| Topic: |
Science > Physics |
| User: |
"Dan in Philly" |
| Date: |
22 May 2006 06:40:01 PM |
| Object: |
Fluid Flow vs Heat Transfer |
One type of fluid flow is a shear force: if I lay a sheet of paper on water
and pull it, the top layer of water will move, the water slightly below it
will move less, etc. Lower down the water doesn't move at all. So there is a
profile of decreasing velocity.
Supposedly, fluid flow has analogies in heat transfer. But I can't see any
heat flow that is equivalent to a shear force. (I do see it for more
conventional flows: put pressure on the left side of fluid and it flows
right; put high temperature on the left side of something and the heat flows
right).
So: is there no heat-transfer equivalent to shear force?
Dan in Philly
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| User: "Dan in Philly" |
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| Title: Re: Fluid Flow vs Heat Transfer |
22 May 2006 08:28:51 PM |
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<actionintegral@yahoo.com> wrote in message ...
Hi Dan,
You say "supposedly", but you provide no examples. Please provide an
example. I am interested in learning about heat flow and fluid transfer.
When I studied ChemEng, we learned the equations for: momentum transfer (ie
fluid flow), heat transfer, and (I think) mass transfer (ie diffusion). The
equations for all three looked very similar.
"Timo Nieminen" <timo@physics.uq.edu.au> wrote in message
news:Pine.LNX.4.50.0605231026280.1395-100000@localhost...
There are many analogies. Fluid dynamics and heat flow are both field
theories: in fluid flow, you have a velocity field v(r,t), and in heat
flow, you have a temperature field T(r,t). Many similarities to other
field theories such as acoustics and electrodynamics. In many cases, you
end up with the same PDEs and the same solutions.
Similar doesn't mean identical. v(r,t) is a vector field, T(r,t) is a
scalar field. Perhaps you have found one of those cases where this kind of
difference matters?
That might be it.
More clarification: the example I described had a velocity profile as
follows (shear force applied on top):
---------->
-------->
------>
---->
-->
Moreover, this is (presumably) laminar flow; there is no flow up or down. I
don't see any way to make heat do this. I.e I dont see any way to make heat
flow quickly from left to right on top of an object, and flow more slowly in
the lower parts of the object, and not flow up or down.
I don't know if this comes close. Consider the following solid object
---
| \
| \
| \
------
Apply a high temp to the left vertical side, and a low temp to the right
slanted side. Then there will be fast heat flow across the top, and slower
heat flow futher down. And the isotherms will be horizontal. Does that mean
that the heat flows only horizontally?
Dan in Philly
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| User: "Dan in Philly" |
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| Title: Re: Fluid Flow vs Heat Transfer |
22 May 2006 08:56:02 PM |
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"Dan in Philly" <djr8@aol.com> wrote in message ...
I don't know if this comes close.
On second thought, I don't think it does.
---
| \
| \
| \
------
Apply a high temp to the left vertical side, and a low temp to the right
slanted side. Then there will be fast heat flow across the top, and slower
heat flow futher down. And the isotherms will be horizontal.
Some heat will flow from the lower left to the upper-mid right. I don't
think the isotherms will be horizontal.
Dan in Philly
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| User: "Timo Nieminen" |
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| Title: Re: Fluid Flow vs Heat Transfer |
22 May 2006 11:09:49 PM |
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On Mon, 22 May 2006, Dan in Philly wrote:
"Dan in Philly" <djr8@aol.com> wrote in message ...
I don't know if this comes close.
On second thought, I don't think it does.
---
| \
| \
| \
------
Apply a high temp to the left vertical side, and a low temp to the right
slanted side. Then there will be fast heat flow across the top, and slower
heat flow futher down. And the isotherms will be horizontal.
Some heat will flow from the lower left to the upper-mid right. I don't
think the isotherms will be horizontal.
The fluid shear flow has a non-zero curl (eg you can choose a coordinate
system so that the only non-zero derivate when you take the curl of the
flow field is dV_x/dz, so curl(V) must be non-zero). In an isotropic
medium, heat flow will be in the direction of the temperature gradient, so
the heat flow is proportional to grad(T). curl(grad(T)) is automagically
zero, so at first glance it's geometrically impossible to get a heat flow
of the form of shear flow in a fluid. In an isotropic medium, that is.
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
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| User: "pete" |
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| Title: Re: Fluid Flow vs Heat Transfer |
25 May 2006 05:49:45 PM |
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Dan in Philly wrote:
Supposedly, fluid flow has analogies in heat transfer.
Fluid flow, is the difference between convection and conduction.
It's awkward for me to think of
a component of heat transfer,
as an analogy of heat transfer.
--
pete
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| User: "" |
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| Title: Re: Fluid Flow vs Heat Transfer |
23 May 2006 07:55:52 AM |
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Here is my contribution:
Temperature is a scalar function, pressure is a scalar function. But
when you permit a shear force, you introduce a vector quantity into the
pressure. Pressure becomes stress. That property which made pressure
similar to temperature no longer applies.
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| User: "" |
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| Title: Re: Fluid Flow vs Heat Transfer |
22 May 2006 07:21:12 PM |
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Hi Dan,
You say "supposedly", but you provide no examples. Please provide an
example. I am interested in learning about heat flow and fluid transfer.
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| User: "" |
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| Title: Re: Fluid Flow vs Heat Transfer |
22 May 2006 07:23:17 PM |
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Sorry - I wasn't being facetious. I meant heat transfer and fluid flow.
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| User: "Timo Nieminen" |
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| Title: Re: Fluid Flow vs Heat Transfer |
22 May 2006 07:31:45 PM |
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On Mon, 22 May 2006, Dan in Philly wrote:
One type of fluid flow is a shear force: if I lay a sheet of paper on water
and pull it, the top layer of water will move, the water slightly below it
will move less, etc. Lower down the water doesn't move at all. So there is a
profile of decreasing velocity.
Supposedly, fluid flow has analogies in heat transfer. But I can't see any
heat flow that is equivalent to a shear force. (I do see it for more
conventional flows: put pressure on the left side of fluid and it flows
right; put high temperature on the left side of something and the heat flows
right).
So: is there no heat-transfer equivalent to shear force?
There are many analogies. Fluid dynamics and heat flow are both field
theories: in fluid flow, you have a velocity field v(r,t), and in heat
flow, you have a temperature field T(r,t). Many similarities to other
field theories such as acoustics and electrodynamics. In many cases, you
end up with the same PDEs and the same solutions.
Similar doesn't mean identical. v(r,t) is a vector field, T(r,t) is a
scalar field. Perhaps you have found one of those cases where this kind of
difference matters?
--
Timo Nieminen - Home page: http://www.physics.uq.edu.au/people/nieminen/
E-prints: http://eprint.uq.edu.au/view/person/Nieminen,_Timo_A..html
Shrine to Spirits: http://www.users.bigpond.com/timo_nieminen/spirits.html
.
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| User: "CWatters" |
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| Title: Re: Fluid Flow vs Heat Transfer |
23 May 2006 08:02:00 AM |
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What happens if you apply heating and cooling to two adjacent corners of a
block. The bottom surface being held at room temp......
H______C
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|______|
RT
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| User: "CWatters" |
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| Title: Re: Fluid Flow vs Heat Transfer |
23 May 2006 08:03:38 AM |
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"CWatters" <colin.watters@turnersNOSPAMoak.plus.net> wrote in message
news:447307a8$0$2654$ed2619ec@ptn-nntp-reader01.plus.net...
What happens if you apply heating and cooling to two adjacent corners of a
block. The bottom surface being held at room temp......
H______C
| |
| |
|______|
RT
Ah I take that back. That can't be a correct example because there would be
a vertical heat flow
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