Sharif University of Technology

1
Sharif University of Technology
School of Mechanical Engineering
2
THERMAL CONDUCTIVITY
OF

LIQUIDS
GASES
3
PRESENTED BY
BEHRANG SADJADI
SUPERVISED BY
Dr. S. KAZEMZADEH
4
Contents
5
Introduction
6
Kinetic Theory of Gases

• The molecules are rigid and non-attracting
  sphere.
• All the molecules travel with the same speed W.
• The volume of molecules is negligible.

7
Ultra-simplified Theory
8
Ultra-simplified Theory
9
Ultra-simplified Theory
10
Ultra-simplified Theory
Deviations of thermal conductivity of various
gases calculated with ultra-simplified kinetic
theory from experimental values.
11
Rigorous Kinetic Theory
12
Rigorous Kinetic Theory
13
Rigorous Kinetic Theory
14
Rigorous Kinetic Theory
15
Rigorous Kinetic Theory

• Spherical molecules with negligible volume
• Binary collisions
• Small gradients

16
Rigorous Kinetic Theory
17
Rigorous Kinetic Theory
18
Rigorous Kinetic Theory
19
Rigorous Kinetic Theory
20
Rigorous Kinetic Theory
21
Rigorous Kinetic Theory
Deviations of thermal conductivity of various
monoatomic gases calculated with rigid sphere
model from experimental values.
22
Rigorous Kinetic Theory
Deviations of thermal conductivity of various
monoatomic gases calculated with Lennard-Jones
model from experimental values.
23
Rigorous Kinetic Theory
Deviations of thermal conductivity of various
polyatomic gases calculated with Lennard-Jones
model from experimental values.
24
Dense Gases

• By considering only two-body collisions and by
  taking into account the finite size of the
  molecules Enskog was able to graft a theory of
  dense gases onto the dilute theory developed
  earlier!

25
Dense Gases

• Flow of molecules

• Flow of molecules
• Collisional transfer

26
Dense Gases

• If Y is collisions frequency factor and y
  defines as

• It can be shown that

• y is determined from experimental p-V-T data and
  b calculated from other properties like viscosity.

27
Dense Gases
Deviations of thermal conductivity of nitrogen
calculated with Enskog theory of dense gases from
experimental values.
28
Liquids
29
Liquids

• But for most liquids c is greater than W by
  factors ranging from 5 to 10.

30
Liquids

• For liquids

• Which is similar to Bridgman empirical relation.

31
Liquids
Comparison between the thermal conductivity of
various liquids calculated with Eyring theory and
experimental values.
32
Liquids
Deviations of thermal conductivity of various
liquids calculated with Eyring theory from
experimental values.
33
Empirical Correlations
34
Empirical Correlations
35
Generalized Charts
36
Further Discussion

• Rigid ovaloids
• Rough spheres
• Loaded spheres

37
Conclusion
Experimental techniques are unavoidable in study
of natural phenomena and theoretical approaches
can just reduce the required experiences.
Transport properties of dilute gases can be
predicted suitably for relatively simple
molecules.
Transport properties of dense gases and liquids
can be predicted just in limited cases.
The appropriate theory for transport phenomena of
polar molecules has not yet been developed.
38
References
1 Hirschfelder, J.O., Curtiss, C.F., Bird, R.B,
Molecular theory of gases and liquids, John Wiley
Sons, 1954. 2 Tsederberg, N.V., Thermal
conductivity of gases and liquids, Translated by
Scripta Technica, Edited by D. Cess, Cambridge
M.I.T. Press, 1965. 3 Bridgman, P.W., The
physics of high pressure, Dover Publications,
1970. 4 Loeb, L.B., The kinetic theory of
gases, Dover Publications, 1961. 5 Kincaid,
J.F., Eyring, H., Stearn, A.E., The theory of
absolute reaction rates and its application to
viscosity and diffusion in the liquid state,
Chemical Reviews, 1941, Vol.28, pp.301-365.
39
(No Transcript)
40
Ultra-simplified Theory