| Topic: |
Science > Physics |
| User: |
"John Schutkeker" |
| Date: |
02 May 2007 12:01:21 AM |
| Object: |
Viscous Heating |
Has the theory of viscous heating of an ordinary fluid been developed?
.
|
|
| User: "Greg Neill" |
|
| Title: Re: Viscous Heating |
02 May 2007 05:55:53 AM |
|
|
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9924A6A4FBlkajehoriuasldfjknak@207.115.33.102...
Has the theory of viscous heating of an ordinary fluid been developed?
What's "an ordinary fluid"? What's not?
Joule measured the mechanical equivalent of heat using
frictional heating in a fluid in about 1845.
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
02 May 2007 01:58:34 PM |
|
|
"Greg Neill" <gneillREM@OVEsympatico.ca> wrote in news:46386dd3$0$30274
$9a6e19ea@news.newshosting.com:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9924A6A4FBlkajehoriuasldfjknak@207.115.33.102...
Has the theory of viscous heating of an ordinary fluid been developed?
What's "an ordinary fluid"? What's not?
The stuff we're familiar with in ordinary life, with no extreme states of
condensed matter or plasmas. I guess I should have said "incompressible
liquid."
Joule measured the mechanical equivalent of heat using
frictional heating in a fluid in about 1845.
Theory, not measurement.
.
|
|
|
| User: "Greg Neill" |
|
| Title: Re: Viscous Heating |
02 May 2007 02:22:03 PM |
|
|
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9924985C53053lkajehoriuasldfjknak@207.115.17.102...
"Greg Neill" <gneillREM@OVEsympatico.ca> wrote in news:46386dd3$0$30274
$9a6e19ea@news.newshosting.com:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in message
news:Xns9924A6A4FBlkajehoriuasldfjknak@207.115.33.102...
Has the theory of viscous heating of an ordinary fluid been developed?
What's "an ordinary fluid"? What's not?
The stuff we're familiar with in ordinary life, with no extreme states of
condensed matter or plasmas. I guess I should have said "incompressible
liquid."
Joule measured the mechanical equivalent of heat using
frictional heating in a fluid in about 1845.
Theory, not measurement.
"Viscous damping", "Hysteretic damping"
.
|
|
|
|
|
|
| User: "Bruce Scott TOK" |
|
| Title: Re: Viscous Heating |
02 May 2007 05:57:03 AM |
|
|
John Schutkeker wrote:
Has the theory of viscous heating of an ordinary fluid been developed?
Are you interested in Navier Stokes fluids (i.e., gasdynamics) or actual
liquids where the quantum physics determines the microproperties?
Yes in both cases though I'm only familiar with the details of the
first. Have a look at _Physical Kinetics_ in the Landau/Lifshitz
series.
If you're interested in non-equilibrium thermodynamics then there are
several texts on that as well. Look up a book called _Process
Thermodynamics_ for a decent example. I've got it loaned out long
enough to have forgotten the author's name.
--
ciao,
Bruce
drift wave turbulence: http://www.rzg.mpg.de/~bds/
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
02 May 2007 01:56:18 PM |
|
|
Bruce Scott TOK <Use-Author-Supplied-Address-Header@[127.1]> wrote in
news:200705021057.l42Av3iH005381@ipp.mpg.de:
John Schutkeker wrote:
Has the theory of viscous heating of an ordinary fluid been developed?
Are you interested in Navier Stokes fluids (i.e., gasdynamics) or
actual liquids where the quantum physics determines the
microproperties?
AFAIK, Navier-Stokes (NS) is just a momentum balance equation, making me
ask, since when don't liquids obey the same force balances on a
differential fluid element as gasses? If that's true, what momentum
equation replaces NS, in the incompressible liquid case you mentioned?
There should be only one equation, and it's NS, although the viscosity
may be a complicted function, rather than a constant. But it should
still be NS, shouldn't it?
I'm interested in a fluid whose properties are hardly even known:
planetary mantles and cores, like Earth and Enceladus. Nobody
knows exactly what are those fluid properties, raising a whole 'nother
theory question that I plan to gloss over.
I'm thinking that under such high pressures, Enceladus' "mantle" may be
a highly viscous liquid, which might be something like a solution of
liquids like N2, NH3, and CH4, etc. Unfortunately, it may also be the
mixture of solid/liquid phases that we colloquially know as "slush."
Whichever it is, I'm betting that it's a highly viscous liquid, more
like a paste or a putty, than what we're used to. Since nobody knows
anything about it, I'll have to just say that it seems obvious enough
that quantum effects will dominate the viscosity, and not hard-body
collisions, like a compressible gas.
Yes in both cases though I'm only familiar with the details of the
first. Have a look at _Physical Kinetics_ in the Landau/Lifshitz
series.
I'm planning to get stared by taking the momentum equation and
applying P = F dot v. A viscous force of F = mu Del^2 v, gives P = v mu
del^2 v, and (ha ha) all that's needed is the velocity profile. Again,
I'm sure I can make some primitive assumptions from known tidal
geometries, to get started, but the next correction would involve
self-consistent flows, which is a whole 'nother physics problem to
solve.
I might try my hand at that one, once I've got the zero order model down
on paper. For that, I'll need the tidal force field of a body under
tidal distortion. Where would you look for that, if you had to?
If you're interested in non-equilibrium thermodynamics then there are
several texts on that as well. Look up a book called _Process
Thermodynamics_ for a decent example. I've got it loaned out long
enough to have forgotten the author's name.
Thanks, that sounds very useful.
.
|
|
|
| User: "dlzc" |
|
| Title: Re: Viscous Heating |
02 May 2007 03:23:20 PM |
|
|
Dear John Schutkeker:
On May 2, 11:56 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
Bruce Scott TOK <Use-Author-Supplied-Address-Header@[127.1]> wrote innews:200705021057.l42Av3iH005381@ipp.mpg.de:
....
Are you interested in Navier Stokes fluids (i.e.,
gasdynamics) or actual liquids where the quantum
physics determines the microproperties?
AFAIK, Navier-Stokes (NS) is just a momentum
balance equation, making me ask, since when don't
liquids obey the same force balances on a
differential fluid element as gasses?
Navier Stokes works with viscosity, which is an energy loss term.
If that's true, what momentum equation replaces
NS, in the incompressible liquid case you mentioned?
It depends you your simplifications from NS.
There should be only one equation, and it's NS,
although the viscosity may be a complicted function,
rather than a constant.
Having viscosity a function of the flow field only makes it more
complex. But you are already talking about an insoluble PDE without
simplifying assumptions. So it just adds to computation time for a
numerical solution.
But it should still be NS, shouldn't it?
I believe so, yes.
I'm interested in a fluid whose properties are hardly
even known: planetary mantles and cores, like Earth
and Enceladus. Nobody knows exactly what are
those fluid properties, raising a whole 'nother theory
question that I plan to gloss over.
I'm thinking that under such high pressures,
Enceladus' "mantle" may be a highly viscous liquid,
which might be something like a solution of liquids
like N2, NH3, and CH4, etc. Unfortunately, it may
also be the mixture of solid/liquid phases that we
colloquially know as "slush."
Any permanent features on the surface? Something like the "Great Red
Spot" of Jupiter notwithstanding...
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
02 May 2007 06:50:01 PM |
|
|
dlzc <dlzc1@cox.net> wrote in
news:1178137400.518483.81940@c35g2000hsg.googlegroups.com:
On May 2, 11:56 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
Bruce Scott TOK <Use-Author-Supplied-Address-Header@[127.1]> wrote
There should be only one equation, and it's NS,
although the viscosity may be a complicted function,
rather than a constant.
Having viscosity a function of the flow field only makes it more
complex. But you are already talking about an insoluble PDE without
simplifying assumptions. So it just adds to computation time for a
numerical solution.
Of course there will be simplifying assumptions, probably based on
Reynolds number. Right mow, my intiution says laminar flow, but of
course that will have to be checked. If it's turbulent or transitional,
I'm not sure what to do, but I think that there are some empirical
models for the spectrum, right?
I'm not sure what to do abut the dissipation in that case, but wouldn't
it be something if tidal flows in the mantle (Earth or Enceladus) turned
out to be turbulent. I don't think it'll happen, because I'm predicting
that fluid in there to be extremely thick.
A turulent flow would be much more efficient at heating, and we observe
that there's healthy quantity of heat being generated in there. Less
for Enceladus, of course, but possibly still enough to make a lot of
liquid water under the crust of a frozen moon.
I need the pressure profiles.
Any permanent features on the surface? Something like the "Great Red
Spot" of Jupiter notwithstanding.
Nope, idealized case, for now, including just fluid layers, and not the
crust. The idea is to see whether crustal or interior losses dominate.
I'd have to assume a boundary condition at the crust.
But thanks for the red spot insight. These planets aren't gas giants,
but I don't know if that makes the issue go away. I wonder if the
presence of a surface crust would be enough to suppress that.
.
|
|
|
| User: "N:dlzc D:aol T:com \dlzc" |
|
| Title: Re: Viscous Heating |
02 May 2007 07:43:41 PM |
|
|
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9924C9C5D2357lkajehoriuasldfjknak@207.115.33.102...
....
Of course there will be simplifying assumptions, probably based
on
Reynolds number. Right mow, my intiution says laminar flow,
but of
course that will have to be checked. If it's turbulent or
transitional,
I'm not sure what to do, but I think that there are some
empirical
models for the spectrum, right?
I would look to heating models of aircraft wings. The leading
edge impact would be non-similar, but shear drag over the surface
woudl be what you are looking for.
Any permanent features on the surface? Something like the
"Great Red Spot" of Jupiter notwithstanding.
Nope, idealized case, for now, including just fluid layers, and
not the
crust. The idea is to see whether crustal or interior losses
dominate.
I'd have to assume a boundary condition at the crust.
But thanks for the red spot insight. These planets aren't gas
giants,
but I don't know if that makes the issue go away. I wonder if
the
presence of a surface crust would be enough to suppress that.
If you are requiring an entirely fluid surface (???), then you
must have some vortex... if not two. One would expect them at /
near the poles. Unlike Jupiter.
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
03 May 2007 10:31:10 PM |
|
|
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in news:Vea_h.233935
$115.32853@newsfe10.phx:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9924C9C5D2357lkajehoriuasldfjknak@207.115.33.102...
But thanks for the red spot insight. These planets aren't gas
giants,
but I don't know if that makes the issue go away. I wonder if
the
presence of a surface crust would be enough to suppress that.
If you are requiring an entirely fluid surface (???), then you
must have some vortex... if not two. One would expect them at /
near the poles. Unlike Jupiter.
The boundary condition between the mantle and crust makes the vortex
problem go away, but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very grateful. A
man can never read too much math. ?:)
.
|
|
|
| User: "N:dlzc D:aol T:com \dlzc" |
|
| Title: Re: Viscous Heating |
03 May 2007 10:40:46 PM |
|
|
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9925EF47470F2lkajehoriuasldfjknak@207.115.33.102...
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in
news:Vea_h.233935
$115.32853@newsfe10.phx:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9924C9C5D2357lkajehoriuasldfjknak@207.115.33.102...
But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.
If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.
The boundary condition between the mantle and crust
makes the vortex problem go away,
Actually, I think it does not. It would tend to "rotate" the
vortex "neutral axis" to be parallel to any differential rotation
between the core (if any) and the crust.
but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?:)
I have the text that brings this up at work ("5 Golden Rules").
I'll try and remember to post the necessary keywords to see if
you agree with my take on it.
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
17 May 2007 08:33:42 AM |
|
|
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in news:UWx_h.297882
$6P2.209655@newsfe16.phx:
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9925EF47470F2lkajehoriuasldfjknak@207.115.33.102...
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in
news:Vea_h.233935
$115.32853@newsfe10.phx:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9924C9C5D2357lkajehoriuasldfjknak@207.115.33.102...
But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.
If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.
The boundary condition between the mantle and crust
makes the vortex problem go away,
Actually, I think it does not. It would tend to "rotate" the
vortex "neutral axis" to be parallel to any differential rotation
between the core (if any) and the crust.
but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?:)
I have the text that brings this up at work ("5 Golden Rules").
I'll try and remember to post the necessary keywords to see if
you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go digging through your
library, to see if you can find it?
.
|
|
|
| User: "dlzc" |
|
| Title: Re: Viscous Heating |
17 May 2007 04:08:28 PM |
|
|
On May 17, 6:33 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
....
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
.... it may not be explicit enough, however.
Be sure you saw this post too... since you were talking about
Enceladus.
http://groups.google.com/group/sci.astro/msg/e40f3045b2986cda
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
18 May 2007 06:58:21 AM |
|
|
dlzc <dlzc1@cox.net> wrote in news:1179436108.546003.159130
@o5g2000hsb.googlegroups.com:
On May 17, 6:33 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
...
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
... it may not be explicit enough, however.
You realize that you just posted a link to THIS THREAD!!
My copy just arrived in the mail, and it has five sections in it - Game
Theory, Topology, Catastrophe Theory, The Halting Theorem and The
Simplex Method. Perhaps you'd care to specify which section covers
planetary vortices on gas giants.
.
|
|
|
| User: "dlzc" |
|
| Title: Re: Viscous Heating |
18 May 2007 12:12:57 PM |
|
|
Dear John Schutkeker:
On May 18, 4:58 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
dlzc<d...@cox.net> wrote in news:1179436108.546003.159130
@o5g2000hsb.googlegroups.com:
On May 17, 6:33 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
...
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
... it may not be explicit enough, however.
You realize that you just posted a link to THIS THREAD!!
My copy just arrived in the mail, and it has five sections in
it - Game Theory,
Minimax Theory
Topology,
Brouwer Fixed-Point Theory (So I was incorrect in spefiying this one).
Catastrophe Theory,
Morse's Theorem, as I specified. Section "Fluid Flow Between Two
Cylinders", with some "logical reference" back to "topology"
The Halting Theorem and The
Simplex Method. Perhaps you'd care to specify
which section covers planetary vortices on gas giants.
Differential rotation of two solid surfaces with a fluid trapped
between them.
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
19 May 2007 07:25:35 AM |
|
|
dlzc <dlzc1@cox.net> wrote in news:1179508377.257593.168080
@e65g2000hsc.googlegroups.com:
Dear John Schutkeker:
On May 18, 4:58 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
dlzc<d...@cox.net> wrote in news:1179436108.546003.159130
@o5g2000hsb.googlegroups.com:
On May 17, 6:33 am, John Schutkeker <jschutke...
@sbcglobal.net.nospam>
wrote:
...
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
... it may not be explicit enough, however.
You realize that you just posted a link to THIS THREAD!!
My copy just arrived in the mail, and it has five sections in
it - Game Theory,
Minimax Theory
Topology,
Brouwer Fixed-Point Theory (So I was incorrect in spefiying this one).
Catastrophe Theory,
Morse's Theorem, as I specified. Section "Fluid Flow Between Two
Cylinders", with some "logical reference" back to "topology"
Those subsections are Crumpling Paper, Taylor's Tayl, Tugging Taylor's
Tayl, Look Alikes, Morse's Theorem, Thom's Theorem, Bridges & Beams,
Bifurcations Catastrophes & Equilibria, How Local Is Local, Shape of
Things, Laughs & Cries
Perhaps you'd care to specify which section covers planetary vortices on
gas giants.
.
|
|
|
| User: "N:dlzc D:aol T:com \dlzc" |
|
| Title: Re: Viscous Heating |
19 May 2007 11:07:50 AM |
|
|
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns993555C5BFD75lkajehoriuasldfjknak@207.115.33.102...
dlzc <dlzc1@cox.net> wrote in news:1179508377.257593.168080
@e65g2000hsc.googlegroups.com:
Dear John Schutkeker:
On May 18, 4:58 am, John Schutkeker
<jschutke...@sbcglobal.net.nospam>
wrote:
dlzc<d...@cox.net> wrote in news:1179436108.546003.159130
@o5g2000hsb.googlegroups.com:
On May 17, 6:33 am, John Schutkeker <jschutke...
@sbcglobal.net.nospam>
wrote:
...
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
... it may not be explicit enough, however.
You realize that you just posted a link to THIS THREAD!!
My copy just arrived in the mail, and it has five sections in
it - Game Theory,
Minimax Theory
Topology,
Brouwer Fixed-Point Theory (So I was incorrect in spefiying
this one).
Catastrophe Theory,
Morse's Theorem, as I specified. Section "Fluid Flow
Between Two Cylinders", with some "logical reference" back
to "topology"
Those subsections are Crumpling Paper, Taylor's Tayl, Tugging
Taylor's Tayl, Look Alikes, Morse's Theorem, Thom's Theorem,
Bridges & Beams, Bifurcations Catastrophes & Equilibria,
How Local Is Local, Shape of Things, Laughs & Cries
Perhaps you'd care to specify which section covers planetary
vortices on gas giants.
I assumed you knew to look at the section I named, "Fluid Flow
Between Two Cylinders", in Morse's Throem section, could read
between the lines, and could confirm or deny what I thought I saw
there. I guess you are denying. If you think it talks about gas
giants, it doesn't. My fluid mechanics books don't talk about
flowing oxygen gas in an annulus between two electrodes, with
corona being made in it... but they expect us to "adapt and
overcome".
Sorry to have made you waste $8 plus shipping.
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
19 May 2007 02:17:02 PM |
|
|
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in news:fhF3i.253377
$ZA5.121774@newsfe15.phx:
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns993555C5BFD75lkajehoriuasldfjknak@207.115.33.102...
dlzc <dlzc1@cox.net> wrote in news:1179508377.257593.168080
@e65g2000hsc.googlegroups.com:
Dear John Schutkeker:
On May 18, 4:58 am, John Schutkeker
<jschutke...@sbcglobal.net.nospam>
wrote:
dlzc<d...@cox.net> wrote in news:1179436108.546003.159130
@o5g2000hsb.googlegroups.com:
On May 17, 6:33 am, John Schutkeker <jschutke...
@sbcglobal.net.nospam>
wrote:
...
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
... it may not be explicit enough, however.
You realize that you just posted a link to THIS THREAD!!
My copy just arrived in the mail, and it has five sections in
it - Game Theory,
Minimax Theory
Topology,
Brouwer Fixed-Point Theory (So I was incorrect in spefiying
this one).
Catastrophe Theory,
Morse's Theorem, as I specified. Section "Fluid Flow
Between Two Cylinders", with some "logical reference" back
to "topology"
Those subsections are Crumpling Paper, Taylor's Tayl, Tugging
Taylor's Tayl, Look Alikes, Morse's Theorem, Thom's Theorem,
Bridges & Beams, Bifurcations Catastrophes & Equilibria,
How Local Is Local, Shape of Things, Laughs & Cries
Perhaps you'd care to specify which section covers planetary
vortices on gas giants.
I assumed you knew to look at the section I named, "Fluid Flow
Between Two Cylinders", in Morse's Throem section, could read
between the lines, and could confirm or deny what I thought I saw
there. I guess you are denying. If you think it talks about gas
giants, it doesn't. My fluid mechanics books don't talk about
flowing oxygen gas in an annulus between two electrodes, with
corona being made in it... but they expect us to "adapt and
overcome".
Sorry to have made you waste $8 plus shipping.
I see it now, although, for some reason, it's not listed in the Table of
Contents.
.
|
|
|
|
|
|
|
| User: "dlzc" |
|
| Title: Re: Viscous Heating |
18 May 2007 09:55:52 AM |
|
|
Dear John Schutkeker:
On May 18, 4:58 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
dlzc<d...@cox.net> wrote in news:1179436108.546003.159130
@o5g2000hsb.googlegroups.com:
On May 17, 6:33 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
...
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
... it may not be explicit enough, however.
You realize that you just posted a link to THIS THREAD!!
Yes. I couldn't believe that I had to.
My copy just arrived in the mail, and it has five sections
in it - Game Theory,
Topology,
... in which Morse's theorem plays a star role.
Catastrophe Theory, The Halting Theorem and The
Simplex Method. Perhaps you'd care to specify which
section covers planetary vortices on gas giants.
Topology. If you have differential motion in a fluid on a closed
surface, you must have at least one vortex.
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
18 May 2007 10:02:52 AM |
|
|
dlzc <dlzc1@cox.net> wrote in news:1179500152.241628.260870
@l77g2000hsb.googlegroups.com:
Dear John Schutkeker:
On May 18, 4:58 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
dlzc<d...@cox.net> wrote in news:1179436108.546003.159130
@o5g2000hsb.googlegroups.com:
On May 17, 6:33 am, John Schutkeker <jschutke...
@sbcglobal.net.nospam>
wrote:
...
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
It's not in "5 Golden Rules." Would you care to go
digging through your library, to see if you can find it?
It *is* in "5 Golden Rules":
http://groups.google.com/group/sci.physics/msg/8f991988e68b5d7a
... it may not be explicit enough, however.
You realize that you just posted a link to THIS THREAD!!
Yes. I couldn't believe that I had to.
My copy just arrived in the mail, and it has five sections
in it - Game Theory,
Topology,
.. in which Morse's theorem plays a star role.
Catastrophe Theory, The Halting Theorem and The
Simplex Method. Perhaps you'd care to specify which
section covers planetary vortices on gas giants.
Topology. If you have differential motion in a fluid on a closed
surface, you must have at least one vortex.
There's nothing there. Check the book.
.
|
|
|
|
|
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
04 May 2007 07:27:37 AM |
|
|
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in news:UWx_h.297882
$6P2.209655@newsfe16.phx:
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9925EF47470F2lkajehoriuasldfjknak@207.115.33.102...
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in
news:Vea_h.233935
$115.32853@newsfe10.phx:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9924C9C5D2357lkajehoriuasldfjknak@207.115.33.102...
But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.
If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.
The boundary condition between the mantle and crust
makes the vortex problem go away,
Actually, I think it does not. It would tend to "rotate" the
vortex "neutral axis" to be parallel to any differential rotation
between the core (if any) and the crust.
I'll bet you $500 that you can't prove it mathematically for either
Earth or Enceladus, your choice. If you can do it reliably, you can get
your name in the papers, for making the next insanely great discovery.
but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?:)
I have the text that brings this up at work ("5 Golden Rules").
I'll try and remember to post the necessary keywords to see if
you agree with my take on it.
I have the sequel, although not the original, but since it's only $30,
maybe it's time to whip out the ol' debit card. If you'd e-mail me
scans, I'd kiss your hand, because my artihitis has kept me away from
the library for over a year now.
.
|
|
|
| User: "dlzc" |
|
| Title: Re: Viscous Heating |
04 May 2007 09:21:10 AM |
|
|
Dear John Schutkeker:
On May 4, 5:27 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
"N:dlzcD:aol T:com \(dlzc\)" <d...@aol.com> wrote in news:UWx_h.297882
$6P2.209...@newsfe16.phx:
Dear John Schutkeker:
"John Schutkeker" <jschutke...@sbcglobal.net.nospam> wrote in
message
news:Xns9925EF47470F2lkajehoriuasldfjknak@207.115.33.102...
"N:dlzcD:aol T:com \(dlzc\)" <d...@aol.com> wrote in
news:Vea_h.233935
$115.32...@newsfe10.phx:
"John Schutkeker" <jschutke...@sbcglobal.net.nospam> wrote in
message
news:Xns9924C9C5D2357lkajehoriuasldfjknak@207.115.33.102...
But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.
If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.
The boundary condition between the mantle and crust
makes the vortex problem go away,
Actually, I think it does not. It would tend to "rotate"
the vortex "neutral axis" to be parallel to any differential
rotation between the core (if any) and the crust.
I'll bet you $500 that you can't prove it mathematically
for either Earth or Enceladus, your choice.
I don't bet. As George Dishman could attest, I also don't do math
(well).
If you can do it reliably, you can get your name in the
papers, for making the next insanely great discovery.
but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?:)
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
I have the sequel, although not the original, but since
it's only $30, maybe it's time to whip out the ol' debit
card. If you'd e-mail me scans, I'd kiss your hand,
because my artihitis has kept me away from
the library for over a year now.
That sucks. I will not violate copyright.
However the appropriate section talks about Morse's Theorem; talks
about fluid flow around / between two cylinders (non-concentric...
parallel rollers); glances briefly across Thom Classification Theorem;
then talks about bifurcations, catastrophes, and equilibria. I am
pretty sure I read this section as *requiring* a rotating fluid over a
closed 2D surface, to have at least one "knot"... a vortex or other
anomaly.
As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't see how
it could not also apply. It might limit the size, or constrain the
location, but ...
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
06 May 2007 07:02:20 PM |
|
|
dlzc <dlzc1@cox.net> wrote in news:1178288470.465507.163000
@n59g2000hsh.googlegroups.com:
Dear John Schutkeker:
On May 4, 5:27 am, John Schutkeker <jschutke...@sbcglobal.net.nospam>
wrote:
"N:dlzcD:aol T:com \(dlzc\)" <d...@aol.com> wrote in
news:UWx_h.297882
$6P2.209...@newsfe16.phx:
Dear John Schutkeker:
"John Schutkeker" <jschutke...@sbcglobal.net.nospam> wrote in
message
news:Xns9925EF47470F2lkajehoriuasldfjknak@207.115.33.102...
"N:dlzcD:aol T:com \(dlzc\)" <d...@aol.com> wrote in
news:Vea_h.233935
$115.32...@newsfe10.phx:
"John Schutkeker" <jschutke...@sbcglobal.net.nospam> wrote in
message
news:Xns9924C9C5D2357lkajehoriuasldfjknak@207.115.33.102...
But thanks for the red spot insight. These planets
aren't gas giants, but I don't know if that makes the
issue go away. I wonder if the presence of a surface
crust would be enough to suppress that.
If you are requiring an entirely fluid surface (???), then
you must have some vortex... if not two. One would
expect them at / near the poles. Unlike Jupiter.
The boundary condition between the mantle and crust
makes the vortex problem go away,
Actually, I think it does not. It would tend to "rotate"
the vortex "neutral axis" to be parallel to any differential
rotation between the core (if any) and the crust.
I'll bet you $500 that you can't prove it mathematically
for either Earth or Enceladus, your choice.
I don't bet. As George Dishman could attest, I also don't do math
(well).
If you can do it reliably, you can get your name in the
papers, for making the next insanely great discovery.
but if you'd still be willing to point my way to a page
that works the math for a free fluid surface, I'd be very
grateful. A man can never read too much math. ?:)
I have the text that brings this up at work ("5 Golden
Rules"). I'll try and remember to post the necessary
keywords to see if you agree with my take on it.
I have the sequel, although not the original, but since
it's only $30, maybe it's time to whip out the ol' debit
card. If you'd e-mail me scans, I'd kiss your hand,
because my artihitis has kept me away fromthe library
for over a year now.
That sucks.
Yeah, it slows me down badly. I haven't been to the library for
eighteen months, but fortunately I've had other important things to do.
I'm just finishing a good project now, so I have no choice, because I
can't very well send it to a jourbal without having all my references in
proper order.
I think I've figured out a way to get over the hump, but I won't know
until I test it. Maybe I'll have to get used to the idea of being
incapacitated for a few days after every library trip. Time will
tell...
I will not violate copyright.
It's "personal use," and neither one of us is asking for money. But I
just ordered it on Amazon for $8, shipping included, so there's no
reason to quarrel. I'll pony up $8 without batting an eye, but it's the
$65 (used) textbooks that I think long and hard about.
Textbooks are a friggin' racket, and if their prices were lower, science
would advance a *lot* faster.
However the appropriate section talks about Morse's Theorem; talks
about fluid flow around / between two cylinders (non-concentric...
parallel rollers); glances briefly across Thom Classification Theorem;
then talks about bifurcations, catastrophes, and equilibria. I am
pretty sure I read this section as *requiring* a rotating fluid over a
closed 2D surface, to have at least one "knot"... a vortex or other
anomaly.
As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't see how
it could not also apply. It might limit the size, or constrain the
location, but ...
I don't think that the surfaces rotate differentially. The mantle just
carries the crust.
.
|
|
|
| User: "N:dlzc D:aol T:com \dlzc" |
|
| Title: Re: Viscous Heating |
06 May 2007 07:42:48 PM |
|
|
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9928CBE417A35lkajehoriuasldfjknak@207.115.33.102...
dlzc <dlzc1@cox.net> wrote in news:1178288470.465507.163000
@n59g2000hsh.googlegroups.com:
....
That sucks.
Yeah, it slows me down badly. I haven't been to the library
for
eighteen months, but fortunately I've had other important
things to do.
I'm just finishing a good project now, so I have no choice,
because I
can't very well send it to a jourbal without having all my
references in
proper order.
I think I've figured out a way to get over the hump, but I
won't know
until I test it. Maybe I'll have to get used to the idea of
being
incapacitated for a few days after every library trip. Time
will
tell...
I will not violate copyright.
It's "personal use," and neither one of us is asking for money.
But I
just ordered it on Amazon for $8, shipping included, so there's
no
reason to quarrel. I'll pony up $8 without batting an eye, but
it's the
$65 (used) textbooks that I think long and hard about.
Textbooks are a friggin' racket, and if their prices were
lower, science
would advance a *lot* faster.
Thought I'd zoom by my local college's bookstores. Thought I'd
pick up some used stuff for fairly cheap... like I used to "20
years ago". That is the price of limited readership, but *damn*.
However the appropriate section talks about Morse's Theorem;
talks
about fluid flow around / between two cylinders
(non-concentric...
parallel rollers); glances briefly across Thom Classification
Theorem;
then talks about bifurcations, catastrophes, and equilibria.
I am
pretty sure I read this section as *requiring* a rotating
fluid over a
closed 2D surface, to have at least one "knot"... a vortex or
other
anomaly.
As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't
see how
it could not also apply. It might limit the size, or
constrain the
location, but ...
I don't think that the surfaces rotate differentially. The
mantle just
carries the crust.
If you have temperature variation, you will have differential
flow. But you tell "me".
David A. Smith
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
07 May 2007 06:01:59 AM |
|
|
"N:dlzc D:aol T:com \(dlzc\)" <dlzc@aol.com> wrote in news:9Cu%h.295208
$7g3.68031@newsfe14.phx:
Dear John Schutkeker:
"John Schutkeker" <jschutkeker@sbcglobal.net.nospam> wrote in
message
news:Xns9928CBE417A35lkajehoriuasldfjknak@207.115.33.102...
dlzc <dlzc1@cox.net> wrote in news:1178288470.465507.163000
@n59g2000hsh.googlegroups.com:
...
That sucks.
Yeah, it slows me down badly. I haven't been to the library
for
eighteen months, but fortunately I've had other important
things to do.
I'm just finishing a good project now, so I have no choice,
because I
can't very well send it to a jourbal without having all my
references in
proper order.
I think I've figured out a way to get over the hump, but I
won't know
until I test it. Maybe I'll have to get used to the idea of
being
incapacitated for a few days after every library trip. Time
will
tell...
I will not violate copyright.
It's "personal use," and neither one of us is asking for money.
But I
just ordered it on Amazon for $8, shipping included, so there's
no
reason to quarrel. I'll pony up $8 without batting an eye, but
it's the
$65 (used) textbooks that I think long and hard about.
Textbooks are a friggin' racket, and if their prices were
lower, science
would advance a *lot* faster.
Thought I'd zoom by my local college's bookstores. Thought I'd
pick up some used stuff for fairly cheap... like I used to "20
years ago". That is the price of limited readership, but *damn*.
I think that there's racketeering going on, because if prices were
lower, demand would rise.
However the appropriate section talks about Morse's Theorem;
talks
about fluid flow around / between two cylinders
(non-concentric...
parallel rollers); glances briefly across Thom Classification
Theorem;
then talks about bifurcations, catastrophes, and equilibria.
I am
pretty sure I read this section as *requiring* a rotating
fluid over a
closed 2D surface, to have at least one "knot"... a vortex or
other
anomaly.
As to whether it would apply to a fluid trapped between two
differentially rotating surfaces closed 2D surfaces, I don't
see how
it could not also apply. It might limit the size, or
constrain the
location, but ...
I don't think that the surfaces rotate differentially. The
mantle just
carries the crust.
If you have temperature variation, you will have differential
flow. But you tell "me".
I think that the no-slip condition at the boundary will be enough to
suppress it. There may be a lingering, miniscule differential flow, but
not enough to drive something so extreme as a Great Vortex. If it
existed on Earth, seismic measurements would have revealed it by now,
and thermal conditions are much more extreme on earth than Enceladus.
If you're absolutely convinced that I'm wrong, I wholeheartedly
encourage you to start doing the work, because if it turns out you're
right, you can be on the cover of Scientific American. It will give you
a fair shot at a Nobel Prize, but it's not my project, it's yours. Mine
is tidal heating of an sphere that has no vortex.
Even if you're right, I have to solve the simple problem before I can
solve the hard one. Solving the simplified problem will be an important
accomplishment for me, and I'm not going to complicate it so badly that
my project dies.
.
|
|
|
|
|
|
|
|
|
|
|
|
|
| User: "Andy Resnick" |
|
| Title: Re: Viscous Heating |
03 May 2007 09:08:02 AM |
|
|
John Schutkeker wrote:
Bruce Scott TOK <Use-Author-Supplied-Address-Header@[127.1]> wrote in
news:200705021057.l42Av3iH005381@ipp.mpg.de:
John Schutkeker wrote:
Has the theory of viscous heating of an ordinary fluid been developed?
Are you interested in Navier Stokes fluids (i.e., gasdynamics) or
actual liquids where the quantum physics determines the
microproperties?
AFAIK, Navier-Stokes (NS) is just a momentum balance equation, making me
ask, since when don't liquids obey the same force balances on a
differential fluid element as gasses? If that's true, what momentum
equation replaces NS, in the incompressible liquid case you mentioned?
There should be only one equation, and it's NS, although the viscosity
may be a complicted function, rather than a constant. But it should
still be NS, shouldn't it?
The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.
I'm interested in a fluid whose properties are hardly even known:
planetary mantles and cores, like Earth and Enceladus. Nobody
knows exactly what are those fluid properties, raising a whole 'nother
theory question that I plan to gloss over.
But the fluid properties are intimately tied into the resultant flows.
Especially if there are magnetic effects.
I'm thinking that under such high pressures, Enceladus' "mantle" may be
a highly viscous liquid, which might be something like a solution of
liquids like N2, NH3, and CH4, etc. Unfortunately, it may also be the
mixture of solid/liquid phases that we colloquially know as "slush."
Right- that's why it's sometimes better to stick with Cauchy's law
rather than the NS- viscoelastic (or viscoplastic, or any other
constitutive relation you can dream up) materials can be handled in one,
but not the other.
Whichever it is, I'm betting that it's a highly viscous liquid, more
like a paste or a putty, than what we're used to. Since nobody knows
anything about it, I'll have to just say that it seems obvious enough
that quantum effects will dominate the viscosity, and not hard-body
collisions, like a compressible gas.
Pastes are not viscous fluids. Is there a yield stress? And forget
quantum effects- for planetary-scale motions, quantum effects are
useless unless the temperature is near 0 K.
<snip>
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
03 May 2007 10:23:40 PM |
|
|
Andy Resnick <andy.resnick@op.case.edu> wrote in
news:f1cmp2$l2l$1@eeyore.INS.cwru.edu:
John Schutkeker wrote:
AFAIK, Navier-Stokes (NS) is just a momentum balance equation, making
me ask, since when don't liquids obey the same force balances on a
differential fluid element as gasses? If that's true, what momentum
equation replaces NS, in the incompressible liquid case you
mentioned? There should be only one equation, and it's NS, although
the viscosity may be a complicted function, rather than a constant.
But it should still be NS, shouldn't it?
The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.
I'm not familiar with Cauchy's first law of motion. Is it east enough
to wrote down here, or can you give me a link to a page that explains
it?
Whichever it is, I'm betting that it's a highly viscous liquid, more
like a paste or a putty, than what we're used to. Since nobody knows
anything about it, I'll have to just say that it seems obvious enough
that quantum effects will dominate the viscosity, and not hard-body
collisions, like a compressible gas.
Pastes are not viscous fluids. Is there a yield stress? And forget
quantum effects- for planetary-scale motions, quantum effects are
useless unless the temperature is near 0 K.
I believe Scott was saying that viscosity os due to intermolecular
interactions, whose physics is very complex. That complex physics
exists at all temperatures, not just near absolute zero.
.
|
|
|
| User: "Andy Resnick" |
|
| Title: Re: Viscous Heating |
04 May 2007 08:52:47 AM |
|
|
John Schutkeker wrote:
Andy Resnick <andy.resnick@op.case.edu> wrote in
news:f1cmp2$l2l$1@eeyore.INS.cwru.edu:
John Schutkeker wrote:
AFAIK, Navier-Stokes (NS) is just a momentum balance equation, making
me ask, since when don't liquids obey the same force balances on a
differential fluid element as gasses? If that's true, what momentum
equation replaces NS, in the incompressible liquid case you
mentioned? There should be only one equation, and it's NS, although
the viscosity may be a complicted function, rather than a constant.
But it should still be NS, shouldn't it?
The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.
I'm not familiar with Cauchy's first law of motion. Is it east enough
to wrote down here, or can you give me a link to a page that explains
it?
It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.
Whichever it is, I'm betting that it's a highly viscous liquid, more
like a paste or a putty, than what we're used to. Since nobody knows
anything about it, I'll have to just say that it seems obvious enough
that quantum effects will dominate the viscosity, and not hard-body
collisions, like a compressible gas.
Pastes are not viscous fluids. Is there a yield stress? And forget
quantum effects- for planetary-scale motions, quantum effects are
useless unless the temperature is near 0 K.
I believe Scott was saying that viscosity os due to intermolecular
interactions, whose physics is very complex. That complex physics
exists at all temperatures, not just near absolute zero.
Yes, and the beauty of continuum mechanics is that all of that
complexity can be subsumed into a constitutive equation, meaning the
microscopic details can be ignored.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
06 May 2007 06:52:34 PM |
|
|
Andy Resnick <andy.resnick@op.case.edu> wrote in news:f1fa8d$4so$1
@eeyore.INS.cwru.edu:
The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.
I'm not familiar with Cauchy's first law of motion. Is it east enough
to wrote down here, or can you give me a link to a page that explains
it?
It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.
This works for fluids, and not just elastic solids?
.
|
|
|
| User: "Andy Resnick" |
|
| Title: Re: Viscous Heating |
07 May 2007 09:01:18 AM |
|
|
John Schutkeker wrote:
Andy Resnick <andy.resnick@op.case.edu> wrote in news:f1fa8d$4so$1
@eeyore.INS.cwru.edu:
The NS equation*s* are for the *conservation* of momentum, and are a
simplification of Cauchy's first law of motion. To solve the general
flows you describe, one also needs the conservation of mass equations
and the conservation of energy equations.
I'm not familiar with Cauchy's first law of motion. Is it east enough
to wrote down here, or can you give me a link to a page that explains
it?
It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.
This works for fluids, and not just elastic solids?
Yes. The key is what you write down for the stress tensor. For
Newtonian fluids, off the top of my head, T = pI + m(grad[V] +
grad[V]^trans), where p is the pressure, I the unit tensor, m the
viscosity, grad[V] the velocity gradient, and the final term is the
transpose of the tensor grad[V].
For other materials, simply write down the stress tensor, whatever you
choose it to be, and off you go.
--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.
|
|
|
| User: "John Schutkeker" |
|
| Title: Re: Viscous Heating |
07 May 2007 02:53:45 PM |
|
|
Andy Resnick <andy.resnick@op.case.edu> wrote in
news:f1n7s7$kk9$1@eeyore.INS.cwru.edu:
John Schutkeker wrote:
Andy Resnick <andy.resnick@op.case.edu> wrote in news:f1fa8d$4so$1
@eeyore.INS.cwru.edu:
The NS equation*s* are for the *conservation* of momentum, and are
a simplification of Cauchy's first law of motion. To solve the
general flows you describe, one also needs the conservation of mass
equations and the conservation of energy equations.
I'm not familiar with Cauchy's first law of motion. Is it east
enough to wrote down here, or can you give me a link to a page that
explains it?
It's quite simple to write: D(pv)/Dt = div(T) + F, where p is the
density, v the velocity, D/Dt the material derivative, T the stress
tensor, and F the body force.
This works for fluids, and not just elastic solids?
Yes. The key is what you write down for the stress tensor. For
Newtonian fluids, off the top of my head, T = pI + m(grad[V] +
grad[V]^trans), where p is the pressure, I the unit tensor, m the
viscosity, grad[V] the velocity gradient, and the final term is the
transpose of the tensor grad[V].
For other materials, simply write down the stress tensor, whatever you
choose it to be, and off you go.
I found this paper (http://tinyurl.com/ywp8vr), which looks like it's
saying the same thing that you are. Do you have any dispute with the
basic equations for Cauchy's Law and the Newtonian stress tensor, and
would you be able to tell me which textbook you used to study this
material?
.
|
|
|
|
|
|
|
|
|
|
|
|
Related Articles |
|
|
