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TERMOTEHNICA 1/2013 5

THERMODYNAMICS WITH FINITE SPEED (TFS) I. The main moments in the development of TFS. Aplication of the direct method to Otto and Diesel

irreversible cycles

Prof. Stoian PETRESCU1, Prof. Monica COSTEA1, Assoc. Prof. Nicolae BORIARU1, Prof. Michel FEIDT2, Prof. Alexandru DOBROVICESCU1, Prof. George STĂNESCU1,

Prof. Tudor FLOREA3, Assoc. Prof. Camelia PETRE1, Cristea LEONTIEV3, PhD., Emil BANCHES3, PhD.

1„POLITEHNICA“ UNIVERSITY – Bucharest, 2LABORATOIRE D'ÉNERGÉTIQUE ET DE MÉCANIQUE THÉORIQUE ET APPLIQUÉE, Vandœuvre, France,

3„MIRCEA CEL BĂTRÂN” NAVAL ACADEMY, Constanţa

Abstract. The Direct Method from Thermodynamics]1 with Finite Speed (TFS) studies the irreversibilities (internal and external) produced during operation of real thermal machines, through progressive analysis and direct integration of the First Law of Thermodynamics, combined with the Second Law of Thermodynamics for processes with Finite Speed, for each process of the cycle. Thus are obtained analytical expressions for the Efficiency (for Power cycles), respectively COP (for Refrigeration Machines and Heat Pumps) and Power (produced, respectively consumed) function of the speed of the processes and of the functional and geometrical parameters of the machine. This paper presents the Main Moments in the Development of Thermodynamics with Finite Speed and Direct Method “invented” in its framework. Recent Progresses in Application of the Direct Method to Otto and Diesel cycles are presented. Keywords: Thermodynamics with Finite Speed, Direct Method, Finite Speed Processes, Irreversible Efficiency, Irreversible Power, Irreversible COP, Stirling Machines, Otto and Diesel cycles Optimization

1. INTRODUCTION

The Origin, Development, Validation, Recent Applications, and Perspectives of a “new branch” of Engineering Irreversible Thermodynamics (EIT), which L. Stoicescu and S. Petrescu called it, from the “very beginning”, namely: Thermodyna-mics with Finite Speed (TFS), in their seminal papers [1-18], in the years 1964-1974, when “everything started”…in this (amazing, extremely challenging and “almost impossible” to understand) field of research, generated and developed by the Romanian School of Thermodynamics, in 50 years (1961-2011), are the Objectives of the following 3 papers: TFS: I, II, III. (In The Proceedings of This Conference NACOT 2013.)

The 3 papers under the general Title of TFS (present paper I and the next two: II and III) presents the Main Moments in the Development of Thermodynamics with Finite Speed (TFS) and the Direct Method (DM) “invented” in its framework:

I – Early Developments and Fundamental Con-cepts (1964-1974); Application of TFS for Otto, Diesel, Semi-Diesel and Otto-Stirling; Extensions of

TFS in the domains of Electrochemical Devices and Solar Energy, (1974-1992); Fuel Cells in Molten Salts; Esential Developments of TFS which con-ducted eventually to its Validation for Stirling Machines (1992-2006).

II – Development of the Scheme of Computation of Performances (Efficiency and Power) for Stirling Machines;Validation of TFS and Direct Method for 12 Stirling Engines and 16 Regimes of functioning.

III – Recent Progresses in TFS (2006-1013): New Validations for Stiling and Solar Stirling Engines. Treatment of Refrigeration Machines cycles with Vapor in the framework of TFS with Direct Method. Perspectives of Development of TFS and “Unification” with Thermodynamics in Finite Time (FTT)…toward a Thermodynamics with Finite Dimensions. (TFD)

2. EARLY DEVELOPMENTS AND FUNDAMENTAL CONCEPTS (1964-1974)

The Dvelopement of TFS started in the years 1964-1965 with 5 fundamental papers published in

Stoian PETRESCU et al.

6 TERMOTEHNICA 1/2013

IPB Bulletin, by L. Stoiescu and S. Petrescu [1-5] which conducted to the First PhD Thesis in this domain wrriten by S. Petrescu-1969 [8], and several papers that followed [6, 7, 9, 10], which were esential for Promotion and Extension of „The new Theory on irrevesible processes with finite speed”, in the period 1965-1972, which eventualy became what is called today Thermodynamics with Finite Speed.

2.1. What are treating those first 5 papers (and S. Petrescu PhD Thesis [8] and what has been acheieved in them? [1-5]

1o. „The First Law for Processes with finite speed” [1] where we presented for the first time in the history of Thermodynamics the next equation, which becams the fundamental basis of the whole Thermodynamics with Finite Speed:

Vc

awPQU imirr d1δd ,

(1)

Vc

awPW imirr d1δ ,

(1a)

where: a = (3k)0.5; w = piston speed; c = average molecular speed = (3RT)0.5;

k = Cp/Cv.

2o. „Thermodynamic Processes with Constant Finite Speed” [2] where we did find the equations of all 5 irevesible processes, prezented in the Table 1.

2

1221

111 kk VTVT

(2)

(See also in Table 1, the other two equations of adiabatic irreversible Processes with finite Speed and the significance of α1 and α2).

3o. „Thermodynamic Processes with Constant Finite Speed” [3] where we discovered that in the case of such processes we have to introduce a correction factor which amplify the term aw/c with 1.24 in order to take into account that in real machines, the piston has a quasi-sinusoidal motion.

Table 1

The equations of all 5 irevesible processes [2, 100]

TFS – APLICATION OF THE DIRECT METHOD TO OTTO AND DIESEL IRREVERSIBLE CYCLES


4o. „Thermodnamic Cycles with finite Speed” [4] where we treated for the first time in the history of TFS, an irreversible Otto cycle with finite Sped and determined using the equations from Table 1, the irrevesible Efficiency of such cycle:

ηOtto,w = 1 – (1/ k–1). (Corection which takes into account the speed) (3)

For all irreversible cycles studied after that moment (1965) until now (2013) we have tried to get a similar expression, namely :

η,irev = 1 – ( Clasical reversibile expression) × × (Correction which takes into account the influence of finite speed generating irreverisibilities in the cycle)

5o. „The Experimental Verification of The New Expression of the First Law for Thermodynamic Processes with Finite Speed” where we did verify the equation (1) which becomes the fundamental equation of the whole Thermodynamics with Finite Speed.

After many years, in 1991, in the book [55] : Petrescu, "Lectures on New Sources of Energy", Helsinki University of Technology, Otaniemi, Finland, p.320, Lectures in October 1991, and in 1992, in the paper [56]: Petrescu, S., Stanescu, G., Iordache, R., Dobrovicescu, A. The First Law of Thermodynamics for Closed Systems, Considering the Irreversibilities Generated by the Friction Piston-Cylinder, the Throttling of the Working Medium and Finite Speed of the Mechanical Interaction, Proc. of ECOS'92, Zaragoza, Spain, ASME, 33-39, 1992, and in 1994 in the paper [61]: Petrescu, S., Harman, C. The Connection between the First and Second Law of Thermodynamics for Processes with Finite Speed. A Direct Method for Approaching and Optimization of Irreversible Processes, J. Heat Transfer Society of Japan, Vol.33, No.128, 1994, we extended this equation for real irrevessible processes in Thermal Machines taking into accaunt two more causes of irrevversibilities, namely: piston-cylinder friction and Throttling processes in the valves.

In the next chapter we show as an example what we [86] did using this equations regarding the computation (entirely analitical) of Efficiency and Power for Otto and Diesel Cycles, taking into account in additon to the term aw/c also, the

presssure losses generated by friction ∆Pf and throttling ∆Pthr.

3. APPLICATION OF THERMODYNAMICS WITH FINITE SPEED FOR INTERNAL COMBUSTION ENGINES [86]

The influence of several irreversibility factors on the Direct Cycle Efficiency and Power Output, was studied in the framework of the Irreversible Thermodynamics with Finite Speed, using the Direct Method:

- The Finite Speed (w) of the Piston (FSIT) during compression and expansion [1 - 10].

- The Mechanical Friction between the piston and the cylinder, generating piston friction pressure losses (PFPL) all around the cycle [141], [142].

- The Fluid Friction due to Throttling of the Gases during intake and exhaust, generating throttling pressure losses (THPL) [141], [142].

One of the studies was conducted onto an irre-versible Otto cycle [87]. In fig.1, one can notice that the reversible approach leads to a linear increase of the power output with the piston speed, while in the irreversible approach the power curve is a parabola, its maximum corresponding to the optimum speed.

Taking into account step by step, different irreversibilities, the maximum power output is decreasing, as well as the corresponding optimum speed (from 145 kW at about 150 m/s, to about 20 kW at 20 m/s, fig. 1).

Fig. 1. Otto Cycle Efficiency and Power versus Piston Speed [87].



0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

0 20 40 60 80 100 120 140 160Speed [m/s]

Eff

icie

ncy

[-]

0

50

100

150

200

250

300

350

400

450

500

Pow

er [

kW

]

Efficiency-Speed influenceEfficiency-Speed&Friction influenceEfficiency-All influencesPower-Speed influencePower-Speed&Friction influencePower-All influences

Fig. 2. Diesel Cycle Efficiency and Power versus Piston Speed [88].

Fig. 3. Comparison between Semi – Diesel reversible (w = 0) and irreversible (w > 0) cycle [90, 91].

A similar study conducted on the adiabatic Diesel cycle with constant pressure combustion [88] showed (fig. 2) in this case also, that while for the reversible adiabatic cycle the power curve is linear, for the irreversible cycle it gets parabolic in shape.

Another important observed issue was that the difference between the reversible and the irreversible performances (efficiency and power) significantly increases with the increase of the piston speed.

Similar results were obtained in the case of Semi – Diesel cycle (constant volume heating first, then constant pressure), fig.3, taking into account the same initial pressure, the same compression ratio and same combustion heat for both reversible and irreversible cycles [90, 91].

Considering the throttling and friction irre-versibilities, the Semi-Diesel cycle efficiency with finite speed, is given by [90]:

3423

2

2

1

11

1

1

1,, 11

113

1

11

TTkTTmc

VPP

k

TR

wa

T

T

v

thrf

k

irk

ir

kir

kthrfir

(4)



while the Power output in all reversible and irre-versible cases (for a 4 cylinders - 4 strokes Diesel engine) has been determined using relation:

z

wQP

z

wQP

z

wn

QW

nWP

inir

inir

r

incycle

rcycleir

120

304

30

6024

(5)

The influence of the piston speed w, com-pression ratio, ε, the pressure increase ratio, λ (at constant volume) and the cut-off ratio, α, has been studied, too.

The diagram form fig. 4 shows the influence of the finite speed (between 0 and 50 m/s) on the Efficiency of the Diesel engine. While for the reversible cycle the efficiency remains constant (at about 65 %), the irreversible cycle efficiency is decreasing with the piston speed obviously and it may even vanish, when the maximum affordable mean piston speed is reached (around 42 m/s, with all irreversibilities considered).

The power output diagram from figure 5 shows a linear increase with the mean piston speed in the case of the reversible cycle, while in the irrever-sible approach, the Power-Piston speed curve is a parabola. By consequence, the same power can be reached at two different piston speeds (with lower efficiency at the higher piston speed).

Taking into account progressively different kinds of irreversibility, the maximum value of the power is decreasing, as well as the value of the corresponding optimum speed.

The same diagram (fig. 5) also reveals the existence of the maximum affordable speed where the Power output drops to zero, in good correspondence with that observed in the Efficiency diagram (42 m/s with all irreversibilities considered, see fig. 4).

Figure 6 shows that the Efficiency and the Power output grow with the compression ratio ε, as well as the maximum affordable speed, the maximum power and its corresponding optimum mean piston speed.

Figure 7 shows that the growth of the pressure increase ratio, λ from 1 to 1.5 has a significant contribution to the growth of the engine Efficiency and the Power output, too.

Fig. 4. Efficiency of reversible and irreversible Diesel cycles atε = 20, λ = 1.5 and α = 2 [91].

Fig. 5. Power of reversible and irreversible Diesel cycles at ε = 20, λ = 1.5 and α = 2 [91].

Fig. 6. Efficiency and Power output of reversible and irreversible Semi-Diesel cycles

at α = 2, λ = 1.5 and ε = 18 - 20 [91].



Fig. 7. Efficiency and Power output of reversible and irreversible Semi-Diesel cycles at α = 2, ε = 20 and λ = 1 - 2.5 [91].

Fig. 8. Efficiency and Power output of reversible and irreversible Diesel cycles at ε = 20, λ = 1.5 and α = 1.8 - 2.2 [91].

Fig. 9. Efficiency Power output of Diesel cycle as function of piston speed for different work fluids [91].

The influence of the cut-off ratio, α on the

performances of the Diesel engine is presented in the diagrams from figure 8, where their growth is obvious. It is to be noticed, however, that α and λ are in competition, as one's growth implies the diminution of the other (to keep constant the total heat input).

The last part of the study focused on the Power and Efficiency of the Diesel cycle for various work fluids as air, H2, He and CO2.

On the graphs from figure 9 it is possible to remark similar performances for Hydrogen and Air. Helium yields the maximum efficiency, but the material requirements do not suggest it as a



solution yet. However, based on this study, Helium seems to be a very good working fluid for an external combustion cycle.

An interesting conclusion is also that the Hydrogen's irreversible properties are closer to the reversible properties than those of the other three work fluids.

By emphasizing the most significant work losses, this kind of analysis gives to the designer the tools to efficiently improve the engine performances.

It opens the way towards sensitivity studies revealing the influence of different parameters (temperatures, speed, compression ratio, dimensions etc.) on the engine performances and the optimization of the engine cycle with respect to these parameters.

The internal source of entropy can also be determined and correlated with the performance parameters of the cycle.

Based on experimental results, J.B. Heywood presented in [142], an integrated mathematical relationship expressing the total friction mean effective pressure loss (mtf.mep) as dependent on the mean piston speed (wp) and the crankshaft rotational speed (N) has been deduced:

21. [kPa] 48 0.4

100p

Nmtf mep C w

(6)

Heywood considered the losses due to the mechanical friction as linearly dependent on wp (or N), while frictional losses in pumping fluids (cylinder gas and cooling air, cooling water and lubricating oil) are taken as proportional to wp

2 (or N2). The compression-expansion process with finite

speed is expected to add, also, a significant con-

tribution in these pressure drops. FST expresses these supplementary losses as proportional to wp

2, too [100].

For the throttling intake Pressure Losses of the working fluid in the air filter, manifolds and valves, considering a stationary and isentropic flow the following relation has been deduced [100]:

2. [ ] 0.076ud i pP kPa w (7)

Comparing with the experimentally obtained relation [100]:

2[kPa] 0.4 pfP w (8)

we get:

. [kPa]/ 0.076/ 2/ 0.4 [ ] 0.095 [kPa]ud a f fP P kPa P

(9)

For the Exhaust Pressure Losses the following relation was deduced [100]:

2. [kPa] 0.083ud e pP w (10)

that is, using (8):

. [kPa]/ 0.083 / 2 / 0.4 [kPa]

0.1 [kPa]

ud e f

f

P P

P

(11)

The deduced equations showed [100] that the Pressure Rates of the intake process (χu.d.i=ΔPu.d/Pu) and exhaust process (χu.d.e = ΔPu.d / Pu) are function of ‘geometrical factors’ ‘fluid characteristic factors’ and of the squared speed of the piston (wp

2). This work can be seen as a way of finding a

correlation between the empiric parameters and the phenomenological assessment of the intake and exhaust process.

Fig. 10. Schematic fluid flow through the orifice of the valve.

Au Av Ad

wu wv wd

p

Pu

Pd

ΔPu.d=χu.d Pu ΔPu.d’=χ’u.d Pu’

Pu' Av’= Av/Cdv

Bdv’=Ad/Av’=Cdv Bdv

Bdv=Ad/Av



Fig.11. Fluid flow through Diesel intake premises [100].

In these theoretical developments for modelling the throttling in the valves, a stationary flow was assumed and only the average piston speed was

used. At high piston speeds, these assumptions may not be realistic, and the analysis needs to be improved in correlation with new experimental

Fig. 12. Fluid flow through the Diesel exhausts valve [100].

wp

5b 5a5 4 3a 3b

wse

Cylinder Crankcase

Pck

Aem Aev

Pa

Vs

ΔPexha

+(δca)

ΔPc

+(δck) 5 ap p;

ΔPp.

Pa

P

V2 V3

V

V

Ap

Pc

wp

3’

P

wge

Pa

Exhaust manifold

ΔPcΔPc

fired cycle

motored & TFS adiabatic cycle

Muffler

1a

Pa

Pa

wp

1b 2 3 3a 3b

wiv

Cyilinder (3) Crankcase (ck) Intake manifold (2)

Pck

Aim Aiv VsΔPa.im

+(δci)

ΔPim.ci

+(δck)

2 ap p; ΔPck.ci.

Pa

P

V2 V3

V

V

Ap

Pc

wci=wp

3’

P

wim

TC BCΔPim.ci

Diesel fired cycle

motored & TFS adiabatic cycle

Air cleaner (1)



data, in order to emphasise, for instance, cylinder gas (cg) effects.

At this moment, this type of research is only at the beginning and it should be further developed in order to get a final Validation of all the relations, obtained using the Thermodynamics with Finite Speed and the Direct Method.

4. THE EXTENTION OF TFS TO ELECTROCHEMICAL DEVICES (1970-1994): FUEL CELLS, ELECTROLYSERS AND BATTERIES [18-50]

With the occasion of a cooperation with the Physical Chemistry Department from IPB, many papers where published in researches dedicated to the extension of TFS in the period 1970-1990 [18-50, 57, 58 ].

Here the collaboration with Prof. Solomon Sternberg, the adviser of PhD Thesis of Valeria Petrescu [18] was essential, conducting eventually to an extremely important paper where the compa-rison between Stirling Machines and Electrochemical devices using TFS is achieved [57, 58 ].

5. DEVELOPMENT OF TFS AFTER 1990 - 2006 [44-83]

Essential for the Development of TFS and “invention and application of the Direct Method”, in this period were 6 PhD Thesis and papers resulting from these [44-83].

1o The beginning of the Direct Method was achieved in G. Stanescu PhD Thesis [60] and in the resulting papers from this researches [53, 56-59, 61, 115-140]. In his Thesis [60] G. Stanescu studied more profoundly, more systematically and with a detailed understanding of the Mechanisms of Generating Internal Irrevesibilities in Thermal Machines and the bases of first experimental vali-dation of the Direct method has been achieved.

In order to Optimize the Thermal Machines Design and functioning by minimizing losses due to various mechanisms of irreversibility genera-tion, George Stanescu PhD Thesis presents in 1994 [60] very important contributions to the “invention and initial development” of the Direct Method (in its “initial stages”) to study irreversible pro-cesses into closed systems. This work and papers resulting from it [53, 56-59, 61, 115-140] have the following original contributions to these problems:

– Generated a Nonlinear Model to study the irreversible adiabatic processes taking into account the working fluid viscosity and the gas mass inertia;

– The coefficient that indicates the weight of losses generated by irreversibility associated to the internal gas friction and to the gas mass inertia is evaluated based on theoretical assump-tions;

– Analytical formulas are established for calculating the pressure variation due to the working fluid viscosity during Finite Speed adiabatic processes;

– Development of a new method for optimizing the volume's configuration where a viscous fluid evolves adiabatically and irreversibly;

– The coefficient that indicates the weight of losses generated by the irreversibility associated to the gas internal throttling into a closed thermo-dynamic system is theoretically set and then calibrated against the own experimental results and from other sources (the study approaches systems with one or two moving walls);

– An experimental device has been built and operated to experimentally calibrate the theo-retical model;

– The integral form for the relationship between the thermal properties is established for irreversible adiabatic processes with Finite Speed when taking into account the working fluid's specific heat dependence with temperature;

– The integral form for the relationship between the thermal properties is established for irreversible adiabatic processes when taking into account the working fluid viscosity and the gas mass inertia;

– The integral form for the relationship between the thermal properties is established for irreversible adiabatic processes with Finite Speed when taking into account the working fluid viscosity and the gas mass inertia;

– The “initial” Optimization of the Otto, Brayton, Stirling and Carnot cycles has been performed based on the "Direct Method" approach highlighting for each case the existence of optimal operating regimes;

– Based on the nonlinear modeling of irreversible processes it is performed the study of thermodynamic pendulums (oscillating systems);

– The property of “isochronism” has been proven for the small oscillations of thermodynamic pendulums;

– A Method to study the "series" coupling and "parallel" coupling of gas springs has been developed;

– A new mechanism of irreversibility genera-tion by dephasating the thermal and mechanical



interactions of a thermodynamic system has been approached;

– A general method for modeling nonlinear irreversible processes has been broadly defined.

2o In M. Costea PhD Thesis [66] and papers which follows this have been acheved the First Validation for Solar Stirling Motors, using the Direct Method from TFS.

3o In T.Florea PhD Thesis [80] has been achieved the most spectacular Validation of the Direct Method, for 12 Stiling engines and 16 regimes of functioning.

4o In C. Petre PhD Thesis [84] has been achieved the Validation of the Direct Method for 4 Solar Stirling Engines, and was developed a new concept called by us SEHE = Solar Energy.Electricity (produced in Stirling engine coupled with Electrical Generator)-Hydrogen (produced in Electroliser and stored)Electricity [93]. This new sitem of Solar Power Plants with storage and cogenera-tion were further developen in recent researches.

6. MAIN DEVELOPMENTS AND ACHIEVEMENTS OF THERMODYNA-MICS WITH FINITE SPEED AND THE DIRECT METHOD AFTER 2006 [83-100]

In 2006 S. Petrescu, after 12 years spent in USA as a Visiting Professor at Duke Universsity (1992-1993) and Bucknell University (1993-1998 and 2001-2006) he came back to Romania and, (despite of his retirement in 2005) obtaining the position of Consultant Professor (and after February 2012- Emerit Professor) at Politehnica University Bucharest, in the same Department of Technical Thermodynamics, Thermal Machines and Refrigeration Machines, (where he worked for 35 years: 1961-1992 and 1998-2002), he continued his research activity with his former coworkers and new ones (master and graduate students).

As a result of these researches his team has obtain new achievements in the Developement of Thermodynamics with Finite Sped and the Direct Method, [83-100]. Some of these achievements are presented in the following papers [TFS II and III] in Proceeding of NACOT-2013.

The achievements of our team [100] after Validation of the Direct Method from TFS obtaind in M. Costea, T. Florea, and C. Petre Thesis have got a very important support and comtribution from Prof. M. Feidt from Henri Poincare University, Nancy, and also from Prof.

L. Grosu and Prof. P. Rochelle from University Paris 10, France.

7. REFERENCES

[1] Stoicescu, L., Petrescu, S. The First Law of Thermodynamics for Processes with Finite Speed, in Closed Systems, Bulletin I.P.B., Bucharest, Romania, Vol. XXVI, No. 5, pp. 87-108, 1964.

[2] Stoicescu, L., Petrescu, S. Thermodynamic Processes Developing with Constant Finite Speed, Bull. I.P.B.Vol. XXVI, No. 6, pp. 79-119, 1964.

[3] Stoicescu, L., Petrescu, S. Thermodynamic Processes with Variable Finite Speed, Buletin I.P.B., Bucharest, Vol. XXVII, No. 1, pp. 65-96, 1965.

[4] Stoicescu, L., Petrescu, S. Thermodynamic Cycles with Finite Speed, Buletin I.P.B., Bucharest, Romania, Vol. XXVII, No. 2, pp. 82-95, 1965.

[5] Stoicescu, L., Petrescu, S. The Experimental Verification of The New Expression of the First Law for Thermodynamic Processes with Finite Speed, Bull. I.P.B., Bucharest, Vol. XXVII, No. 2, pp. 97-106, 1965.

[6] Petrescu, S., An Expression for Work in Processes with Finite Speed based on Linear Irreversible Thermo-dynamics, Studii si Cercetari de Energetica si Electrot., Acad. Romana, Tom.19, No.2, pp. 249-254, 1969.

[7] Petrescu, S. An Expression for Work in Processes with Finite Speed based on Linear Irreversible Thermo-dynamics, Cercetări de Energetică şi Electrotehncă, Acad. Roamana, Tom.19, No.2, pp. 249-254, 1969.

[8] Petrescu, S. (Adviser: L. Stoicescu), Contribution to the study of thermodynamically non-equilibrium inter-actions and processes in thermal machines, Ph.D. Thesis, I.P.B., Bucharest, Romania, 1969.

[9] Petrescu, S. An Elementary Deduction of Lorentz-Einstein Transformations Relations, R. Fizica si Chimie Seria A, Vol. VIII, Nr. 11, pp. 424-430, 1971.

[10] Petrescu, S. Kinetically Consideration Regarding the Pressure on a Movable Piston, Studii şi Cercetări de Energetică şi Electrotehnică, Tom 21, No.1, pp. 93-107, 1971.

[11] Paul, M. Uber die Abhangigkeit der Entropie-vermehrung quasiadiabatiche Arbaitsprozesse von der Temperatur und Dehnungsgeschwindigkeit, Ann. D. Phys. 5, 29, S.179, 1937.

[12] Petrescu, V., Petrescu, S. A Treatment of the Con-centration Overpotential Using the Thermodynamics of Irreversible Processes, Revue Roumaine de Chimie, Romanian Academy, 16, 9, pp. 1291-1296, 1971.

[13] Petrescu, S., Petrescu, V. Cu privire la locul si importanţa conceptului de interactiune în tratarea Termodinamicii, R. Fizică şi Chimie, S. A, Vol. 1X, Nr. 12, pp. 468, Dec. 1972.

[14] Petrescu, V., Petrescu, S. Conceptul de Polarizare, Revista de Fizică şi Chimie, Seria A, Vol. 1X, Nr. 7, pp. 241-248, Iulie 1972.

[15] Petrescu, S., Sternberg, S., Petrescu, V. The Galvanostatic Study of the Electrochemical Adsorption Process on the Chlorine-Active Carbon Electrode in Molten Salts, II. - Remanent Potential, Rev. Roum. de Chimie, Tome 18, Nr. 10, pp. 1715-1729, Oct. 1973.

[16] Petrescu, S. Study of the Gas - Gas Interaction with Finite Velocity for Flow Processes, Studii şi Cercetări de Energetică şi Electrotehnică, Tomul 23, No.2, pp. 299-312, 1973.



[17] Petrescu, S. Experimental Study of the Gas - Piston Interaction with Finite Speed in the Case of an Open System, St. si Cerc. de Mec. Aplicata, T 31, No.5, pp. 1081-1086, 1974.

[18] Petrescu, V. PhD Thesis (Adviser: S. Sternberg), Procese de electrod si fenomene de transport la interfata Clor-Carbune-Sare topita, (Electrode Processes and Transport Phenomenon at the interface of Chlorine-Carbon Electrode-Molten Salt), I.P.B. 1974.

[19] Sternberg, S., Petrescu, S., Petrescu, V. The Galvanostatic Study of the Electrochemical Adsorption Process on the Chlorine-Active Carbon Electrode in Molten Salts, III. - Anodic Polarization (Charging) Equation, R. Roum. de Chimie, T. 19, Nr. 6, pp. 955-965, 1974.

[20] Petrescu, V., Petrescu, S. Solubiliatea Clorului in halogenuri topite, Revista de Chimie, 26, Nr. 4, pp. 289-293, 1975.

[21] Petrescu, S., Petrescu, V., Luncescu, M., Tanase, D. Determinarea curentului electric de difuziune in porii carbunelui activ. Revista de Chimie, 26, Nr. 9, pp. 737-739, 1975.

[22] Petrescu, V. Petrescu, S. Procesul de descarcare a clorului in saruri topite. I, Aspecte teoretice, Revista de Chimie, 26, Nr. 10, pp. 814-817, 1975.

[23] Petrescu, S., Sternberg, S., Petrescu, V. Galvanostatic Study of the Electrochemical Adsorption Process on a Chlorine-Activated Carbon Electrode in Molten Salts. IV - Catholic Polarization Curve Equation (Discharge), Rev. Roum. de Chimie, 21, 6, pp. 813-823. 1976.

[24] Petrescu, S., Sternberg, S., Galasiu, I., Petrescu, V. Application du Modele du Pore Partiellement Rempli Dans le Processus d'Adsorption Electrochimique Sur Les Electrodes Halogen - Carbon Actif Dans Les Sels Fondus, R. Roum. de Chim.., 21, 4, pp. 517-529. 1976.

[25] Petrescu, V., Petrescu, S. Procesul de descarcare a clorului in saruri topite. II. Aspecte Experimentale, Revista de Chimie, 27, Nr. 1, pp. 15-19, 1976.

[26] Petrescu, V., Petrescu, S. Difuziunea clorului gasos in cloruri topite, Revista de Chimie, 27, Nr. 4, pp. 296-299, 1976.

[27] Petrescu, S., Sternberg, S., Petrescu, V., Brusalis, T. Influenta presiunii de presare a pastilei de carbine activ asupra capacitatii de adsorbtie, Revista de Chimie, 27, Nr. 6, pp. 489-490, 1976.

[28] Petrescu, S., Petrescu, V., Sternberg, S., Stefanescu, D. Studiu comparativ privind adsorbtia clorului pe electrod de carbine activ si semiactiv in amesecul topit AgCl-KCl la 40 oC, A 5-a Conf. Rep. de Chimie Fizica, Generala si Aplicata, 1- 4 Septembrie 1976.

[29] Petrescu, S., Petrescu, V., Sternberg, S. Studiu comparativ privind adsorbtia clorului pe electrodul de carbune activ si semiactiv in amesteul de saruri topite de AgCl-KCl, la 400 o C, R. Chim, 28, Nr. 2, pp. 136-139, 1977.

[30] Petrescu, S., Petrescu, V., Galasiu, I. Curentul de difuziune in electrodul halogen-carbune activ in halogenuri topite, Revista de Chimie, 29, Nr. 8, pp. 735-738, 1978.

[31] Sternberg, S., Petrescu, V., Petrescu, S. Primary Electrochemical Cell Cu/Li with molten Salt Mixtures Using as Oxidant CuCl or CuCl2, Patent de Invention OSIM 68529, Romania. 02.28.1978.

[32] Sternberg, S., Petrescu, V., Visan, T., Petrescu, S. Secondary Electrochemical Cell Li/CuCl2/C with Molten Salts, Patent of Invention OSIM 68604, Romania. 08. 15. 1978.

[33] Petrescu, V., Petrescu, S. O ecuatie a curentului de difuziune in electrodul halogen-carbune active in halogenuri topite, R. de Chimie, 30, Nr. 11, pp. 1098-1100, Nov. 1979.

[34] Petrescu, S., Petrescu, V. O formula universala pentru cuantificarea spectrului de masa al particulelor elementare si a rezonantelor, R. de Chimie, 31, Nr. 10, pp. 935-946, 1980.

[35] Danescu, A., Bucurenciu, S., Petrescu, S., , Utilization of Solar Energy, E.T., 1980.

[36] Petrescu, S., Petrescu, V., Galasiu, I., Brusalis, T. The Equation of Chatodic Polarization in Fused Salts of Halogen - Active Carbon Electrode Applied to Bromine and Iodine, Rev. Roum. de Chimie, Romanian Academy, 28, 5, pp. 451-456, 1983.

[37] Petrescu, S., Petrescu, V. Principiile Termodinamicii. Evolutie, Fundamentari, Aplicatii, Ed. Tehnica, Bucuresti, Romania, pp. 294, 1983.

[38] Sternberg, S., Petrescu, S., Petrescu, V., Visan, T. Primary and Secondary Batteries Li/Cu2+ with Eutectic Mixture LIC1-KCI, Proceedings of the 5th Conference for Chemistry of Molten Salts. Kiev, Science Ukrainian Academy. Inst. for General and Anorganic Chemistry, 8-14 October, 1984.

[39] Sternberg, S., Petrescu, S., Visan, T., Petrescu, V., Cotarta, A., Cristea, P., Tuduce, R. Pila electrochimica primara sau secundara Li/Pb in amestecuri de saruri topite folosind ca oxidant PbCl2, Invention Patent, OSIM. Nr. 91085/ 30. 07. 1986.

[40] Sternberg, S., Petrescu, V., Petrescu, S., Visan, T. Baterie primara Li/Cu cu cloruri topite, Revista de Chimie, 37, Nr. 9, pp. 776-779, 1986.

[41] Petrescu, V., Petrescu, S. Experimental Method for deter-mination of the Stored Energy in the form of Latent Heat of Melting, Revista Energetica, 35, Nr.10, pp. 447-451, 1987.

[42] Petrescu, S., Petrescu, V. Modele si Metode in Termodinamica. Corelatii cu Legea Conservarii si Transformarii Energiei, E.T., pp. 268 pagini, 1988.

[43] Petrescu, S., Brusalis, T., Iordache, R., Costea, M., Petrescu, V., Varzaru, V. Receptor de radiatie solara concentrate cu stocaj termic in topituri, A 5-a Consfa-tuire: Valorificarea Resurselor Energetice Refolosibile si a Surselor Neconventionale, Eforie, 11-12 Mai 1989.

[44] Petrescu, S., Costea, M. Comparison Between the Brayton Cycle Using Piston Machines and Gas Turbine Cycle with Heating at Constant Volume from the Point of View of Being Used in Solar Energetics, Revista Energetica, 38, 5, pp. 223-228, 1990.

[45] Petrescu, V., Petrescu, S., et al. Electrochemical Sources with Molten Chloride and Nitrates, 3-rd International Congress of the International Union of Pure and Applied Chemistry, Sect. III Electrochemistry and Electro analysis, 17 - 22 Aug., Budapest, Hungary, 1990.

[46] Petrescu, V., Petrescu, S. A Small Heat Exchanger (Calorimeter) and a Method for Research of Thermal Energy Storage Materials, Baltic Heat Transfer Congress, Goteborg, Sweden, 24-28 August, 1991.

[47] Visan, T., Petrescu, V., Cotarta, A., Petrescu, S. High-Temperature Batteries: Li/CuCl2/C ; Li/PbCl2/Pb ; Al/PbCl2/Pb, Proceedings of The 3-rd International Symposium on Molten Salt Chemistry and Technology, July 15-20, Paris, France, 1991.

[48] Petrescu, V., Petrescu, S. Calorimetric estimations of thermal properties of some molten materials for thermal energy storage, Revista de Chimie., 43, nr. 3-4, 1991.

[49] Petrescu, S., Brusalis, T., Iordache, R., Petrescu, V., Varzaru, V. Concentrated Solar Radiation Receiver with Thermal Energy Storage in NaNO3, for Solar Stirling Engine, in: THERMASTOCK' 91, Proceedings of 5-th International Conference on Thermal Energy Storage, Scheveningen, Netherlands, pp. 8.8-1 to 8.8-10, May 13-16, 1991.



[50] Petrescu, V., Petrescu, S., Cotarta, A., Visan, T. Calorimetric Method for Determination of Some Thermodynamical Properties Necessary for Design and Achievement of Thermal Energy Storage Systems (TESS) Using Molten Materials, THERMASTOCK'91, Proceedings of the 5-th International Conference on Thermal Energy Storage, Scheveningen, Netherlands, pp. 7.6-1 to 7.6-8, May 13-16, 1991.

[51] Petrescu, S., Costea, M., et al. Numerical Method for Optimization of the Brayton Cycle, Proceedings of SIAC Symposium, Bucharest, Nov. 1991.

[52] Petrescu, S., Stanescu, G., Asupra unei metode de determinare a parametrilor caracteristici optimi ai ciclului Brayton tinind cont de viteza de desfasurare a proceselor termodinamice. Prima Conferinta Nationala de Termotehnica, 24-25 Mai 1991, Vol. 1. ICEMENERG, Bucuresti, pp. 72-77, 1992.

[53] Petrescu, S., Costea, M. Optimization of the Brayton Cycle with Finite Speed. First National Conf. of Engineering Thermod., Bucharest 24-25, May 1991, ICEMENERG, 1992.

[54] Petrescu, "Lectures on New Sources of Energy", Helsinki University of Technology, Otaniemi, Finland, p.320, Lectures in October 1991.

[55] Petrescu, S., Stanescu, G., Iordache, R., Dobrovicescu, A. The First Law of Thermodynamics for Closed Systems, Considering the Irreversibilities Generated by the Friction Piston-Cylinder, the Throttling of the Working Medium and Finite Speed of the Mechanical Interaction, Proc. of ECOS'92, Zaragoza, Spain, ASME, 33-39, 1992.

[56] Petrescu, S., Stanescu, G. The Direct Method for studding the irreversible processes undergoing with finite speed in closed systems, Termotehnica, No.1, E. T., 1993.

[57] Petrescu, S., Stanescu, G., Petrescu, V., Costea, M. A Direct Method for the Optimization of Irreversible Cycles using a New Expression for the First Law of Thermodynamics for Processes with Finite Speed, 1st Int. Congress on Energy ITEC'93, Marrakesh, Morocco, 650-653, 1993.

[58] Petrescu, S., Petrescu, V., Stanescu, G., Costea, M., A Comparison between Optimization of Thermal Machines and Fuel Cells based on New Expression of the First Law of Thermodynamics for Processes with Finite Speed, 1st Conf. on Energy ITEC' 93, Marrakesh, Morocco, 650-653, 1993.

[59] Stanescu, G. (Adviser: S. Petrescu), The study of the mechanism of irreversibility generation in order to improve the performances of thermal machines and devices, Ph. D. Thesis, U.P.B., Bucharest, 1993.

[60] Petrescu, S., Stanescu, G., Costea, M. The Study of the Optimization of the Carnot cycle which develops with Finite Speed, Proc. of the Inter. Conf. ENSEC' 93, Cracow, Ed. by J. Szargut et al. 269-277, 1993.

[61] Petrescu, S., Harman, C. The Connection between the First and Second Law of Thermodynamics for Processes with Finite Speed. A Direct Method for Approaching and Optimization of Irreversible Processes, J. Heat Transfer Society of Japan, Vol.33, No.128, 1994.

[62] Petrescu, S., Harman, C., Bejan, A. The Carnot Cycle with External and Internal Irreversibility, Proc. of Florence World Energy Research Symposium, Energy for The 21st Century: Conversion, Utilization and Environmental Quality, Firenze, Italy, 1994.

[63] Costea, M., Petrescu S., Danescu R.,Thermal and Dimensional Optimization of a Solar Stirling Engine Cavity Type Receiver, Proc. FLOWERS'94, E. Padova, Italy, pp. 1075. 1994

[64] Petrescu, S., Harman, C., Petrescu, V. Stirling Cycle Optimization Including the Effects of Finite Speed Operation, ECOS' 96, Stockholm, Sweden, Ed. P. Alvfors ,167-173, 1996.

[65] Petrescu, S., Zaiser, J., Petrescu, V. Lectures on Advanced Energy Conversion, Bucknell University, Lewisburg, PA, USA, 1996.

[66] Costea, M. (Adv: S. Petrescu and M. Feidt), Improve-ment of heat exchangers performance in view of the thermodynamic optimization of Stirling Machine; Unsteady-state heat transfer in porous media, Ph.D. Thesis, P. U. B & U.H.P. Nancy 1, 1997.

[67] Petrescu, S., Zaiser, J., Petrescu, V. Lectures on New Sources of Energy - Vol. I and Vol II, Bucknell University, Lewisburg, USA, January 1998.

[68] Petrescu, S., Zaiser, J., Petrescu, V. Advanced Energy Conversion-Vol. I, Bucknell University, Lewisburg, PA-17837, USA, pp. 196, January 1998.

[69] Petrescu, S., Zaiser, J., Petrescu, V. Lectures on Advanced Energy Conversion-Vol. II, Bucknell Univ., Lewisburg, PA USA, March 1998.

[70] Florea, T. (Adviser: S. Petrescu), Grapho-Analytical Method for the study of the operating processes irre-versibility in Stirling Engines, Ph.D. Thesis, UPB 1999.

[71] Costea M., Petrescu S., Harman C. The Effect of Irreversibilities on Solar Stirling Engine Cycle Performance, En. Conversion & Management, Vol. 40, pp. 1723-1731, 1999.

[72] Petrescu, S., Costea, M., Malancioiu, O., Feidt, M. Isotheral Processes treated base on the Firtst Law of Thermodynamics for Processes with Finite Speed, Vol. Conf. BIRAC’2000, Bucharest, 2000.

[73] Petrescu, S., et al., 2000, Determination of the Pressure Losses in a Stirling Cycle through Use of a PV/Px Diagram, ECOS'2000, Enschede, Netherlands, pp. 659. 2000

[74] Petrescu, S., et al., A Method for Calculating the Coefficient for the Reg. Losses in Stirling Machines, 5th European Stirling Forum, Osnabruck, Germany, pp. 121-129, 2000.

[75] Florea, T., Petrescu, S., Florea, E. Schemes for Computation and Otimization of the Irreversible Processes in Stirling Machines, Leda & Muntenia, Constanta, 2000.

[76] Petrescu, S., et al. Optimization of a Carnot Cycle Engine using Finite Speed Thermodynamics and the Direct Method. ECOS'2001, Istanbul, Turkey I, 151-162 (2001).

[77] Petrescu, S., et al., Les cycles des machines à froid et des pompes à chaleur à vitesse finie, Rev. Entropie, 232, 48-54 (2001).

[78] Petrescu S., Harman C., Costea M., Popescu G., Petre C., Florea T. Analysis and Optimisation of Solar/Dish Stirling Engines, Proceedings of the 31st American Solar Energy Society Annual Conference, Solar 2002, “Sunrise on the Reliable Energy Economy”, Reno, Nevada, vol.CD,. Editor: R. Campbell-Howe, June 15-20, USA, 2002.

[79] Petrescu, S., Feidt, M., Harman, C., Costea, M. Opti-mization of the Irreversible Carnot Cycle Engine for Maximum Efficiency and Maximum Power through Use of Finite Speed Thermodynamic Analysis, ECOS’2002, Berlin, Germany, Vol. II, p. 1361-1368, 2002.

[80] Petrescu, S. Costea M., Harman C., Florea T. Application of the Direct Method to Irreversible Stirling Cycles with Finite Speed, International Journal of Energy Research, Vol. 26, 589-609, 2002.

[81] Petrescu, S., Harman, C., Costea, M., Feidt, M. Thermo-dynamics with Finite Speed versus Thermodynamics in



Finite Time in the Optimization of Carnot Cycle. Proc. of the 6-th ASME-JSME Thermal Engineering Joint Conf., Hawaii, USA, March 16-20, 2003.

[82] Petrescu S., et al. A Scheme of Computation, Analysis, Design and Optimization of Solar Stirling Engines, The 16-th ECOS'03, Copenhaga, Ed. N. Houbak, et.al., Vol.I, p.1255-1262, 30 June -2 Iuly, 2003.

[83] Petrescu, S., Zaiser, J., Harman, C., Petrescu, V., Costea, M., Florea, T., Petre, C., Florea, T.V., Florea, E. Advanced Energy Conversion- Vol I and II, Bucknell University, Lewisburg, PA -17837, USA, 2006.

[84] Petre, C. (Adv.: S. Petrescu, M. Feidt, A. Dobrovicescu), Utilizarea Termodinamicii cu Viteza Finita in Studiul si Optimizarea ciclului Carnot si a Masinilor Stirling, Ph.D. Thesis, UPB & U.H.P. Nancy 1, 2007.

[85] Petrescu, S. Treatise on Engineering Therodynamics. The Principles of Thermodynamics. AGIR, Bucuresti, Romania, 2007.

[86] Petrescu, S., Cristea, A. F., Boriaru, N., Costea, M., Petre, C. Optimization of the Irreversible Otto Cycle using Finite Speed Thermodynamics and the Direct Method, Proc. of the 10th WSEAS Int. Conf. on Mathematical and Computational Methods in Science and Engineering (MACMESE'08), Computers and Simulation in Modern Science, Bucureşti, Ed. N. Mastorakis, Vol II, p. 51-56, 7- 9 Noiembrie ROMANIA, 2008.

[87] Petrescu, S., Boriaru, N., Costea, M., Petre C., Stefan, A., Irimia, C. Optimization of the Irreversible Diesel Cycle using Finite Speed Thermodynamics and the Direct Method, Bulletin of the TRANSILVANIA University of Braşov, Vol. 2(51) – Series I, No.1, vol.1 Ed. Universităţii Transilvania, p. 87-94, 2009.

[88] Cullen, B., McGovern, J., Petrescu, S., Feidt, M. Preliminary Modelling Results for Otto-Stirling Hybrid Cycle, ECOS 2009, Foz de Iguasu, Parana, BRAZIL. pp. 2091-2100, August 31- September 3, 2009.

[89] Leontiev, C. (Advisers: Prof. S. Petrescu, Prof. M. Costea), Irreversible Diesel Cycle Study and Opti-mization based on the Direct Method from Finite Speed Thermodynamics, Master Thesis, University Politehnica Bucharest. July (2010).

[90] Petrescu, S., Leontiev, C., Boriaru, N., Costea, M., Petre, C. Irreversible semi-Diesel cycle approach based on the Direct Method from Finite Speed Thermo-dynamics, Polytechnic Institute of Iasi Bulletin, LVI (LX), 103-114 (2010).

[91] Petrescu, S. The Development of Thermodynamics with Finite Speed and the Direct Method, Polytechnic Institute of Iasi Bulletin, LVI(LX), 65-85 (2010).

[92] Petrescu S., Harman C., Costea M., Petre C., Dobre C. Irreversible Finite Speed Thermodynamics (FST) in Simple Closed Sistems. I. Fundamental Concepts, Termotehnica, AGIR, Bucuresti, Romania, 1, 2010.

[93] Petrescu, S., et al. A Methodology of Computation, Design and Optimization of Solar Stirling Power Plant using Hydrogen/Oxygen Fuel Cells, Energy, Volume 35, Issue 2, Pages 729-739. February 2010.

[94] McGovern, J., Cullen, B., Feidt, M., Petrescu, S., Validation of a Simulation Model for a Combined Otto and Stirling Cycle Power Plant, Proc. of ASME 2010, 4th Int. Conf. on Energy Sustainability, ES2010, May 17- 22, Phoenix, Arizona, USA, 2010.

[95] Petrescu, S. The Development of Thermodynamics with Finite Speed and the Direct Method, Tomul LVI, Fasc 3a, COFRET 2010, 5-7mai, Iasi, Romania, 2010.

[96] Petrescu, S., Grosu, L., Costea, M., Rochelle, P., Dobre, C., Analyse théorique et expérimentale d’une

machine á froid de Stirling, COFRET’10, 5-7 mai, Iasi, Romania, 2010.

[97] Petrescu, S., Costea, M., Tirca-Dragomirescu, G., Dobre, C. Validation of the Direct Method and its applications in the optimized design of the Thermal Machines for the increase of the Efficiency,28-29 Aug, ASTR Conference, Craiova, Romania, 2010.

[98] Petrescu, S., Tirca-Dragomirescu, G., Feidt, M., Dobrovicescu, A., Costea, M., Petre, C., Dobre, C., Combined Heat and Power Solar Stirling, ECOS 2010, 14-17 June, Lausanne, Switzerland, 2010.

[99] 99. Petrescu, S., Costea, M., Tirca-Dragomirescu, G., Dobre, C., Validation of the Direct Method and its applications in the Optimized Design of the Thermal Machines for the increase of the efficiency, A V-a Conferinta STR, Craiova, 28-29 Sept. 2010.

[100] Petrescu, S. Costea M., et.al., “Development of Thermo-dynamics with Finite Speed and Direct Method”, AGIR, Bucharest, 2011.

[101] Curzon, F.L., Ahlborn B. American Journal of Physics 43, 22. 1975.

[102] Andresen, B. Finite-Time Thermodynamics, Physics Lab., Univ. of Copenhagen, 1983.

[103] Heywood, J.B. Int. Comb. Engine Fundamentals, McGraw-Hill Book Comp., N. Y, 1988.

[104] Bejan, A. Advanced Engineering Thermodynamics, Wiley, New York, 1988.

[105] Sieniutycz, S., Salamon, P. Finite-Time Therm. and Thermoec. Taylor &Francis, NY, 1990.

[106] Ibrahim, O. M., Klein, S. A., Mitchell, J. W. J. Eng. Gas Turbine Power 113, 514, 1991.

[107] Gyftopulous, E. P. Fundamentals of analysis of processes, Energy Conversion & Management, Vol. 38, pp. 1525-1533, 1997.

[108] Moran, M. J. A Critique of Finite Time Thermo-dynamics, ECOS' 98, Nancy, France, Ed. by A. Bejan, M. Feidt, M. J. Moran and G. Tsatsaronis, Nancy, France, pp. 1147-1150, 1998.

[109] Moran, M. J. On Second Law Analysis and the failed promises of Finite Time Thermodynamics, Energy 23, pp. 517-519, 1998.

[110] Feng Huijun, Chen Lingen, Sun Fengrui Optimal ratios of the piston speeds for a finite speed endoreversible Carnot heat engine cycle. R. Mexicana de Fisica, 56(2): 135-140, 2010.

[111] Feng Huijun, Chen Lingen and Sun Fengrui Optimal ratio of the piston for a finite speed irreversible Carnot heat engine cycle, International Journal of Sustainable Energy, 30: 6, 321, December 2011, 321-335, First published on: 23 September 2010.

[112] Feng Huijun, Chen Lingen and Sun Fengrui, Effects of unequal finite speed on the optimal performance of endoreversible Carnot refrigeration and heat pump cycles, International Journal of Sustainable Energy, 30: 5, 289-301, October 2011, First published on: 22 September 2010.

[113] Chen, L.G., Feng, H.J., Sun, F.R. Optimal piston speed ratio analyses for irreversible Carnot refrigerator and heat pump using finite time thermodynamics, finite speed thermodynamics and direct method, International Journal of Energy Institute, 2011.

[114] Bo Yang, Lingen Chen, and Fengrui Sun Performance analy sis and optimization for an endoreversible Carnot heat pump cycle with finite speed of the piston, International Journal of Energy Environment, 2011.

[115] Stanescu, G., “A study of the large oscillations of the thermodynamic pendulum by the method of cubication”, in Thermodynamic optimization of complex energy



systems, edited by Adrian Bejan and Eden Mamut, Dordrecht: KluwerAcademic Publishers, 445-452, 1998.

[116] Stanescu, G., Study of a CARNOT - like cycle with variable finite speed, Proceedings of the 3rd Inter-national Congress on Thermal Energy and Environment – ITEEC'97, Marrakech, Morocco, 1997.

[117] Stanescu, G., Limit cycles of the dissipative thermo-dynamic pendulum, Proceedings of the 6th Romanian Conference of Engineering Thermodynamics, v. 1, 53-58, Iasi - Chisinau, Romania, 1996.

[118] Stanescu, G., Harman, C. M., Petrescu, S., Study of nonlinear oscillations of the thermodynamic pendulum, AES-Thermodynamics and design, analysis and improvement of energy systems, v.33, 305-312, 1994.

[119] Stanescu, G., Petrescu, S., Study of the CARNOT cycle with irradiative heat sources, Proceedings of the 4th Romanian Conference of Engineering Thermodynamics, v. 1, 48-53, Timisoara, Romania, 1994.

[120] Costea, M., Petrescu, S., Stanescu, G., Danescu, R., Study of the performances of a concentrated solar radiation receiver for a solar STIRLING engine, Proceedings of the 4th Romanian Conference of Engi-neering Thermodynamics, v. 4, 193-199, Timisoara, Romania, 1994.

[121] Stanescu, G., Petrescu, S., Costea, M., The gas-springs coupling: the thermodynamic pendulums series coupling, Proceedings of the 4th Romanian Conference of Engineering Thermodynamics, v. 1, 42-48, Timisoara, Romania, 1994.

[122] Costea, M., Petrescu, S., Stanescu, G., Danescu, R., Thermal and dimensional optimization of a solar STIRLING engine cavity type receiver, Proceedings of the Florence World Energy research Symposium - FLOWERS'94, v. 1, 1075-1082, Florence, Italy, 1994.

[123] Petrescu, S., Stanescu, G., Iordache, R., Study of the reversible thermodynamic pendulum in the small oscillations hypothesis, Energetica Review, Romania, v.41, 66-70, 1993.

[124] Petrescu, S., Stanescu, G., The optimization calculation of the spark ignition engine theoretical cycle which develops within finite time taking the burning speed into consideration, Polytechnic University of Bucharest Scientific Bulletin, v. 55, 92-102, 1993.

[125] Petrescu, S., Stanescu, G., The optimization of the Otto cycle which develops within finite time, Polytechnic University of Bucharest Scientific Bulletin, v. 55, 108-113, 1993.

[126] Petrescu, S., Stanescu, G., Iordache, R., Ceciu-Andrian, Dinu, R., The reversible and irreversible adiabatic thermodynamic pendulum in the hypothesis of large oscillations, Energetica Review, Romania, v. 41, 116-122, 1993.

[127] Stanescu, G., Petrescu, S., Study of the double thermo-dynamic pendulum forced oscillations, Proceedings of the 3rd Romanian Conference Of Engineering Thermodyna-mics, v. 1, 150-153, Bucharest, Romania, 1993.

[128] Petrescu, S., Iordache, R., Stanescu, G., Costea, M., The dimensional optimization of a cavity type receiver for a solar STIRLING engine taking into account the influence of the pressure losses, finite speed losses, friction losses, and the convective heat transfer, Proceedings of the International Conference on Energy Systems and Ecology - ENSEC'93, v. 2, 891-898, Krakow, Poland, 1993.

[129] Stanescu, G., Petrescu, S., Costea, M., The gas-springs coupling. the thermodynamic pendulums parallel coupling, Proceedings of the 3rd Romanian Conference

of Engineering Thermodynamics, v. 1, 154-157, Bucharest, Romania, 1993.

[130] Stanescu, G., Petrescu, S., The study of some oscillating systems of type of thermodynamic pendulum, Pro-ceedings of the International Conference on Energy Systems and Ecology - ENSEC'93, v. 1, 225-232, Krakow, Poland, 1993.

[131] Petrescu, S., Stanescu, G., Iordache, R., A calculation and optimization diagram of the Stirling engines, Polytechnic University of Bucharest Scientific Bulletin, v. 54, 145-151, 1992.

[132] Petrescu, S., Stanescu, G., Iordache, R., Study of the finite speed adiabatic taking into account the viscosity of the working medium and the inertia forces, Polytechnic University of Bucharest Scientific Bulletin, v. 54, 105-116, 1992.

[133] Petrescu, S., Stanescu, G., Iordache, R., Irreversibility generation mechanisms in case of the polytropic thermodynamic oscillator, Proceedings of the International Symposium on Efficiency, Costs, Optimization and Simulation of Energy Systems - ECOS'92, v. 1, 41-47, Zaragoza, Spain, 1992.

[134] Petrescu, S., Stanescu, G., Numerical method for determination of characteristic parameters of theoretical OTTO –like cycle taking into account the finite speed of processes, Proceedings of the 1st Romanian Conference of Engineering Thermodynamics, v. 1, 78-83, Bucharest, Romania, 1992.

[135] Petrescu, S., Stanescu, G., Iordache, R., The influence of the nature of working fluid on the behavior of adiabatic pendulum, Proceedings of the 1st Romanian Conference of Engineering Thermodynamics, v. 1, 33-38, Bucharest, Romania, 1992.

[136] Stanescu, G., Petrescu, S., Iordache, R., Thermodynamic analysis of some methods for thermal energy storage, Proceedings of the 1st Romanian Conference of Engineering Thermodynamics, v. 2, 50-55, Bucharest, Romania, 1992.

[137] Petrescu, S., Stanescu, G., Iordache, R., Thermodynamic oscillators. comparative study of adiabatic and iso-thermal oscillators, Proceedings of the 1st Romanian Conference of Engineering Thermodynamics, v. 1, 27-32, Bucharest, Romania, 1992.

[138] Petrescu, S., Stanescu, G., Iordache, R., Popescu, G., Numerical method for optimization of the BRAYTON – like cycle, Proceedings of the Romanian Society of Engineering Aided by Computer Symposium - SIAC'91, v. 1, 339-345, Bucharest, Romania, 1991.

[139] Petrescu, S., Iordache, R., Stanescu, G., The dimen-sional optimization of a concentrated solar radiation receiver for a solar STIRLING engine taking into account the influence of the pressure losses and convective heat transfer, Proceedings of the Romanian Society of Engineering Aided by Computer Symposium - SIAC'91, v. 1, 5-12, Bucharest, Romania, 1991.

[140] Petrescu, S., Stanescu, G., Iordache, R., Popescu, G., The influence of the increasing pressure coefficient during the combustion process and the initial temperature on the OTTO – like cycle efficiency taking into account the dependence of specific heats of the working fluid on the temperature, Proceedings of the Romanian Society of Engineering Aided by Computer Symposium - SIAC'91, v. 1, 302-307, Bucharest, Romania, 1991.

[141] Heywood, J.B. International Combustion Engine Funda-mentals, McGraw-Hill Book Company, New York (1988).

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