OA17162A - Process producing useful energy from thermal energy - Google Patents

Abstract

The invention relates to a process producing useful energy from thermal energy. An overall population of mobile particles confined to a unidirectional flow closed circuit of conducting channels (1-2-3-3'-4-1) is subjected to a conservative or effectively conservative force field. The circuit is thermally insulated with the exception of two non juxtaposed areas a first area (2-3) allowing thermal exchange for heating (Qin) from a warmer environment outside the circuit, a second area (4-1) allowing thermal exchange (Qout) for cooling, as necessary, by a colder environment outside the circuit. The closed circuit is provided with a load (3'-4;) designed to convert the energy it receives from the mobile particles flow to a useful output energy. In two portions of the unidirectional circuit located before (3-3') and after (1-2;) said load, flow velocity vector is parallel or has a component which is parallel to the conservative or effectively conservative force field one portion with a warm flow and the other portion with a cool flow of mobile particles and in that if the density of the chosen mobile particles decreases when the temperature increases, the direction of the conservative force field is the same as that of the cool flow velocity vector or of a cool flow velocity vector component in the said circuit portion and the inverse if the density of the chosen mobile particles increases when the temperature increases.

Description

The présent invention relates to a process producing usefui energy from thermal energy

In WO 2010/115654 of the présent Patent Application inventor discloses a process and an installation based on princlples of action related to the présent invention but is limited to a process which is applicable only in a centrifugal force field acting on a fluid which Is requtred to be In state of Idéal gas or liquid.

DE 102 34 568 A1 and WO 2010/097260 disciose processes which are based on principies of action that are related to the présent invention but are limited to processes which are applicable only in a gravitational force fieid acting on a fluid which Is requtred to be in state of idéal gas or liquid.

US 7,486,000 B1 disclose a process using the commonly known heat source, heat slnk and load. The electric field generates motion of a working substance such as a tumlng table or ribbon. This mechanical energy is afterwards output for usefui work. This motion is generated by manlpulating the dielectric constant of the working substance through a heating/cooling cycle. In such modulation of the dielectric constant, the heat added/removed is used to modify the inhérent dielectric characteristics of each element In the working substance and so créâtes two types of matter one which is stronqlv interactinq with the electric field and the other which Is repelled or indiffèrent to the electric field. This process is defined by the inventor precisely as the thermo dielectrophoretic effecf* used in the claims (pg. 2, line 30).

In opposition to the above, in the herein proposed process the heat does not change the type of each particle and each particle’s interaction with the conservative force field (such as electric field) remains identical throughout a full hot/cold cycle. The heating/cooling process modulâtes the Inter-particles’ average distance or denslty and therefore acts by influencing thelr overall distribution in the steady state process and not their substance.

In addition, in US 7,486,000 B1 process, each element moves In one direction as one type of substance, with a strong force (F) and distance (S) converting its potentiel energy In the electric field to other mechanical form and on its way back, encounters weak or no counterforce (since It has changed Its actual type of substance) over the same distance. That cycle Is therefore not a conservative one and the electric field has a net Input energy contribution to each cycle, contrary to the herein proposed process.

In the présent Invention process, each particle, through a full steady state cycle encounters the same force downstream as upstream, over the same distance, and the force field has therefore zéro net energy contribution to each fuil particle cycle making the cycle conservative. The flow through the load, under the influence of the conservative force field, acts to homogenize the

-2partiels distribution throughout the closed flow circuits and the heat reestablishes the uneven distribution, maintaining It stable in steady state.

EP 0369670 A2 discloses a process also using the commonly known heat source, heat sink and load. It converts heat differentials to produce useful output electric energy (and vice versa) by hamessing the effects occurring In a junction between two metals or two channel types as related to the seebeck/peltier effects and as referred to in their daims. The process proposed In the présent Invention does not relate to any junctions nor variations In channel types. In addition that process uses a variable electric field, but for a different purpose and in a different configuration than the herein proposed process. The EP 0369670 A2 process uses the electric field to impose a rapid stop-go current allowing it to improve efficiency by resoiving the problem of ’cold spot’ occurrences by maklng the current paths random.

The présent invention purpose is to improve the above discussed processes by extendîng the process to additional force field types, matériels and material states, physical forms and circumstances of use.

The process of the présent invention Is defined In clalm 1.

What The process does and how does it work: It recelves heat and, as necessary, coolïng, and It generates useful energy. It acts by subjecting an overall population of mobile particles (also, herein ’fluid’) formlng a closed circuit, to a conservative force field and to sélective heating/cooling. This combination of parameters causes the overall particles population In the circuit to hâve, as a whoie, a spontaneous tendency to accelerate along the closed circuit. The energy for this fluid flow and conséquent energy output In steady state cornes from the Input heat rather than from the source generating the force field.

This rotational accélération tendency along the fluid circuits caused by constantly havlng, In steady state of the process, two sub-populations of fluid: one denser relative to the other. The conservative force applies a stronger accumulattve force on the denser fluid population compared with the accumulative force on the less dense one. This results In an équivalent net force, tangential to the circuit, applied to the overall fluid forcing its flow.

This denslty differential which exists between the warmer/colder volumes of the circuit, Is caused by the fact that the input heat, coupled with output useful energy and heat output as necessary, impose on the overall particles' population to stabilize in steady state, as two distinct separate sub populations of flowing fluid of different average températures and densities, appearing as immobile cold area and immobile hot area in the référencé frame.

The tendency of the overall fluid mass to acceierate rotationally aiong the circuit, créâtes energy denslty differential on the load's extremities which the load converts to useful output work. The

-3flow of the fluid In steady state has no net energy exchange with the force field slnce the mass distribution withln the force field remalns unchanged over time and is therefore balanced In equllibrium only by the net heat flow (input minus output) and work output.

The most Important particularity of the process is that heat input Is converted directly to increased potentiel energy, In addition to other forms of energy, which Is then together with the other forms, converted to output. In steady state of the System, subjected to the process’ parameters, each of the above mentioned fluid sub-populations has a different potentlal energy relative to the same reference point due to thelr energetic center of mass helghts In the conservative force field. Thls results In the total fluid présent In the System behaving as having an overall rotational potentiai energy differential manifested as rotational asymmetric Inertia for which In steady state there Is no related movement in fluid’s mass distribution. The fluid as a whole has the tendency to spontaneously accelerate In a circular motion along the flow path which translates to directional force, and consequently, pressure and energy denslty differential on the ioad.

The process detalled description starts here: as part of the various known phenomena hamessed by the process, such as the laws of conservation of energy and mass, there are two phenomena which are worth mentioning as background: The first: When particles are in a conservative force field, the field applying a force on them, will cause their accélération In the direction of the field lines, as per the second law of Newton. This means that In a given reference frame, for which a nonzero conservative force field exists, the particles manifest asymmetric Inertial behavior- when these particles are subjected only to the force field represented by Its lines, they will spontaneously accelerate In thelr direction, recelving energy from the field as their center of mass changes position. In such a field each partîcle has potentiai energy, whether positive or négative, relative to a reference position. Its movement In the direction of the force converts Its négative change In potentiai energy ïnto work or other form, or combination of forms, of energy and, inversely, Its movement against the force reduces the other form/s of energy as lt gains potentiai energy. in such a System, the particle’s potentiai energy change Is related to Its center of mass’s physical position change (path Independent) relative to a reference position. The second: Thermal energy, essentialiy an electromagnetic energy, travels empty space only as electromagnetic waves until lt Interacts with particles. Once transfened to particles, it Is aiso manifested In them and propagates between them as Interparticle klnetic and potentiai energy (internai energy) and doing work on thelr surroundings, occupying volume. The internai energy represents the various Internai klnetic and potentlal energy forms made possible by each type of particle, its environment, and by Its Inhérent degrees of freedom. In charged particles, for example, electric and magnetic fields aiso play a rôle In the propagation pattern and particle distribution at equllibrium. Thls has the conséquence of Impacting the average distance between the particles and therefore their

-4quantity In a given fixed volume or In other words- their density. The temperature-density corrélation, however, dépends on the particles’ type and the conditions to which they are subjected. In Idéal gas, for example, this reiationship exists in a pronounced way- the Increased température would reduce the gas density, at constant pressure and vice versa. In degenerate gases, such as free électrons in a métal, this reiationship stili exists but is much less pronounced and depending on the type of meta! can even be Inverted, hlgher température more density. In liquids and solids this reiationship also exists to a much lesser extent than idéal gas and may even be Inverted depending on their particuiar parameters such as type of particies and température.

The process of the présent Invention will now described using varlous représentations based on the enciosed figures.

Figure 1 is a schematlc représentation of a flrst embodiment of the process;

Figure 2 Is a schematic représentation of a second embodiment of the process;

Figure 3 Is another schematic représentation of the first embodiment of the process ;

Figure 4 is another schematic représentation of the second embodiment of the process;

Figures 5 to 8 are schematic représentations of the process the conservative force field belng respectively, electric, magnetic, according to the présent invention and gravitationai and centrifugal according to the prior art

Process options: The process may be represented In severai ways. To provide a sufficiently broad view of the process, It wili be herein analyzed in two optional représentative configuration examples: one, by which heating is carried out in circuit channel 2-3 and cooling In circuit channel 4-1 and ail the rest of the process is thermally Isolated (figure 1). The other by which heating is carried out in circuit channel 33-33’ and cooling in circuit channei 31-32 and the rest of the process Is thermally isolated (Figure 3). The load Is represented as positioned in circuit channel 3’-4 or 33-34. In a practical process the heating configuration may vary, and It may also be based on a combination of these two options.

First option as above: The process, in its generalized basic form, as per figure 1, consists of mobile particles confined to a closed circuit 1,2,3,3^4,1 distributed inside or around the outer skin In cases of charged particles, of conducting channels. The System is subjected to a conservative force field as shown. The force iines are parallel to the vertical columns with direction from 1 to 2 and from 3’ to 3. The circuit is, for simplicity of the expianation, completely thermally insuiated, with the exception of a heat exchange area between stations 2-3 for heating from the warmer environment outside it, and another one at 4-1 for cooling by the colder environment outside It, as necessary. The circuit Includes a ioad at 3'-4, converting the energy it

-5receives from the flow of the particies to useful output energy. The conservative force field may be any kind of conservative field which applies force on ali /part of the mobile particies présent In the process in the shown direction. This conservative force fieid may be electrical, magnetic or other. Some of the field types will be de facto conservative only in spécifie conditions as wiil be clarified further down. The mobile particies are particies which are free to move in a circuit relative to the process channels 1-2-3-3’-4-1 and may be practicaily of any type: electrically charged or not, for example, électrons, Ions, electrically neutral atoms, molécules etc, and may be In any state such as idéal or degenerate gas, liquid, solid, semi solid (such as a ring/belt), plasma, superconductor. The load in 3’-4 can be any device adapted to the clrcuit's clrcumstances, converting the mobile particies* energy into a useful output as, for example, a propelier or piston activating a generator, an electrical résistance (heat output from the System), eiectric motor etc.

In a steady state process cycle, presented In its most simplified form and anaiyzed herelnafter, the fluid flows from 1 to 2, subjected to the force field in the same direction as the flow. It loses potentiai energy as it flows from 1 to 2 and gains in Its total combined energy of other forms, regardless of their detalied Indivldual types. With the absence of net energy exchange with the outside through the waüs of the channel .flowing adiabatically, the total of the potentiai energy plus ail other forms of a given m_(t) mass is a constant at any position along the flow path 1- 2. In

2-3, the fluid flows perpendicular to the force field and receives Input heat. In 3-3' the heated fluid flows agalnst the force field. it gains potentiai energy (relative to any given fixed position of référencé) as It flows from 3 to 3' and Its total combined energy of other forms Is reduced, regardless of their detailed individual types. With the absence of net energy exchange with the outside, flowing adiabatically, the total of the potentiai energy plus ail other energy forms of a given m_(l) mass is a constant at any position along the flow path 3-3’. In 3’-4 the fluid flows through the load, where its energy is converted to a useful form which is output from the System. In 4-1 the fluid outputs heat, outside of the System, cooling It as required, for the portion of the input heat which was not converted to useful output at 3'-4, to reach station 1 at the energy level required to malntain the steady state. In 3*-1 the fluid flows perpendicular to the force fieid. In the optimlzed process, channels 1-2, 3-3' are of the same length along the force field lines. in the process basic form, for simpiieity of the représentation, consider that on each particle of the fluid an Identlcal, constant, force vector applies (direction and magnitude). Note the process will be anaiyzed in a rectangular channel structure but can equally be In practice of a circular channel structure, forming a ring, or any other form In a circuit Another considération Is that fluid density Is reduced with increased température of the fluid. Ail channel sections are Identlcal and therefore 1-2, 3-3* are of same volume. These assumptions are not a necessity, but ailow for a simplified generalized représentation of the process. Channel flow losses and thermal losses are ignored.

In steady state, the channels in the System are filled with flowing/ traveling fluid. Thls thermodynamic analysis of the process Is based on the energy and energy distribution of thls fluid In the given force field. The energy types involved in thls process consldering a generic fluid type subjected to a generic conservative force field: every given fluid mass In thls process may be represented as having any combination of various types of relevant energy, in varying degrees of detail depending on the type and state of the mobile partides, such as Enthalpy, flow kinetic energy. In addition, in a conservative force field, such a mass has potential energy relative to a reference point. For a fluid mass situated In channel 1-2 for example, between stations 1, and 2, thls potential energy Is positive relative to station 2 and négative relative to station 1 slnce the mass has an accélération vector with direction away from station 1 towards

2. Same for fluid In 3-3, the fluid mass In It has positive potentialenergy relative to station 3 and négative relative 3*.

Energy components

In thls analysis, the relevant energy of the fluid or portion of It, being the ‘System', can be represented by a combination of two components: potential energy relative to a reference point in the surrounding System plus ali other relevant types of energy attributable to the System combined, which would be referred to as E other Thls energy component E other may be further detailed as a combination of two components: directional kinetic energy relative to the surrounding System In the chosen reference frame, and ail other relevant types of energy attributable to each System, correlating to each fluid mass portion. This latter component is équivalent the total enthalpy of the System, or Is the relevant portion of it, which may be further divided Into two sub-components: Internai energy, whether Internai kinetic, or internai potential, energy being the energy required to croate the System, and the amount of energy required to make room for it by displacing the environment establishlng its volume and pressure (shall be referred to herein as pressure-volume energy):it can be stated that Ec^ H+ E_Wn = U+PV+E_Wn= KPV+Ekih , H being enthalpy, U being the Internai energy, PV the pressure-volume energy, P the pressure or the pressure-volume energy density, V Is the volume occupied by the System, E_Wn Is the kinetic energy of a System, K Is the ratio between the enthalpy and the pressure-volume energy. Although K may vary from state of equilibrium to another, and In some Systems, slgnificantly, It shall be herein considered as constant for the simplification of the équations as It is approximately so In many circumstances of relatively small variations of system's parameters. This parameter’s dynamlc behavior shall be Incorporated, where it is not negliglble, for each practical apparatus uslng this process, to obtain accurate résulte.

In steady state of a System containing flowing fluid, the energy, température, energy density etc. of a given fluid mass quantity In a given station are constant over time. in other words, the température, for example, of the fluid In station 1 will be constant through time. Furthermore, the

-7parameters of the flowing fluid, being constant over time In each station, are Interdependent and their relationshlp Is therefore fixed over time. Thls means that, for example, two randomly plcked parameters, the klnetic energy In station 1 and the energy denslty In station 2, are part of a fixed overall equilibrium. For thls reason, the parameters of the fluid In each station In steady state are requlred to be quantified In the context of, and In conséquence of, thls overall equilibrium. In view of the above, the chosen approach to analyzing the process Incorporâtes the overall equilibrium as the base for the analysis of the relevant parameters station to station.

In steady state, at any given point In time the total relevant energy of the: Total fluid présent In channel 3-3'(also, the “hot coiumn) relative to 1 and to 3’, Total fluid In channel 1-2 (also, the cold coiumn) relative to 1 and to 3’, Total fluid présent In channel 3-3’ relative to 3 and to 2 , Total fluid présent In channel 1-2 relative to 2 and to 3, may be represented as follows:

1· Ehi ⁼ Ehoiw Ephi⁼ EHother m_Ha h_H

2. Eci-Eccther Epci= Eq other ΓΠο3 tic

3. Eh2 ⁼ Eh Other⁺ EpH2~ Eh Other + ΓΠηΘ (R- I1h)

4. Ec2 ⁼ Ecother⁺ Epc2= Eq other⁺ ΓΠοβ (R-hc)

5. Eh2/V= Ecî/V which are the energy densities of the overall fluid In 1-2 relative to 2 and the overall fluid In 3-3' relative to 3 (also to 2) are equal as In steady state they retain their parameters stable over time (pressures, températures etc.) and there Is no ioad between them In 2-3 which would allow an energy denslty différentiel to be sustained. As mentioned earlier losses are Ignored.

6. (Ehorner + ΓΪΙηΘ (R- I1h)]/V= [Ecother⁺ rnca (R-hc)]/V

7. From 6, Ec_oth«⁼ Eh other + PhV a (R· hn)- PcV a (R-hc), (γπη- PhV, mc= PcV)

Where,

-Ephi, - Epci, are the potential energy components, relative to station 1 (or 3‘) of the total fluid Inslde 3-3’, 1-2 respectively. Ephî, Epcî. are the potential energy components, relative to station 2 (or 3) of the total fluid Inslde 3-3’, 1-2 respectively. Note: Ail these values are based on the fluld's energetic center of mass In each coiumn. E_H n Total relevant energy of the fluid In the hot coiumn 3-3’ relative to station 1 (or 3'). Eh*Total relevant energy of the fluid In the hot coiumn

3-3’ relative to station 2 (or 3). E_H other Total energy of the fluid In the hot coiumn 3-3' of ail relevant types combined other than potential energy relative to a référencé point In the surrounding system.Ed: Total relevant energy of the fluid In the cold coiumn 1-2 relative to station 1 (or 3’). E^: Total relevant energy of the fluid In the cold coiumn 1-2 relative to station 2 (or 3). Ecothen Total energy of the fluid In the cold coiumn 1-2 of ail relevant types combined other than potential energy relative to a référencé point In the surrounding System, a: The accélération rate of each mass unit of the fluld particles, caused by the conservative force field, In the direction of the force lines (In direction 1 to 2 and 3* to 3). V: Volume of the hot column and also of the cold column. m_H: Mass of ail the fluid In the hot column 3'-3. m_c: Mass of ail the fluid In the cold column 1-2. R: The overall length of channel 1-2 and of channel 3-3'. hw: The distance between station 3’ and the center of mass (m_H) of the fluid Inslde the hot column(3-3'). h_c: The distance between station 1 and the center of mass (m_c) of the fluid inslde the cold column (1-2). pu. is the average density of the fluid in 3-3 and defined as γγιη/V. p_c Is the average density of the fluid in 1-2 and defined as mc/V, U_H is the total internai energy of the whole fluld In the hot column. u_H Is the velocity of the fluid In the hot column considered at center of mass. Ph is the pressure or density of the pressure-volume portion in the Enother energy of the whole fluid In the hot column.

Process Input/ output: The Energy 3-1, Ea-.i^whlch is work output in 3’-4 and additional cooling by heat output In 4-1, as necessary to malntaln steady state over a period of time (t) is quantified as equal to the energy of the fluld recelved from the hot column over that time less the energy of the fluid of same mass, which exlts to the cold column over the same time.

8. Ehi(q-Eci(i)

Where.Ey.^tj : The total output work recelved over a period of time (t) by conséquence of the fluid flow In 3*-4 In addition to the total heat outflow over the same period of time (t) in 4-1, as necessary to maintain steady state . Ε_Ηΐ(φ the energy relative to 3’ or to 1, of the warmer fluid of mass mjt) entering into 3*-1 over a period of time (t) from the hot column 3-3'. Eckd: the energy relative to 1 (or 3’) of the colder fluid of same mass, m_(t), exlting 3’-1 over the same period of time (t) towards the cold column 1-2

In conséquence of energy levels remaining unchanged In each position In the System over time, and, the channels 3-3', 1-2, being thermally Insulated from the outside, the ratio between the energy of the fluid entering 3*-1 from the hot column 3’-3 over a period of time (t), E_Hi(t)and the overall energy of the fluid In the hot column, E_Ki. is equal to the ratio between the mass m₍₁₎ passlng through It overthattime (t)and the overall mass (m_H) of thefluid In the hot column 3-3.

9. (E_Hi(₀/EHi) = (m(₀/m_H)

And, in the same way: the ratio between the energy of the entering fluid, arriving from 3'-1 Into the cold column 1-2 over a period of time (t) Eci^and the overall energy of the fluld in the cold column 1-2 : Eci, Is equal to the ratio between the mass m_(1> entering the cold column 1-2 over that time (t) and the overall mass of the fluld In the cold column m_c- Therefbre,

10. (Εαρ/Eci) - (mjt/me)

Combining the above équations:

11. Ey.iw - (γπ₍₁/ππη)[ Eh«μγ m_Ha Ηη] · Ec<xher nrica hc]

12. Ey.i(t}⁼ (^m(o /VX Ph*¹ EHothw -Pc¹ Ecother)- nri(i) a(hrt* hc)

And therefore when combined with équation 7:

13. Ey.itt)- (nift)/V)( Ph¹ Enother Pc ¹(Eh other ⁺ PhV a (R- hn)- pcV a (R-hc)) - n\t> a(hn- hc)= m^lPtVpc)[a(R- hH)+ mH*¹ EHother]= m_w(1-pH/pc) [Mh ¹ E_Hother- a Ah] + rMIWPc)«R

14. E_Hothw= Uh+Ph V+Enwn = KhP_h V+ m_HUH²/2 from ‘energy components, pg. 4

15. E3-.i(ij= m₍ij(1-pH/pc)I Kh(Ph/ Ph)⁺ a(R- hn)+ Uh²/2]

On the other side, the net thermal energy received over a period of time (t) due to heating, Q2-30 In energetic equilibrium:

16. Qî-^t) = Q|n(t) =Ε3Μ(ΙΓ ΓΠ(₍)(1 -Ph/Pc) [a(R- hn)+ ΓΠη*¹ EHother]⁼ ΠΜΙ-Ph/Pc) [^mH'¹ Ehother a hn] + m_(t)(1-pH/pc) aR= m_(t)(1-pH/pc)[ MPh/ Ph)+ a(R- h_H)+ u_H ²/2]

As per eq. 15, 16, the energy of the input heat in the System increases its three relevant energetic components: enthalpy, potential energy and directional kinetic energy and the output in 3-1 decreases them. The proportions of the split dépend on the relative magnitude of each component as shown in these équations.

To calculate the useful energy output from the System through the load:

E₃^_t)) Eom(t). is the output work from the System over a period of t time, through the load. Ε_3Μ, Εφ) are the total energy values of m_t mass in stations 3* and 4. They both hâve the same potentiai energy components, E_P| as 3'-4 is perpendicular to the force fîeld. Their energy, as clarified in the “energy components” detaiied previously, can be represented as beilow.

U<₍), are the internai energies of the fluid m_t in stations 3', 4 respectively. P₃- , P₄ are the pressures in stations 3’, 4 respectively. V_3(t) .V^re the volumes occupied by m_tin stations 3’, 4, respectively. K?, K», represent the ratios between enthalpy and pressure-volume components of the fluid energy In stations 3’, 4 respectively these coefficients are Inhérent to the type of fluid (and to its particles* degrees of freedom) and Its parameters of operation withln the process. In many circumstances, such as In Idéal gas, liquide etc, for conditions not greatiy varyîng, can be considered constant. E_Wn3·, E_K]m are the directional kinetic energy components of m_t, in the direction of the flow in stations 3', 4 respectively. p₃·, p₄are the densities of m_tln stations 3’, 4, respectively. The efficlency η, Is defined herein as the ratio between the usefui output work to the heat Input, for the same period of time, t:

(E₃M{t/ 02-3(1))·

17. Ε₃μ(ιγ Eoutar

18. Ej_{l)= U_3(t)+P₃· V3(t)+EKjn3· +Ep= Ka Ps· Vsxtj+Exw+Ep, (U₃(tj+P₃· V₃(tj= K₃P₃ V₃(ij )

19. ^4(1)” U4(t)+P4 V4(t) +Εκΐη4 ⁺Ep = K4P4 V4(t) +Εκ)η4⁺Ερi (U4(t)+p4V4(t) ^e K4P4 V^t) )

Assumlng for slmpllclty of the représentation, K₃= K4= Kh=K, and from conservation of mass:

20. m^p ν₃·(ή p₃= V4(t) p4= Vq_tj p_c therefore:

21. E₃M<tj⁼( KP₃· Vyjtj+Exwj+Ep ) - (KP4 V4«) +Εκΐη4⁺Ερ )=

V_3W (KP₃· + P, u₃·² /2)- V40/KP4 + P4 u₄ ² /2)

On the basis that the energy denslty differential between an m^mass at 3' and m_(t) mass at 1 is the same as that imposed by the columns, the following applles :

22. Ehî/V- Eci/V= Eyji/Vyjtj· E-qt/Vi(t)⁼ E4<t)/V4(t) (slnce there Is no load on 4-1 and ail the parameters of the fluid remaln fixed over time in steady state).

Therefore comblned with eq. 7:

23. E₃(_t/ V₃(t) - E4(t/ V4(t) »[ Eh oaw mna hJ/V - [Ec other ^mc3 hc]/V=[ Eh other PhV a hn- Eh other pHV a (R- hH)+ pcV a (R-hc)+ pcV a hc]/V= (Pc-Ph) a R=(1-Ph/Pc) Pc a R= (KP3· + p3· u3·² /2)(KP4 + p4U4²/2)

24. E₃'^tj= V₃(t) (KP₃· + p₃'U₃ ² /2)- V4<t)(KP3· + ρ3·υ3·² /2-(1-pn/pc) Pc a R) - (KPj + ρ3·υ₃ ² /2)( V₃(_tr V^tj)⁺ (1 -Ph/Pc) Pc a R) ⁼m(t> (1- p₃·/ P4X KP₃·/ pj + u₃·² /2)+ ( pc/ p4)m(t] (1-pH/Pc)a R

25. Q₂^_t) = E₃-.i(t)= m_(t)(1-PH/Pc)( KhPh/ Ph- a h_H+ u_H ²/2) + m_(t)(1-pH/pc) aR from eq.16.

26. η= E₃·^,/ Ch-xtr [m₍t) (1- Ps/ P<)( KP₃/ p₃· + u₃ ² /2)+ ( pc/ p4)mw (1-pH/pc)a R]/ [m(l)(1-pH/Pc)( KPh/ Ph- a hH+ uH²/2) + m(t)(1-pH/pc) aR]

27. m_w ( KP₃·/ p₃· + u₃·² /2)= mw ( KPh/ Ph- a hH+ uH²/2) as the energy of m(t) at hot column’s center of mass relative to 3* Is conserved and Is the same as that of m^ at station 3' relative to 3*. Therefore:

28. η= Q₂<j<t)⁼ [m(t) (1- p3·/ P4X KPh/ Ph- a hH⁺ Uh²/2)+ ( pc/ p4)m(t) (1-pH/pc)a R] / [m^l* Ph/Pc)( KPh/ Ph- a Jih+ Uh²/2) + m_(t)(1-pH/Pc) aR] in fluid expansion through the load (1- p₃·/ p4) Is négative and the first element (1- p₃·/ P4X KPh/ Ph- a h_H+ u_H ²/2) is négative. Thls element Is subjected to two counter effects: on one hand expansion making P4 <p₃· ,on the other, cooling through the useful output of energy acting to Increase denslty, thus attenuating the denslty drop between p₃· and p₄. With Increased overall •11densîty of the fluid, the ratio p₃·/ p< gets doser to 1, with tendency In very high density to get dose to 1. In addition, thls first element becomes smaller by the négative potential energy: m₍t) a h_H , which is of Increased négative value as the field becomes stronger. Thls means that stronger the conservative field's strength and, higher the density, smaller the first element m_{l) (1- p₃7 p«)( KPh/ Ph- a hH* u_H ²/2). In analysis of the dependence of the process effidency on the various parameters, it can therefore be stated that higher density, comblned with higher force field strength, combined with lower enthalpy (and température) increases the effidency. In very hlgh density and force field strength the first element m_(l) (1- p₃/ p<)( KPh/ Ph- a h_H+ u_h ²/2) becomes negligible and the ratio Pc/ p4 close to 1, making the theoretical effidency approximately:

29. η= E₃_^t/ Q?-3<t)⁼[ m_(t) (1-pH/pc)a RJ/ [m(t)(1 -Ph/Pc)[ (KPh/ Ph- a hH⁺ Uh²/2)+ (aR)] ]

Defining KPh/ Ph- a hn+ Uh²/2= Tôt, Tôt gets smaller as the field strength Increases (but always remains higher than 0 since otherwlse there Is no circuit of the fluid). Therefore:

30. η= (a R)/(Tot+aR) <1. At maximum.

Whether In its more complété form (Eq. 28) or in its approxlmate form (Eq. 30): The effidency, as defined, In this process results as depending on the proportion between the force field strength and the overall energy of the hot fluid. Thls is based on the assumption that the energy density differentîal between the columns relative to 3' and 1 (and 4) Is equal to the energy density différentiel between two masses m_w in 3' and 1 (and 4).

To analyze the energy exchange between an mass with the force field in its flow from station 1 (or 4) to station 3', the following is consldered:

The fluid, of given mass m₍t), in the various stations in channel 1-2 has constant energy relative to 1 (or 3’) according to the law of conservation of energy. Same is applicable to the fluid In 3-3':

Total other energy forms (excluding potential energy) + potential energy = Total

31. Ei=(m_(t/mc)[ E_Cotw m_ca h_c] -0 = (m₍₀/mc)[ Ec other m_cahc]

32. E₂= m_{l/m_c)[ Ec other + m_ca(R- h_c)J - m_ta R = (m_(t/m_c)[ Ecother m_ca h_c]

33. E₃= m_{t/m_H)[ E_Mother + mHa(R- h_H)J - m_ta R = (m₍t/m_H)[ E_Hother m_Ha h_H]

34. E₃=(m(t/mH)[ Enoewr nina I1h] -0 = (m^/mnX Eh other mHahH]

It can be seen that from a station to station point of view: the added combined other energy (meaning- ail forms of energy combined, excluding potential energy relative to a reference point

-12In the System) from station 1 to station 2 Is m_ta R being the same as from station 3 to 3' - m_ta R (when consldering the spécifie value, m_(l) drops). The flow of a glven fluid mass In channels 2-3,

3-1 does not change Its potentlal energy relative to a référencé position since that flow Is perpendicular to the force field lines. Each fluid mass, therefore, In every cycle has zéro net energy exchange with the conservative force field since It recelves m_ta R as It travels from 1 to 2 and retums It from 3 to 3’. Note: Over every glven period In time, In steady state, the same mass flows In the direction of the force field lines as that whlch flows against them, the colder fiuld Is denser but flows proportionally slower than the warmer one since mass Is conserved.

The overall fluid's potentiel energy by conséquence of the conservative force field and denslty variation between the columns, a fondamental factor In thls process, can be quantified as follows: Every mass m^ anywhere along 1-2 In a random position with Its center of mass at distance h_cfrom station 1, has a combination of energy forms which, ail added together, with the exception of the potentlal energy are referred to as Ecojother. In view of Its potentiel energy, however, It has energy relative to station 2 and energy relative to station 1 which is different:

35. Ec(t)⁼m(t)[ Ec(t)oth«·· ⁰ hc] relative to 1

36. E_C{l)=m_{l)I Ecojother + a(R-h_c)l relative to 2

37. m^ R is the differential.

Same for a mass which Is In 3-3', In a random position with its center of mass at distance hn· from station 3'

38. EH-(t)⁼m(t) [ E^tjother - ⁰ tM relative to 3'

39. Εη·(ι)⁼γΠ(()[ EH(t)othw ⁺ a(R- htr)] relative to 3

40. m_(t)a R Is the differential.

Note: ail the values accompanied by the signs h,c· , are the values for that glven random station.

Thls means that this differential does not change station to station anywhere along the flow path from 1 to 2 or from 3 to 3'.However,

The whole fluid In 1-2 is constituted of mc/m_t unlts of m_t , and The whole fluid In 3-3’ is constituted of mn/mt unlts of m_t.

Therefore , for the whole fluid In 1-2, the differential between Its total energy relative to 2 and Its total energy relative to 1 Is me a R, and for the whole fluid in 3-3’ the total energy differential between relative to 3 and relative to 3' is πίη a R.

It is due to the respective position of each mobile particie In the System, in conditions of conservative force field and density differential which is caused by température differential.

Thls représente a potentlal energy differential between relative to 3’ and relative to 1, which Is:

41. m_c a R - m_H a R = me a R (1- mH/m_c)= m_c a R (1- pulpe) or, represented differently:

42. rr>ca R - m_Ha R = m_H a R(mc/mH-1)= m_Ha R( p_c/pH-1 )

This potential energy Is not attributable to a spécifie partlcle or mass but rather to the fluld mass as a whole and to the distribution of mass along the circuler flow path. For thls reason, to represent Its value, applicable to an m(t) portion (also incorporating its position and occupied volume), the value changes depending on which m_{t) we choose to serve as référencé: which Is part of m_H in the hot column, which Is part of m_c, In the cold column or one which 10 represents an m<t) portion of the whole fluld mass.

For an m_{t) portion of the mass In the context of équation 15, representing the 3’-1 output energy using the hot column fluld energy as référencé:

43. m_{l)a R (1-pype) by calculating the same représentation of E₃’-i(t) using the cold column fluld’s energy as 15 référencé rather than that of the hot column, the resuit would be:

F3M{t)⁼ nWPc/Pn-1) [oie*¹ Fcother^- a hc] + πΐβ) (pc/pn-1) aR , and thls potentiel energy component would be :

44. m_{t) aR(pc/pH-1) me a R (1- Pf/Pc) Is potential energy attributable to the fluld as a whole, which Is stored 20 rotatlonally along the clrcular path, 1-2-3-3’-4-1 of the process rather than In the direction of the original conservative fieid. it Is manifested In the tendency of the overail fluîd to spontaneously accelerate In a rotational motion or, In other words, it is manifested as rotational asymmetric Inertia of the fluld relative to the frame of référencé (which in the process is countered by the load to reach steady flow). Because of the position of the load In 3’-4, it is quantified as a 25 potential energy différentiel between 3’ and 1. Through thls potential energy, the added heat, makes the fluld In 1-2-3-3' Impose a net energy denslty differential on the fluld In 3’-4. It falls on 3’-4 as energy denslty differential (and consequently also as pressure differential) because It is there where the load présents a disruption allowing an energy denslty gradient to perslst in steady state and its value is me a R/V m_H a R /V=(1-pn/pc) Pc a R. This energy denslty 30 differential would exist at any position along the process circuit where the load would be placed.

The process environment’s thermal energy, which Is manifested in matter as symmetric, random micro inter-partlcle collisions, without a spécifie overail direction , transforme directly through this mechanism to energy which generates a net force(and energy density differential), tangential to the circuit acting In a spécifie rotational direction, this potential energy of the overail

-14fluid, or of a portion m_tof it, Is of magnitude that dépends on two éléments: a R depending on the strength of the force field, and (1- Ph/Ph) depending on the hot/cold fluid density ratio and, at its origin, the température ratio(multlplied by a coefficient Imposed by the process various parameters).

In the output/ input energy represented by; Q₂^t/ m^ E₃.i_m / m₍₁₎= (1-Ph/pc) [nW¹ Ehoow a hj + (1-Ph/Pc) aR, the input heat Increases the comblned energy of the ‘other energy forms plus Increases the potential energy of each m(1) passing from the cold to the hot coiumn through 2-3. The output work (and heat outflow, as necessary) decreases the comblned energy of the “other energy forms and decreases the potential energy of each πχη passing from the hot to the cold coiumn through 3'-1. The strength of the force field impacts the distributed proportions of each input heat unit between the potential energy component and the other energy forms component. For a given energy unit input: Stronger the force field, leads to: higher aR (and more négative - a hH), leads to: higher potential energy component portion Increase, leads to: smaller ‘other energy forms portion Increase, higher ratio of useful output to Input heat, or efficlency. If we consider flow kinetic energy variations to hâve a negligibie impact on the températures distribution in the process, for better understanding of the behavlor of the process station to station, It can be stated that because hH Is doser to 3’ than hc Is to 1, the température différentiel between that of the whole fluid in 3-3’ (TH), at its energetic center of mass, at hH, relative to the température of the whole fluid in 1-2 (Te), at its energetic center of mass, hc, ls smaller than the température rise between 2 to 3. The température fall in 3’ to 1, In steady state, is equal to the rise in 2-3. The température différentiel between 3-3’ Is equal to that of 1-2. It is to be noted that In the ‘other energy forms’ component, (1-pn/pc) [οπη¹ Eh other- a hH] the element - a h_H exlsts because the value mn'¹ Eh oth« Is this component’s value at the center of mass of the warmer fluid in 3-3' and each given m_(t) mass portion of this fluid reaches the load at station 3', after lt has retumed to the System m₍₍₎ahH of potential energy, this can be seen also in équation 39 quantifying E₃·.

Second configuration option as per figure 3: This option Is identical to the first option In ail respects with the exception of the positions of the heating/cooling sources (hot/cold environments) and the thermaily Insulated/conductlve areas. In the analysis of this option losses are also lgnored, dimension proportions and force field are as per the first option. The circuit Is, for sîmplicïty of the explanation, completely thermaily insuiated, with the exception of a heat exchange area at station 33-33’ for heating and another one at 31-32 for cooling, as necessary. The circuit Inciudes a load at 33-34 which Is nowthe same as 3'-1 and it ls thermaily Insuiated, converting the energy it receives from the flow of the particies to useful output energy. The heating and cooling, as necessary are therefore taking place In the hot/cold columns respectively which has the following conséquences: while In the first configuration option the energy of an m_{l) mass flowing upwards In 33-33' would hâve a constant total value anywhere

-15along the flow path with Its energy components changing their value relative to each other gradually along the path, but not their total value, In the second option It Is not so. In the second configuration option, to this constant total energy value of m_(t) Is added the Input heat from the now thermally non insulated walls. This Input heat Is added to the m_(l) energy level gradually In a way that the total heat added to an m^mass from entry at station 33 to exit at station 33', which is also the point of entry into the load, Is defined as Q^and to allow for comparison, parallel to 02^(1) from the first option.

The same thing is applicable to the fluid in the cold column: while in the first configuration option the energy of an m_(t) mass flowing downwards In 31-32 would hâve a constant total value anywhere along the flow path with Its energy components changing their value relative to each other gradually along the path, but not their total value, in the second option it Is not so. In the second configuration option, from this constant total energy value of m^ is removed the output heat from the now thermally non Insulated walls. This output heat is removed from the m^ energy level gradually In a way that the total heat output from an m_(t)mass from entry at station 31, which now Is also the point of exit from the load.to exit at station 33', is defined as Qouw.and to allow for comparison, parallel to from the first option. In the second option 32-33 Is Insulated and perpendicular to the force field and the energy of In station 32 Is equal to Its energy In station 33.

In steady state, at any given point in time, even though the energy in each of the columns is variable along the flow path by cause of the heat flow, the total energy values of the whole fluid In the columns are quantifiable: Total fluid présent In channel 33-33’(also, the hot column) relative to 31 and to 33', Total fluid in channel 31-32 (also, the cold column) relative to 31 and to 33’, Total fluid présent in channel 33-33’ relative to 33 and to32 , Total fluid présent In channel 31-32 relative to 32 and to 33, may be represented as follows:

Where: variables Eh3i , Ecsi, Eh32 , Ec32, Eh other, Ecother, Ephsi ,Eph32. mn, me, R a, V, P3331, Pm-34 , K , Ph V340), Ekiiûj , Ekwm. U33·, ρ₃3·, Ρ34, Par, Pm hâve the sa me meaning as per the first heating configuration, hcls the distance between station 31 and the center of mass me, of the fluid in the cold column applicable to quantify its potential energy relative to 31. h_H is the distance between station 33* and the center of mass, m_Hl of the fluid in the hot column applicable to quantify its potential energy relative to 33*. Ehsiîq ,Εαι_(ι) The average energy values, relative to station 31 (or 33’), of an m_(l) mass portion situated in the hot and cold column respectively. E^i) theoreucai is the energy differential between the energy of m_(lj in 33' to the energy of m_(l) in 31, calculated on the basis of the energy equliibrium In the process In steady state and law of conservation of energy appiied between 33' and 31. It Is also the same as this calculated value for E33'-3i(t), Ea3’.₃4(t). Eout(tyeai is the energy differential between the energy of m_(l) in 33' to the energy of m_(l) In 31, calculated on the basis of the energy density drop on the load

-16and law of conservation of energy applied between 33’ and 31 for the process In steady state. It Is also the same as this calculated value for £33 -31(^. Esa^t). Qm^ heat Input added to the fluid In 33-33', being the energy différentiel between that of m_(l) In station 33 and that of m_{1) In station 33’ In steady state. Q^t) heat output removed from the fluid in 31-32, being the energy différentiel between thet of m₍₁) In station 31 and that of m_{t) in station 32 In steady state. p_c, Ph are average densities of m_c ,m_H, In the cold/hot columns respectively. η Is the efficiency of the process, being the ratio between the useful output work E^tj produced over a period of time t, and the heat Input over the same time, Q_in<t)·

45. Eh31 ⁼ EHothef EpH3l= EnotheT ΓΠηΘ IIr

46. Ec31 = Ecother EpC31⁼ Ecothef ΠΠοθ hc

47. Eh32 = EHothef*· EpH32⁼ ^Rother + ΓΠκθ (R- hn)

48. Ec32 ” Ecother ⁺ EpC32⁼ Ecothef^{+ m}c3 (R-hc)

49. Er32/V= Ec32/V which are the energy densities of the overali fluid in 31-32 relative to 32 and the overali fluid In 33-33' relative to 33 (also to 32) are equai as there Is no load to cause energy denslty differential.

50. [EHothef ⁺ niRa (R- Ι1κ)]/ν= [Ecother*· ^mc3 (R-hc))/V

51. From above, Ec_other= Er^ + p_HV a (R-h_H)-p_cVa (R-h_c), (m_H= p_HV, m_c= PcV)

52. Eh3i/V- Ecai/V - E₃(t)/V33’(t)- E^t/V^t) ⁼[ Er other* ΓΠπθ hn]/V - [Ecother ^mc3 hcl/V=[ Er othefp_HV a hn- Enother- PhV a (R- h_H)+ p_cV a (R-h_c)+ p_cV a h_c]/V= (Pc-Ph) a R=0-Ph/Pc) Pc a R

53. E33>^i{t).E33^_t)⁼E33(t)-Esgt)

54. E₃2^3(t)-0 ; E32(t)⁼ E₃3(_t)

The average energy value, relative to station 31 (or 33*), of an m_w mass portion situated In the hot column:

55. Er31(₍)= Er3i (nrï(t)/ m r)

The average energy value, relative to station 31 (or 33'), of an m_(l) mass portion situated In the coid column:

56. Ecagtjr Eci (m_{t/ m c)

For the simplicity of the représentation, since In/out heat flow pattern along the columns is complex and dépends on many variables, the Input heat will Initially be assumed to be added to m(_t) along the flow path 33-33' at a rate that would allow the average energy of m₍₍) in the column to Include ZQ^j. Same for the cold column: The output heat wili be assumed to be removed from m_(t) along the flow path 31-32 at a rate that would aliow the average energy of

-17m_(t) in the column to Include -ZQ_Mt)· Z Is a positive number smaller than 1 and represents the heat flow pattern to each of the columns: When the majority of heat transfers near fluld’s point of entry to the column after entry, Z Is higher and vice versa.The heat In/out flow are the conséquence of a warmer environment outslde, near 33-33’ and, as necessary, a colder environment outslde, near 31-32.

57. Eout(t)= Eî3'^i(t)=E33'(tj-E3i(Q

58. E3t(tj-Q_0Ut(t)⁺Qin(i)=E33-(_l)

59. Therefore : Eq^^ θιτχο ^_Qout(t)

60. Eh31(1>~ ^33(1) +ZQ_ln(t)

61. Ec3i(t)= E3i(t)-ZQout(t)⁼ E3î(o ⁺(1*Z)Qout(t)⁼ E₃₃(₍) +(1-Z)Qout(t)

62. Eh31(o -Ec3i(t)= Z(Qin(t)- Qout(t))⁺(2Z-1 ) Qo^t)

Therefore, In steady flow :

63· Eout(t) theoreUcal =( 1/Ζ)[(Εη31(ι) ·Εθ31(ΐ))- (2Z-1) Qout(t)l⁼ (1^) [(^t) /V)( Ph¹ EHother *Pc ’ Ecolher) a(hH- hc) - (2Z-1 ) Qout(tJ⁼ (1/Z)[m(t)(1-pH/pc)[ K(Ph/ Ph)+ a(R- h_H)+ u_H ²/2] - (2Z-1 ) 0^)1

This means that If Z is equal to 1, the resuit represents the same conditions as per the flrst configuration option, by which for each process cycle, ali the heating of the fluid Is done before entering the hot column at station 33 and ali the cooling of the fluid Is done before entering the cold column at station 31. The flrst option Is therefore, itself, a private case of the second configuration option, and Its resuit would be:

64. Qout(t)⁼ (1/1 )frn(t)(1-pH/pc)[ K(Ph/ Ph)+ a(R- Hh)⁺ Uh²/2] - (2-1) QoutttJ

65. Qirxt)= [m₍,)(1-pH/pc)[ K(Ph/ Ph)+ a(R- h_H)+ u_H ²/2]

Z, of course, can be tweaked to be two different variables, one for the heat Input and one for the heat output adjusting them separately to optimlze practical process performance. To represent, In a simplified manner the efficiency, a Z=0.5, common to both columns, will be hereafter used as an example:

66. Eoutct) β™*»!*·] -2(Εη31(() -Ec3i(t)) ⁼ 2(m(t) /V)( Ρη'¹ Εηο^ -Pc*¹ Ec other )- γπ(Ι) a(hw- hc) =2ΠΠ(,)(1PhM K(Ph/ Ph)+ a(R- h_H)+ u_H ²/2]

This Calculated as per law of conservation of energy and on the basis of energy density drop on the load, practical usefui output:

67. EouKtjreai ⁼E33'(t)-E3i(t) -( KP33· V33(t)+EKIn33'⁺Ep ) — (KP34 V^t) +Εκΐη34⁺Ερ )= V33-(t) (KP33· + Ρ33· U33·² /2)- V^t)(KP4 + P34 U34² /2) ⁼V33(t) (KP33' + P33· U33·² /2)- V34(t)(KP33' + P33· U33² /2-(1-Ph/Pc) Pc a R)= =(KP33- + Pî3’ U33·² /2)( V33'(t)- V_W))+ (1-Ph/Pc) Pc a R) V3^_t)⁼m(t) (1- p37 P4)( KP33·/ P33· + U33·² /2)+ ( pc/ p34)m(t) (1-pH/pc)a R

68. Qjn(t)⁼ Eout(t)+ 2 (En31(t) ’Ec31(t))⁺ Qoutft)

In order to quantify the efficlency In conséquence of the practica! conditions : Εου^ι Is always equal to Eoutftxbeoretjcai provided there Is output heat Qo^) in 31-32 which Is at the necessary level to sustain the steady state of the process. However, for a 100% efficlency theoretlcal process the following condition applies: Eou^xheweucai = Qw) and therefore for that theoretical process, would be equal to zéro.

The efficlency can therefore be defined as the ratio between practica! useful output energy and Input heat Q^t) in a theoretlcal perfect efficlency process;

69. η= Εοϋφχββΐ/ Qm(t) = {^m(t) (1- Pm·/ P34X KP33·/ P33' + u33·² /2)+ ( Pc/ P34)^m(tj (1^_Pi7pc)^a R) / {2m_(tï(1-pH/pc)[ K(Ph/ Ph)+ a(R- h_H)+ u_H ²/2]J or, in the approximated version, as per option 1:

70. q= a R/{2< mn’¹ E_HolhM+ a(R- h_H)))= a R/2(Tot+aR) <1/2, (when 2=(1/2))

Summary of some main requlrements to optlmally reproduce the process In a practica! apparatus :

- The fluid sub-populations In 1-2 and 3-3' respectively 31-32 and 33-33' need to be exposed to equal field strengths. The accumulative force applied by the conservative force field, spécifie to the apparatus, In the direction 1 to 2 and 3' to 3 respectively 31 to 32 and 33’ to 33, varies In corrélation with, or, Is proportlonal to, the number of the mobile particles constituting the fluid sub population. Maximal field strength.

- The température of the fluid impacts its density

- 1-2, 3-3'; 31-32, 33-33' are equal in length

- Adapted load Ideally positioned in 3’-4; 33'-34.

- Conducting channels allowing for minimal résistance to flow of the mobile particles and allowing the other hereln requlrements.

- No net interaction between mobile particles' flow in steady state and the force field.

Requlrements for the application of the process to real and effectively conservative flelds: The process, as a prerequlsite subjects the mobile particles to a non-zero conservative field. Some fields, such as constant Electric field and Gravity are stralght-forward and are manifested In Inertial référencé frame. Others, such as centrifuga! and, magnetic (as for example variable magnetic field or magnetic field acting on a moving electric charge), require spécifie conditions to reproduce the conservative nature of their force field, as it pertains to the

-19process, but once these conditions are met, these fields can be consldered by the process as effectively conservative.

In such conditions the process can be reproduced as per the principles presented in this paper.

In figures 5 to 8 are presented four examples of the process under four different force fields:

subjected to gravitational, centrifugal, described In prior art documents and electric and magnetic fields. In ali four examples the process Is presented In a relevant reference frame: gravitational and electric In inertial reference frame, centrifugal In rotating reference frame and magnetic in translationai reference frame, which In this case Is an Inertial reference frame with glven translationai velocity of the channels perpendicuiar to the magnetic field lines. The choice 10 of reference frame used for the magnetic field Is one example out of many options slnce its effective conservative nature for the process can be reached in translationai, rotational or other motion of the System or even In immobile System subjected to an electromagnetic force field, In which the electromagnetic field strength is variable over time, a wave.

The particles In the example circuits 1-2-3-3'-4 are ali, each in its appropriate reference frame, 15 subjected to a conservative force field by which each particle changes Its potentiai energy relative to a point In the reference frame as It flows from 1 to 2 and from 3 to 3', and once a full cycle Is completed, for example from 1, around the circuit, back to 1, the particles’ potentiai energy Is unchanged.

in the two latter examples, In addition to the conservative force éléments acting with or against 20 the flow, the fields apply, forces which ad to decelerate, or, accelerate, (depending on the fluid flow diredion in the channel), the channels’ movement perpendicuiar to the flow. In steady state, by having the same mass moving In one direction as In the other, not changing the mass distribution in the System, over time, these forces cancei out each other completely.

While the conservative forces ad on the two populations, on one in their flow diredion and on 25 the other, against their flow direction, the strength of these forces dépends on their total quantity In each group and therefore dépends on their denslty and for a non-zero density différentiel between the columns, their total is not zéro.

For the forces acting perpendicuiar to the flow, these counter forces dépend on their density but also on their speed and therefore cancei each other out completely this is true in ali private 30 cases as It Is conséquence of the conservation of mass. One group siows the channel velocity and the other accelerates It, having a total effed of zéro.

In any circumstances of operation, whether in moving channels or in Immobile channels subjected to electromagnetic wave field, same size channels, one containing the cold fluid population and the other containing the hot fluid population, flowing In opposite directions:

-20The opposite fluid flow, of equal mass per unit of time flowing in each direction between the two sub populations, renders the flow’s total energy exchange with the force field (or with its source) to be zéro. Once this prlnciple is established, In the chosen référencé frame, these fields can be analyzed as directional, conservative force fields acting on the mobile particles with the circuit being 1-2-3-3'-4-1 , performance optimized by equal iength1-2, 3-3' channels. To be noted that these forces, perpendicular to the flow do hâve an effect on the particles distribution along the channels* cross section, a factor that may influence the effective cross channel section area, A, and may affect channel losses. Once taken into account, however this effect can be rendered negligible and in any event, It does not change the counter force mutua! cancellation and does not change the zéro net energy exchange between the fluid flow and the field, In steady state. The type of conservative force applicable to each circuit replacing the generic F=ma used in this paper dépends on the type of force field/particles in each spécifie case as for example F=qE +qBu, F= γπΩ²γ, F= mg.

The efficiency in both configuration options may be analyzed from the point of view of the overall fluid’s rotational accélération characteristic in the force field resulting In certain conditions in unstable behavlon

For first configuration option:(figure1): The whole fluid manifests asymmetric rotational inertial behavior relative to the référencé frame and has therefore a tendency to accelerate in a rotational motion, aiong the circuit. This means that to hâve steady state, the load needs to présent a counter force, equal to the one accelerating It and therefore a pressure differential, Independently from effects of variation In directional kinetic energy, slnce in steady state the station to station kinetic energy variations hâve neither accelerating nor decelerating effect, on the fluid In the circuit 1-2-3-3’-4 as a whole. which is identical to the pressure differential Imposed by the coiumns. This would make the calculation of the efficiency behave as follows:

The energy density differential Em/V- Eci/V is equal to (1-Ph/Pc) Pc a R· in the process's clrcumstances It is also pure pressure differential, as it is the resuit of a static force on the fluid's sub populations caused by the conservative force field:

71. AF₃-i=AF₃’4=m_ca-mHa=mc(1- pu/ Pc)a= PcV(1- pd pc)a

72. AP₃-i-AP₃'4⁼(mca-m_Ha)/A=(mc(1- pd pc)a)/A= (pcV(1- Ph/ Pc)a)/A=( 1-Ph/Pc) Pc a R

This force and conséquent pressure differential is the force/pressure differential required to zéro the overall rotational accélération tendency, of the whole fluid population. It is a requirement of the steady state being of steady flow velocity. The variations of the directional kinetic energy from station to station in steady state do not influence this force differential as the flow of the fluid as a whole.does not change any of Its parameters over time and therefore does not interact with this force, which, viewed in the process’s référencé frame Is static and

-21tangentlal to the flow circuit, acting on the fluid as a whole by conséquence of the conservative force field.

The fluid situated in 3', of mass m₍₁₎is at pressure which Is the conséquence of the interaction between the fluid band 4-1-2-3-3’ (which Is of tendency to accelerate towards 3' )and the load.

The fluid In 4 of same mass nri(i), Is at pressure which is the conséquence of the Interaction between the same fluid band 4-1-2-3-3’(whlch is of tendency to accelerate away from 4 ) and the ioad. The pressure differential between these two stations is (1-pH/pc) Pc a R regardless of the variations in températures, volumes or velocities of the spécifie m^ masses situated in 3’ and 4 In steady state but dépends rather on the process's overall equilibrium.

Therefore: the efficiency, as per thls requlrement would behave as:

73. η'= Qî-3(()⁼[( KPy Vsaj+Exins+Ep ) - (KP4 +Εχΐη4+Ερ )]/ Q2-3(t)⁼ [Vjft) (KP3· + p₃· U3·² /2)- V4ft)(KP₄ + p₄U₄ ² /2))/ 02-3(0= [Vyft) (KP3·⁺ P3'U3·² /2)- V^tjiKfPs- (1-pb/Pc) Pc θ R )+ p4u4² /2)]/ Q2-3(t)⁼ [KPsÎVjjt)- V^tj) +( Pc/ P4)Km(l; (1-pH/pc)^ R+ m(t) u3² /2- m(t; u₄ ² /2]/ Q₂^o Therefore :

74. η - [m₍o (1- p₃·/ p₄)( KP₃-/ p₃)+ m_(l} (1- p₃·²/ p4²)(u3·² /2)+( pc/ p4)Kmw (1-pH/pc)a R] / [m((}(1Ph/PcX KPr/ Ph- a hH+ uH²/2) + m(t)(1-pH/pc) aR]

In Its approxlmate form, on the basls of hlgh pressure and density, strong force field, m_(t) (1p₃·/ p₄)( KP₃·/ p₃)+ m₍Q (1- p₃·²/ p4²)(u3² /2) gets smaller and if, on basls of these criteria, considered negligible, pc/ p₄consldered close to 1, the approximate form of the η' becomes:

75. η'= [Ka R]/ (Tôt + aR] In such an event in conditions of strong enough force field, the state will be stable up to a given threshold level by which η-1. Passed thls ievel the state will not be stable and excess requlred energy necessary to reach the appearance of η’>1 would be taken from the field, for the unstable transition and from the fluid causlng the progressive cooling of the System until efficiency drops (real efficiency Is not exceeding parity. In the non steady state transition, in the energy input are particlpating the externat field and the fluid’s energy previous to additional heat Input) to regalnlng steady state. Thls would mean an effective one source System with no additional cooling requlred from an extemal colder environment and/or without requîring a portion of the useful output energy to be used for additional cooling of the System as may be requlred by the analysis of η. Such one source resuit would be in contravention of the second law of Thermodynamlcs.

For the second configuration option (figure 3), as per the Z=0.5 example, this becomes:

76. η'= [Ka R]/ 2|Tot + aR]

The process in conditions by which the mobile particies* temperature-density is Inversed, when Increasing fluid’s température Increases Its density: In such conditions, the process Works as per the same principles, provided direction of the force fieid is inverted. An Important conséquence would be that in these circumstances, on the load, the expansion effect by reason 5 of loss of pressure, acts in the same way as the température drop due to the output of energy through 3’-4 or 33’-34: they both act to reduce the density.

A portion of the useful output energy at 4 or 24 or 34 or 44 may be fed back to cooi the mobile particies as necessary to maintain steady state.

In case the coollng of the flow during its passage through the Load at 23-24 or 43’- 44 (figures 10 2, 4) 1s suffirent it Is not necessary to cool further the flow after the station 24 or 34 and In this case the section 24-21 or 41-42 are also isolated as no heating exchange for cooling by a colder environment outside the circuit is necessary.

Claims (5)

1. A process producing useful energy from thermal energy, characterized In that a fluldîc overall population of mobile partlcles confined to an unldirectional flow closed circuit of conducting channels (1-2-3-3’-4-1;31-32-33-33’-34-31) Is subjected to a conservative or effectively conservative force field with the exception of centrifugal and gravitational force field, the circuit being thermally insulated with the exception of two non juxtaposed areas a first area (2-3;33-33’) allowing thermal exchange for heating (Q,_n) from a warmer environment outside the circuit, a second area (4-1;31-32) allowing thermal exchange (Qou) for cooling, as necessary, by a colder environment outside the circuit, In that said closed circuit is provided with a load (3’-4;33'-44) designed to convert the energy It recelves from the mobile particles flow to a useful output energy located In the flow direction after the first non Insulated area (2-3;33-33’), in that In two portions of the unidirectional circuit located before (3-3’;33-33’) and after (1-2;31-32) said load, flow velocity vector Is parallel or has a component which is parallel to the conservative or effectively conservative force fieid one portion with a warm flow and the other portion with a cool flow of mobile partlcles and In that if the density of the chosen mobile particles decreases when the température Increases, the direction of the conservative force fieid is the same as that of the cool flow velocity vector or of a cool flow velocity vector component In the said circuit portion and the Inverse If the density of the chosen mobile particles increases when the température Increases.

2. The process according to clalm 1, characterized in that the length of each of the said two non Insulated thermally areas varies as necessary.

3. The process according to clalm 1 or 2, characterized In that a portion of the useful output energy is fed back to cool the mobile particles as necessary to malntaln steady state.

4. The process according to cialm 1 or 2 or 3, characterized In that the mobile particles are particles which are free to move in the circuit channels and may be of any type: electrically charged or not as électrons, ions, electrically neutral atoms, molécules, and may be in any state such as idéal or degenerate gas, liquid, solid, seml solid plasma, superconductor.

5. The process according to one of the clalms 1 to 4, characterized In that the conservative or effectively conservative force field is electric (E) or magnetic.