Title :THERMAL TRANSFER AND FLUID MECHANICS IN THE THEORY OF ETHER Author:Thierry DELORT Date:1 st May 2013

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1 Title :THERMAL TRANSFER AND FLUID MECHANICS IN THE THEORY OF ETHER Autho:Thiey DELORT Date: st May 03 Abstact: In a pevious aticle (), we pesented a vey complete cosmological theoy of ethe. In this aticle we bing complements to this cosmology. In paticula we study fluid mechanics fo a spheical concentation of ethe-substance moving inside the integalactic ethesubstance. We make also appea kinds of adius fo a galaxy and we establish the evolution as a function of time of the st kind. We also veify a simple elation between the adius of the milky way at an age of the univese equal to 5 billion yeas. We also study the themal tansfe linked to the motion of a galaxy inside the integalactic ethe-substance (ethesubstance occupying the space between galaxies)..introduction In a pevious aticle (), we exposed a vey geneal Cosmological theoy of ethe. In this aticle, we saw that a (spial) galaxy could be modeled as a spheical concentation of ethe-substance moving inside the space. A pioi we could expect that a consequence of the motion of such a concentation of ethe-substance inside the integalactic ethe-substance should lead to a change of mass and of velocity of this concentation. We ae going to study this phenomenon in the pesent aticle. Moeove we will see that we can define diffeent kinds of adius fo a galaxy, the st one being the adius of the spheical concentation of ethe-substance, called etheed adius of the galaxy. We ae going to study the evolution as a function of time of this etheed adius, and we will veify a vey simple elation that must exist between the adius in the case of the milky way. Also we will see that the themal model used to obtain the Tully-Fishe s law must be modified if we want to take into account the motion of the galaxy, but that with a simple appoximation ou themal model emains valid. We emind that this Cosmological theoy of ethe is a pat of a vey geneal theoy of ethe, exposed in the efeences ()(3) and in aticles published by the same autho in the eview Physics Essays. Nonetheless, the Cosmological theoy of ethe exposed in the aticle () and in the pesent aticle can be undestood and stands by itself..motion OF A GALAXY INSIDE THE INTERGALACTIC ETHER-SUBSTANCE We could think that a spheical concentation of ethe-substance such as a galaxy (o close to a sta) moving inside the integalactic ethe-substance should be baked o be modified in mass because of the ethe-substance suounding this concentation. In fact, we have phenomena that we ae going to justify futhe: A.The moving spheical concentation of ethe-substance keeps its mass. B.The moving spheical concentation of ethe-substance keeps its velocity: It is not baked no acceleated; Indeed, let us conside a spheical concentation of ethe-substance (cente O) diven with a velocity V inside the integalactic ethe-substance. Let us conside S, suface of a disk of the sphee having its cente in O, the plane of the disc being pependicula to V. Then in an inteval of time dt, we have the phenomena: C.A volume SVdt of ethe-substance is absobed by the spheical concentation.(in font of the sphee).

2 D.A volume SVdt is emitted by the spheical concentation (to the back of the sphee). Moeove we emak that the emitted and the absobed volume have the same velocity and the same density. Then the points A and B appea to be consequences of the points C and D and of the last emak. 3.BARYONIC AND ETHERED RADIUS OF A GALAXY We know that the galaxy Andomeda is appoximately at.5 billions yea-light of ou galaxy the milky way. We conside fo instance the case of the milky way in ode to pesent the kinds of adius of a galaxy. We emind that we consideed if is the distance to the cente O of a galaxy, that the expession of the density of ethe-substance ρ() is, k 3 being a constant: k3 ρ ( ) = () So we obtain, M being the mass of the sphee having its cente in O and a adius : M()=4πk 3 () Consequently, v being the velocity of a sta at a distance of O: v = = 4πk 3G (3) Consequently: v k = 3 4πG (4) We know also that if ρ 0 is the density of the integalactic ethe-substance, then the adius R of the concentation of ethe-substance constituting the galaxy is given by the expession: k3 ρ ( R ) = = ρ (5) R Consequently: k3 R = = v (6) ρ 4πG 0 0 We will call R the etheed adius of the consideed galaxy. Let ρ 0 (5) be the density of the integalactic medium when the age of the univese was 5 billion yeas, and ρ 0 (5) at an age of 5 billion yeas (pesently). We know that if f is the facto of expansion of the univese between 5 and 5 billion yeas (we know that f=3, see the aticle () : ρ 0 (5)=ρ 0 (5)/f3 (7) So in a (spial) galaxy we have diffeent kinds of adius: The st kind of adius, called etheed adius, is the adius of the concentation of ethesubstance. The nd kind of adius is the adius of the disc containing all the stas. We will call bayonic adius this second kind of adius. We emak that at a given time, the etheed adius must be geate than the bayonic adius. We can define B (5) as the pesent bayonic adius of the milky way. We know that B (5) is appoximately equal to yeas light. If R(5) is the pesent etheed adius of the milky

3 way, we could assume that R(5) is appoximately 0 times geate than B (5) (appoximately yeas light): R(5)=0 B (5) (8) Of couse we ignoe the eal value of R(5), bu ou hypothesis gives a possible acceptable value. Let B (5) be the bayonic adius of the milky way when the age of the Univese was 5 billion yeas. Consideing that the bayonic adius inceases with time, we have the elation: B (5) B (5) (9) Moeove, using the equation (7), we obtain: R(5)=R(5)/5= B (5) (0) Using the equation (9) and (0) we obtain that at an age of the Univese of 5 billion yeas, the etheed adius was geate than the bayonic adius: B (5) R(5) () We emak that the pevious elation would emain tue fo a galaxy with the same etheed adius but with a bayonic adius twice geate than the adius of the milky way. (We just take B (5) equal to yeas light and eplace the equation (8) by the equation: R (5)=5 B (5)). Ou model is valid if we conside that the definitive etheed adius is eached when the Univese was 5 billion yea old, o late. 4.THERMAL TRANSFER TO A MOVING GALAXY We emak that the phenomena of absoption and of emission of ethe-substance by a galaxy that we descibed in the Chapte modifies the themal equilibium that we used in the aticle () in ode to obtain the Tully-Fishe s law. We emak that we can conside that the absoption and the emission of ethesubstance by a galaxy leads to a themal tansfe defined by a powe ε(t) dissipated by the galaxy. (Obviously, ε(t) depends on the etheed adius of the moving galaxy, its velocity and the density of the integalactic ethe-substance). If we make the appoximation that ε(t) is negligible compaed with the powe emitted by the bayons of a galaxy towads the ethe-substance, than we can keep the themal model used to obtain the Tully-Fishe s law. 5.CONCENTRATION OF ETHER-SUBSTANCE AROUND STARS AND PLANETS It is logical to assume that because of gavitation, a concentation of ethe-substance occus aound planets and stas. Let us fo instance conside the sun with a mass M. The equation of equilibium is, fo an element of ethe-substance with a density ρ(), a width d, a suface ds situated at a distance fom O the cente of the sun, P() being the pessue at this distance of O: ρ( ) dds P( + d) ds P( ) ds + = 0 () 3

4 We emind () that we have P()=k ρ() with k =k 0 T, T tempeatue of the concentation of ethe-substance. So we obtain, solving easily the pevious diffeential equation: ρ ( ) = K exp( ) (3) k It is logical to assume that if ρ 0 is the density of the ethe-substance suounding the concentation of ethe-substance linked to the sun, K=ρ 0. So we have: ρ ( ) = ρ0 exp( ) (4) k We want now to obtain the adius of the concentation of ethe-substance linked to the sun.let R be this adius. It is logical to assume, as we did fo a galaxy in the aticle (), that ρ(r) is vey close to ρ 0. Fo instance we have ρ 0 ρ(r) ρ 0 (+ε 0 ). We obtain immediately that this condition is equivalent, appoximately to: = ε (5) k R With 0 ε ε 0. So we obtain: R = (6) k ε The themal equation of equilibium between the concentation of ethe-substance linked to the sun (Tempeatue T) and the suounding ethe-substance (Tempeatue T 0 ), is,using the convective themal tansfe that we used in the aticle () : 4πR h(t-t 0 )=KM (7) We emind () that h(t-t 0 ) is the expession of the convective flow and KM is the powe emitted by the bayons towads the ethe-substance. With the appoximation T 0 <<T we obtain: G M 4π ht = KM (8) k ε T 4πG Mh = (9) Kε k 0 Kεk0 R = = (0) k0tε 4πGh So we have the emakable esult that R is independent of M. We have also the conditions R 0, 0 adius of the sun and 0 ε ε 0. It is natual to assume that the adius of the concentation of ethe-substance linked to the sun is the minimal possible adius. So we obtain the emakable esult: R= 0 () 4

5 We emind that in Chapte 4 we saw that some enegy was dissipated because of the absoption and emission of some ethe-substance linked to the sun due to its motion. Again, if ε(v,t,r,ρ 0 ) is the dissipated powe, we can make the assumption: ε(v,t,r,ρ 0 )<<KM. But we emak that even if we have not this elation, the enegy dissipated by the concentation of ethe-substance linked to the sum is completely eceived by the suounding ethe-substance. Consequently the net emitted powe emains KM. It is impotant to ealize that the tempeatue of the ethe-substance linked to the sun can be vey geat. Indeed we know that the density of the ethe-substance linked to the sun is appoximately 0 - kg/m 3 density of ou galaxy), and the density of the sun is appoximately equal to 000 kg/m 3. Consequently the atio of those densities is 0-4. Then we see that if the bayons lose 0-0 degees in one second (which coesponds to degees pe yea) then the elevation of tempeatue communicated to the ethe-substance linked to the sun is, supposing that the ethe-substance has the same caloific capacity as odinay matte (pe kg), 0 4 degees, o equivalently hunded thousands billions of degees pe second. If the caloific capacity of ethe-substance is one thousand less than capacity of odinay matte, the communicated tempeatue inceases fom the same facto. We emind that in ou aticle (), we made the hypothesis that the bayons tansmitted some enegy to the ethe-substance suounding them only if thei tempeatue was supeio. This is not possible: We make in fact the hypothesis that bayons tansmit heat to ethesubstance even if thei tempeatue is infeio. We can justify this by the following agument: We can admit that a bayon vibates if it is at any tempeatue (The moe it vibates the highe is its tempeatue). Then the ethe-substance suounding the bayon bakes this vibation and consequently bayons communicate, whateve be thei tempeatue, an enegy to this ethesubstance that is conveted in themal enegy. 6.TEMPERATURE OF THE INTERGALACTIC ETHER-SUBSTANCE In ou aticle (), we made the hypothesis that it existed a convective tansfe fom the Univese (constituted of ethe-substance) towads the nothingness suounding it. So the flow F emitted by the univese can be expessed as the expession F=hT, T tempeatue of the integalactic ethe-substance. It is easy to veify that if we took the constant h used fo the tansmission of heat fom ethe-substance towads ethe-substance (Fo instance equation (7)), then we would obtain a vey high tempeatue of the integalactic ethe-substance. So in fact we think that h, used fo themal tansfe between the integalactic ethe towads the nothingness is infinite. Then we obtain a tempeatue of the integalactic ethe-substance equal to 0 o vey close to 0, at any age of the Univese. 7.CONCLUSION So we obtained the vey inteesting esult that the motion of a spheical concentation of ethe in the integalactic space does not alte its mass no its velocity. Moeove we defined diffeent adius fo a galaxy, the etheed adius and the bayonic adius. We veified in the case of the milky way that the etheed adius must be geate that the bayonic adius at a given age of the Univese. We also established the evolution as a function of time of the etheed adius. We also made an impotant appoximation in the themal model pemitting to obtain the Tully-Fishe s law. Refeences:.Thiey Delot, Ethe, dak matte and topology of the Univese, open achives Vixa, Intenet achives (03). 5

6 .Thiey Delot, Théoies d o 5e edition, Editions Books on demand, Pais (03) 3.Thiey Delot, Theoy of ethe, Physics Essays 3,4 (000) 4.D.J Raine,E.G Thomas, An intoduction to the science of Cosmology, Institute of Physics, London (00) 5.J.V Nalika, An intoduction to Cosmology, Cambidge Univesity pess, Cambidge (00) 6