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Viscous Heating
Has the theory of viscous heating of an ordinary fluid been developed? |
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Viscous Heating
"John Schutkeker" wrote in message
. 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. |
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Viscous Heating
Bruce Scott TOK ] wrote in
: 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/Lif****z 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. |
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Viscous Heating
"Greg Neill" wrote in news:46386dd3$0$30274
: "John Schutkeker" wrote in message . 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. |
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Viscous Heating
"John Schutkeker" wrote in message
. 17.102... "Greg Neill" wrote in news:46386dd3$0$30274 : "John Schutkeker" wrote in message . 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" |
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Viscous Heating
Dear John Schutkeker:
On May 2, 11:56 am, John Schutkeker wrote: Bruce Scott TOK ] wrote : .... 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 |
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Viscous Heating
On Wed, 2 May 2007, John Schutkeker wrote:
Has the theory of viscous heating of an ordinary fluid been developed? I was recently reading about free convection driven by isothermal spheres. Heating due to viscosity was mentioned in passed, and in the case being considered, dismissed as negligible. There's probably some number that can sit alongside the Reynolds number, the Grashoff number, and the Nusselt number that tells you whether you can ignore it. It's important in high-speed flows (where there's a lot of kinetic energy available to convert to heat). From attending the occasional talk on scramjets, I get the impression that this kind of heating is what gets the flow to ignition temperatures. The local shock tunnels start off at room temperature and the flow gets hot enough to ionise stuff. If my copy of Anderson was not sitting in a box downstairs, I'd look in it to see if viscous heating is covered. -- Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/ E-prints: http://eprint.uq.edu.au/view/person/...,_Timo_A..html Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html |
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Viscous Heating
dlzc wrote in
ups.com: On May 2, 11:56 am, John Schutkeker Bruce Scott TOK ] 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. |
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Viscous Heating
"Timo A. Nieminen" wrote in
: On Wed, 2 May 2007, John Schutkeker wrote: Has the theory of viscous heating of an ordinary fluid been developed? I was recently reading about free convection driven by isothermal spheres. Heating due to viscosity was mentioned in passed, and in the case being considered, dismissed as negligible. I'm wondering if they used the right viscosities. If the core and mantle are so extremely thick, I'm wondering if they might not be negligible. Something tells me that nobody's ever measured viscosities of liquids under the extreme pressures of a planetary interior. Of course, I could be wrong, in which case I'm wasting time. But I'm more interested in the math and the model as much as the answers, so this is as much for my own edification as it is for a result. There's probably some number that can sit alongside the Reynolds number, the Grashoff number, and the Nusselt number that tells you whether you can ignore it. Thank you. That's a really good point. It's important in high-speed flows (where there's a lot of kinetic energy available to convert to heat). From attending the occasional talk on scramjets, I get the impression that this kind of heating is what gets the flow to ignition temperatures. The local shock tunnels start off at room temperature and the flow gets hot enough to ionise stuff. If my copy of Anderson was not sitting in a box downstairs, I'd look in it to see if viscous heating is covered. I forgot about that, but sonic flows do generate a lot of friction. What's the title of Anderson? |
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Viscous Heating
Dear John Schutkeker:
"John Schutkeker" wrote in message . 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 |
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