.3390/e5050404 - 31 Dec 2003

Cited by 50 | Viewed by 10675

Abstract

A numerical solution to the entropy generation in a circular pipe is made. Radial and axial variations are considered. Navier-Stokes equations in cylindrical coordinates are used to solve the velocity and temperature fields. Uniform wall heat flux is considered as the thermal boundary [...] Read more.

A numerical solution to the entropy generation in a circular pipe is made. Radial and axial variations are considered. Navier-Stokes equations in cylindrical coordinates are used to solve the velocity and temperature fields. Uniform wall heat flux is considered as the thermal boundary condition. The distribution of the entropy generation rate is investigated throughout the volume of the fluid as it flows through the pipe. Engine oil is selected as the working fluid. In addition, water and Freon are used in a parametric study. The total entropy generation rate is calculated by integration over the various cross-sections as well as over the entire volume. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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13 pages, 582 KiB

Open AccessArticle

Entropy Analysis in Pipe Flow Subjected to External Heating

by Iyad Talal Al-Zaharnah

Entropy 2003, 5(5), 391-403; https://doi.org/10.3390/e5050391 - 31 Dec 2003

Cited by 5 | Viewed by 8747

Abstract

In the present study, heat transfer and entropy analysis for flow through a pipe system is considered. The Reynolds number and the pipe wall temperature effects on entropy distribution and total entropy generation in the pipe are investigated. Numerical scheme employing a control [...] Read more.

In the present study, heat transfer and entropy analysis for flow through a pipe system is considered. The Reynolds number and the pipe wall temperature effects on entropy distribution and total entropy generation in the pipe are investigated. Numerical scheme employing a control volume approach is introduced when solving the governing equations. Steel is selected as pipe material, while water is used as fluid. It is found that increasing pipe wall temperature and Reynolds number increases the entropy production rate, in which case, entropy generation due to heat transfer dominates over that corresponding to fluid friction. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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14 pages, 76 KiB

Open AccessArticle

Ecological Optimization and Parametric Study of an Irreversible Regenerative Modified Brayton Cycle with Isothermal Heat Addition

by Sudhir Kumar Tyagi, Subhash Chandra Kaushik and Vivek Tiwari

Entropy 2003, 5(5), 377-390; https://doi.org/10.3390/e5050377 - 31 Dec 2003

Cited by 32 | Viewed by 9423

Abstract

An ecological optimization along with a detailed parametric study of an irreversible regenerative Brayton heat engine with isothermal heat addition have been carried out with external as well as internal irreversibilities. The ecological function is defined as the power output minus the power [...] Read more.

An ecological optimization along with a detailed parametric study of an irreversible regenerative Brayton heat engine with isothermal heat addition have been carried out with external as well as internal irreversibilities. The ecological function is defined as the power output minus the power loss (irreversibility) which is ambient temperature times the entropy generation rate. The external irreversibility is due to finite temperature difference between the heat engine and the external reservoirs while the internal irreversibilities are due to nonisentropic compression and expansion processes in the compressor and the turbine respectively and the regenerative heat loss. The ecological function is found to be an increasing function of the isothermal-, sink- and regenerative-side effectiveness, isothermal-side inlet temperature, component efficiencies and sink-side temperature while it is found to be a decreasing function of the isobaric-side temperature and effectiveness and the working fluid heat capacitance rate. The effects of the isobaric-side effectiveness are found to be more than those of the other parameters and the effects of turbine efficiency are found to be more than those of the compressor efficiency on all the performance parameters of the cycle. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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11 pages, 137 KiB

Open AccessArticle

Vibrational Effect on Entropy Generation in a Square Porous Cavity

by Shohel Mahmud and Roydon Andrew Fraser

Entropy 2003, 5(5), 366-376; https://doi.org/10.3390/e5050366 - 31 Dec 2003

Cited by 18 | Viewed by 7417

Abstract

We investigate the nature of entropy generation for natural convection in a two-dimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used [...] Read more.

We investigate the nature of entropy generation for natural convection in a two-dimensional square section enclosure vibrating sinusoidally perpendicular to the applied temperature gradient in a zero-gravity field. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of average Nusselt number (Nu_av), entropy generation number (Ns_av), Bejan number (Be_av), and kinetic energy (KE_av). Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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8 pages, 377 KiB

Open AccessArticle

Free Convection and Irreversibility Analysis inside a Circular Porous Enclosure

by Shohel Mahmud and Roydon Andrew Fraser

Entropy 2003, 5(5), 358-365; https://doi.org/10.3390/e5050358 - 31 Dec 2003

Cited by 19 | Viewed by 6670

Abstract

We investigate the nature of heat transfer and entropy generation for natural convection in a two-dimensional circular section enclosure. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential [...] Read more.

We investigate the nature of heat transfer and entropy generation for natural convection in a two-dimensional circular section enclosure. The enclosure is assumed to fill with porous media. The Darcy momentum equation is used to model the porous media. The full governing differential equations are simplified with the Boussinesq approximation and solved by a finite volume method. Whereas the Prandtl number Pr is fixed to 1.0. Results are presented in terms of Nusselt number, entropy generation number, and Bejan number. Full article

(This article belongs to the Special Issue Entropy Generation in Thermal Systems and Processes)

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