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Entropy in Endoreversible Engines

The objective of this study was to to investigate the thermal efficiency and power production of typical models of endoreversible heat engines at the regime of minimum entropy generation rate. The study considers the Curzon-Ahlborn engine, the Novikov’s engine, and the Carnot vapor cycle. The operational regimes at maximum thermal efficiency, maximum power output and minimum entropy production rate are compared for each of these engines. The results reveal that in an endoreversible heat engine, a reduction in entropy production corresponds to an increase in thermal efficiency. The three criteria of minimum entropy production, the maximum thermal efficiency, and the maximum power may become equivalent at the condition of fixed heat input.

Entropy in Irreversible Engines


A thermodynamic analysis is presented by means of mathematical formulation to examine the performance of the most common types of heat engines including Otto, Diesel, and Brayton cycles, at the regime of minimum entropy generation. All engines are subject to internal and external irreversibilities. It is shown that minimum entropy production criterion neither correlates with maximum thermal efficiency design nor with maximum work output criterion. The results demonstrate that the production of entropy is not necessarily equivalent to the energy losses taking place in real devices.

Entropy & Chemical Equilibrium

A literature survey reveals significant inaccuracy of the prediction of equilibrium models. A thermodynamic analysis is presented to show that the equilibrium calculations rest on a critical assumption of reversible heat exchange between a reactive system and its surrounding. Indeed, a correct application of the energy conservation and entropy balance equation leads to a modified Gibbs function. Minimization of the modified Gibbs function happens to be identical to maximization of the total entropy generation. The actual chemical equilibrium is shown through a methane steam reforming, as an illustrative example, to be correctly predicted by kinetic modeling. The state of chemical equilibrium does not necessarily correspond to maximum entropy generation. Once a chemical equilibrium has been established, both the total entropy generation and the modified Gibbs function remain unaltered and independent of time.

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Entropy & Fuel Cells

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We apply the conservation of energy and entropy balance equations to derive expressions for the maximum work of hydrogen-oxygen, hydrogen-air and methane-air fuel cells. We show that the theoretical efficiency of a fuel cell may exceed that of a Carnot engine operating between the same low and high temperatures. Contrary to past studies in that the efficiency of an ideal hydrogen fuel cell is shown to decline with temperature, the maximum efficiency is observed to first decrease with reactants temperature, then remains unaltered and finally rises. The lowest value of the maximum efficiency is found to be 79.3%, 75.7%, and 82.1% for hydrogen-oxygen, hydrogen-air and methane-air fuel cells, respectively. By increasing the stoichiometric coefficient of air, the efficiencies of both hydrogen-air and methane-air fuel cells monotonically increase and they approach the 100% limit at a stoichiometric coefficient of 7.2 and 9.8, respectively. It is shown that a Carnot engine whose heat is supplied by an isothermal combustor proposed in some past studies is not a correct means for comparison of the ideal performance of fuel cells and heat engines.

Pyrolysis of Biomass Particle

An accurate formulation of energy conservation to model pyrolysis of a biomass particle needs to account for variations in the heat of reaction with temperature, usually neglected in most past studies. It is shown that by including this effect in a pyrolysis model with three parallel reactions yielding char, gas and tar, a wide range of experimental data can be accurately predicted. In particular, through comprehensive comparisons of the simulation results with various measurements, a consistent and single value of 25 kJ/kg is obtained for enthalpy of pyrolysis, which represents a lumped heat of volatiles and char formation at a reference temperature. It is found that the kinetic parameters of Chan et al. [W.C. Chan, M. Kelbon, B.B. Krieger, Fuel 64 (1985) 1505–1513] and Thurner and Mann [F. Thurner, U. Mann, Ind. Eng. Chem. Process Des. Dev. 20 (1981) 482–488] provide reasonable agreement between the model predictions and experiments compared to other reported kinetic constants. These comparisons also indicate that inclusion of tar cracking reactions to yield additional light gases does not give a better prediction of the process parameters. The presented thermo-kinetic model is capable of successfully predicting various experimental observations such as the internal temperature peak reported in some past studies. It is shown that the sensible heat released due to the conversion of virgin biomass to the reaction products is responsible for this phenomenon. Simulation results reveal that a temperature peak at an internal location of the particle may occur when the corresponding local temperature reaches the particle surface temperature while the local biomass conversion is not finalized yet.

Combustion of Biomass Particle

A detailed one-dimensional model for combustion of a single biomass particle is developed. It accounts for particle heating up, pyrolysis, char gasification and oxidation and gas phase reactions within and in the vicinity of the particle. The biomass pyrolysis is assumed to take place through three competing reactions yielding char, light gas and tar. The model is validated using different sets of experiments reported in the literature. Special emphasis is placed on examination of the effects of pyrolysis kinetic constants and gas phase reactions on the combustion process which have not been thoroughly discussed in previous works. It is shown that depending on the process condition and reactor temperature, correct selection of the pyrolysis kinetic data is a necessary step for simulation of biomass particle conversion. The computer program developed for the purpose of this study enables one to get a deeper insight into the biomass particle combustion process. Typical numerical results related to the combustion of 1 mm wood particle in air are illustrated


This study examined transport phenomena involving the reaction of cupric chloride (CuCl2) particles and superheated steam within a fluidized bed as part of a thermochemical hydrogen production plant. The study was carried out by performing hydrodynamics and mass transport analysis, which was necessary for analyzing the mass transport of the reaction in a fluidized bed. In the first part, the effects of superficial velocity, bed inventory, particle diameter and spherecity on bed height, average bubble diameter and bed voidage were investigated through a newly developed solution procedure. In the second step, the conversion of steam as a fluidizing gas and conversion of CuCl2 were numerically investigated using a new non-catalytic gas-solid reaction model, proposed in past literature but here updated for the purposes of the present study. The results were illustrated considering two cases of kinetics models for the consumption of particles: Volumetric Model (VM) and Shrinking Core Model (SCM). Consistent results in terms of the conversion of reactants versus superficial velocity, bed inventory and bed temperature were obtained by developing new solution algorithms based on each of the above kinetic models. The methodology presented in this study was useful in the next phases of the research when building an experimental apparatus and estimating the optimal values of reactor parameters.


This study examined a comparative assessment in terms of CO2 emissions from a hydrogen passenger train in Ontario, Canada, particularly comparing four specific propulsion technologies: (1) conventional diesel internal combustion engine (ICE), (2) electrified train, (3) hydrogen ICE, and (4) hydrogen PEM fuel cell (PEMFC) train. For the electrified train, greenhouse gases from electricity generation by natural gas and coal-burning power plants are taken into consideration. Several hydrogen production methods were also considered in this analysis, i.e., (1) steam methane reforming (SMR), (2) thermochemical copper-chlorine (Cu-Cl) cycle supplied partly by waste heat from a nuclear plant, (3) renewable energies (solar and wind power) and (4) a combined renewable energy and copper-chlorine cycle. The results show that a PEMFC power train fuelled by hydrogen produced from combined wind energy and a copper-chlorine plant is the most environmentally friendly method, with CO2 emissions of about 9% of a conventional diesel train or electrified train that uses a coal-burning power plant to generate electricity. Hydrogen produced with a thermochemical cycle is a promising alternative to further reduce the greenhouse gas emissions. By replacing a conventional diesel train with hydrogen ICE or PEMFC trains fuelled by Cu-Cl based-hydrogen, the annual CO2 emissions are reduced by 2,260 and 3318 tonnes, respectively. A comparison with different types of automobile commuting scenarios to carry an equivalent number of people as a train was also conducted. On an average basis, only an electric car using renewable energy-based electricity that carries more than three people may be competitive with hydrogen trains.


In this project, the performance of a high-temperature solid oxide fuel cell combined with a conventional recuperative gas turbine (GT-SOFC) plant was examined. Individual thermodyanmic models were developed for each component. The overall system performance was then analyzed by employing the thermodyanmic model developed to evaluate the thermal efficiency of the plant. It was found that increasing the turbine inlet temperature results in decreasing the thermal efficiency of the cycle, whereas it improves the total specific power output. A comparison between the GT-SOFC plant and a traditional GT cycle, based on identical operating conditions, was also made. The superior performance of a GT-SOFC, in terms of thermal efficiency and environmental impact (lower CO2emissions), over a traditional GT cycle was evident. It has about 27.8% higher efficiency than a traditional GT plant. In this case, the thermal efficiency of the integrated cycle becomes as high as 60.55% at the optimum compression ratio.


Through development of the fundamental equations of Film Theory, condensation of steam in the presence of air in a TEMA ‘E’ type shell and one-path tube condenser was modeled. The interaction between heat and mass transfer and hydrodynamics in the shell-side was taken into consideration. A comparison of the predictions of the model with experimental data revealed excellent accuracy of the formulation. The consistency of the method was validated by generating the profiles of the temperature drop and pressure drop of the gas flowing through the baffles, at various air leakages. Additionally, the effects of air leakage and upstream cooling water temperature were investigated to observe how they influence the total condensation rate, shell-side gas temperature and pressure drops. The results show that the total condensation rate decreases 5% and 20.5% at an air leakage of 1% and 5%, respectively, compared to a case with pure vapor. Also, increasing the inlet cooling water temperature from 46.50C to 48.50C leads to 16.2% reduction in the total condensation rate, i.e., 8.1% per 10C. However, this ratio is higher at high temperatures. For example, as the cooling water temperature rises from 500C to 510C under identical process conditions, the total condensation rate decreases 11.7% (per 10C).

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