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Lecture notes in Fluid Dynamics
(1.63J/2.01J)
by Chiang C. Mei, MIT
CHAPTER 4. THERMAL EFFECTS IN FLUIDS
4-1-2energy.tex
4.1
Heat and energy conservation
Recall the basic equations for a compressible uid. Mass conservation requires that :
t +
q = 0
(4.
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Lecture notes in Fluid Dynamics
(1.63J/2.01J)
by Chiang C. Mei, MIT
4-6selw-therm.tex
4.6
Selective withdrawl of thermally stratied uid
[References]:
R.C. Y. Koh, 1966 J. Fluid Mechanics, 24, pp. 555-575.
Brooks, N. H., & Koh, R. C. Y., Selective withdr
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Lecture notes in Fluid Dynamics
(1.63J/2.01J)
by Chiang C. Mei, MIT
4-6dispersion.tex
[Refs]:
1. Aris:
2. Fung, Y. C. Biomechanics
4.7
Dispersion in an oscillatory shear ow
Relevant to the convective diusion of salt and/or pollutants in a tidal channel,
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Lecture notes in Fluid Dynamics
(1.63J/2.01J)
by Chiang C. Mei, MIT
4-3MTwind.tex
4.3
Buoyancy-driven convection - The Valley Wind
ref: Prandtl: Fluid Dynamics.
Due to solar heating during the day, a mountain slope may be warmer than the surrounding air
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Lecture notes in Fluid Dynamics
(1.63J/2.01J)
by Chiang C. Mei, MIT
4- 2approx.tex
4.2
4.2.1
Approximations for small temperature variation
Mass conservation and almost incompressibilty
Recall the law of mass conservation:
1 D
=
Dt
q
Let the time scale
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Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
5-1KHinstab.tex
5.2
5.2.1
Kelvin-Helmholz Instability for continuous shear
and stratication
Heuristic reasoning
Due to viscosity, shear ow exists along the boundary of a jet, a wake or
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Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
CHAPTER 6.
SEEPAGE AND THERMAL EFFECTS
IN POROUS MEDIA
6-1darcy-EM.tex
Applications : Groundwater ow and transport, building insulation, energy storage and recovery, geothermal reservo
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Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
Refs: Benoussan, Lions, & Sanchez-Palencia, Asymptotic Analysis of Periodic Structures.
North-Holland, 1978.
Mei : Mathematical analysis in Engineering, Cambridge , University Press. 1
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Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
6-7double-di.tex
6.7
Thermohaline instability in a porous layer
-doubly-diusive instability
[Refs]: Porous Media:
Cheng, Ping, 1978. Heat Transfer in Geothermal Systems, Advances in He
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Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
6.6
Rayleigh-Darcy (or Horton-Rogers-Lapwood) instability in a porous layer
6-6-Lapwood.tex
Nield & Bejan, Chapter 6 Convection in Porous Media
Related: Rayleigh-Bernard Problem (Chand
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Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
6-3SaTay.tex
6.3
Saman-Taylor instability in porous layer- Viscous
ngering
Refs:
P. G. Saman & G. I. Taylor, 1958, The penetration of a uid into a porous medium or
Hele-Shaw cell conta
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Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
5.4
Viscous eects on the instability of parallel ow
The instability of parallel ows (in pipes, channels, boundary layers, jet wakes, plumes) is
important to understand the transition t
1
Lecture Notes on Fluid Dynamics
(1.63J/2.21J)
by Chiang C. Mei, 2002
5.3
Inviscid instability mechanism of parallel ows
We now turn to an older problem of the instability of parallel ow without stratication and
gravity, such as channel ows, jets, wakes