http://www.mdpi.com/journal/entropy/special_issues/thermal_systems_processes/ http://www.mdpi.com/1099-4300/13/9/1595/ 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. http://www.mdpi.com/1099-4300/13/9/1595/ Fri, 02 Sep 2011 00:00:00 CEST Entropy 2011-09-02 13 9 Article 1595 1610 1099-4300 The Effect of Thermal Radiation on Entropy Generation Due to Micro-Polar Fluid Flow Along a Wavy Surface 2011-09-02 doi: 10.3390/e13091595 Cha’o-Kuang Chen Yue-Tzu Yang Kuei-Hao Chang http://www.mdpi.com/1099-4300/5/5/519/ 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. http://www.mdpi.com/1099-4300/5/5/519/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 519 530 1099-4300 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 2003-12-31 doi: 10.3390/e5050519 Tong Zheng Lingen Chen Fengrui Sun Chih Wu http://www.mdpi.com/1099-4300/5/5/506/ 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. http://www.mdpi.com/1099-4300/5/5/506/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 506 518 1099-4300 Entropy Generation During Fluid Flow Between Two Parallel Plates With Moving Bottom Plate 2003-12-31 doi: 10.3390/e5050506 Latife Berrin Erbay Mehmet S. Ercan Birsen Sülüs M. Murat Yalçÿn http://www.mdpi.com/1099-4300/5/5/496/ 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. http://www.mdpi.com/1099-4300/5/5/496/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 496 505 1099-4300 An Analysis of The Entropy Generation in a Square Enclosure 2003-12-31 doi: 10.3390/e5050496 Latife Berrin Erbay Zekeriya Altaç Birsen Sülüs http://www.mdpi.com/1099-4300/5/5/482/ 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. http://www.mdpi.com/1099-4300/5/5/482/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 482 495 1099-4300 Analytical Entropy Analysis of Recuperative Heat Exchangers 2003-12-31 doi: 10.3390/e5050482 Antun Galovic Zdravko Virag Marija Zivic http://www.mdpi.com/1099-4300/5/5/467/ 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. http://www.mdpi.com/1099-4300/5/5/467/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 467 481 1099-4300 Convective Heating of Solid Surface: Entropy Generation Due to Temperature Field and Thermal Displacement 2003-12-31 doi: 10.3390/e5050467 Yagoub Nassar Al-Nassar http://www.mdpi.com/1099-4300/5/5/452/ 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. http://www.mdpi.com/1099-4300/5/5/452/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 452 466 1099-4300 Statistical and Physical Analysis of the External Factors Perturbation on Solar Radiation Exergy 2003-12-31 doi: 10.3390/e5050452 Juan Carlos Moreno Javier Cañada José Vincente Boscà http://www.mdpi.com/1099-4300/5/5/444/ 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. http://www.mdpi.com/1099-4300/5/5/444/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 444 451 1099-4300 Optimization of a Thermoacoustic Engine with a Complex Heat Transfer Exponent 2003-12-31 doi: 10.3390/e5050444 Feng Wu Chih Wu Fangzhong Guo Qing Li Lingen Chen http://www.mdpi.com/1099-4300/5/5/432/ 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. http://www.mdpi.com/1099-4300/5/5/432/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 432 443 1099-4300 Reduced Exergy Method for Heat-Electricity Cost Allocation in Combined Heat and Power Plants 2003-12-31 doi: 10.3390/e5050432 Xue-min Ye http://www.mdpi.com/1099-4300/5/5/417/ 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. http://www.mdpi.com/1099-4300/5/5/417/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 417 431 1099-4300 Droplet Size Distribution in Sprays Based on Maximization of Entropy Generation 2003-12-31 doi: 10.3390/e5050417 Xianguo Li Meishen Li http://www.mdpi.com/1099-4300/5/5/404/ 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. http://www.mdpi.com/1099-4300/5/5/404/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 404 416 1099-4300 Entropy Generation in Laminar Fluid Flow through a Circular Pipe 2003-12-31 doi: 10.3390/e5050404 Ahmet Z. Sahin Rached Ben-Mansour http://www.mdpi.com/1099-4300/5/5/391/ 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. http://www.mdpi.com/1099-4300/5/5/391/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 391 403 1099-4300 Entropy Analysis in Pipe Flow Subjected to External Heating 2003-12-31 doi: 10.3390/e5050391 Iyad Talal Al-Zaharnah http://www.mdpi.com/1099-4300/5/5/377/ 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. http://www.mdpi.com/1099-4300/5/5/377/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 377 390 1099-4300 Ecological Optimization and Parametric Study of an Irreversible Regenerative Modified Brayton Cycle with Isothermal Heat Addition 2003-12-31 doi: 10.3390/e5050377 Sudhir Kumar Tyagi Subhash Chandra Kaushik Vivek Tiwari http://www.mdpi.com/1099-4300/5/5/366/ 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 (Nuav), entropy generation number (Nsav), Bejan number (Beav), and kinetic energy (KEav). http://www.mdpi.com/1099-4300/5/5/366/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 366 376 1099-4300 Vibrational Effect on Entropy Generation in a Square Porous Cavity 2003-12-31 doi: 10.3390/e5050366 Shohel Mahmud Roydon Andrew Fraser http://www.mdpi.com/1099-4300/5/5/358/ 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. http://www.mdpi.com/1099-4300/5/5/358/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Article 358 365 1099-4300 Free Convection and Irreversibility Analysis inside a Circular Porous Enclosure 2003-12-31 doi: 10.3390/e5050358 Shohel Mahmud Roydon Andrew Fraser http://www.mdpi.com/1099-4300/5/5/357/ n/a http://www.mdpi.com/1099-4300/5/5/357/ Wed, 31 Dec 2003 00:00:00 CET Entropy 2003-12-31 5 5 Editorial 357 357 1099-4300 Special Issue on Entropy Generation in Thermal Systems and Processes 2003-12-31 doi: 10.3390/e5050357 Ibrahim Dincer