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Transport Phenomena II lecture. A breif lecture.
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Thermal Conductivity, k
1
Thermal conductivity is the property of a material that indicates its ability to conduct heat. It has unit W/mK.
Table 9.5-1 (Gases) at 1atm pressureTable 9.5-2 (Nonmetallic Liquids) at saturation pressuresTable 9.5-3 (Liquid Metals) at atmospheric pressureTable 9.5-4 (Solids)
k depends on temperature and pressure (same as )
2Page 265
- For rough estimation only
- Should not be used in the neighborhood of the critical point
- Tc, pc information in Table D.1(Page 738)
Estimation of thermal conductivity under different T and p conditions
Critical Properties
3Table not complete, see page 738
Example
4
Please estimate the thermal conductivity of methane (CH4) at 110.4 atm and 127 F.
Express your answer with SI unit (W/mK).
Fundamental Mechanisms
5
Atomic vibrations and free electron in hotter region transport energy to cooler regions.
6Thermal Conductivity: Comparisoni
n
c
r
e
a
s
i
n
g
k
PolymersPolypropylene 0.12Polyethylene 0.46-0.50 Polystyrene 0.13 Teflon 0.25
vibration/rotation of chain molecules
CeramicsMagnesia (MgO) 38Alumina (Al2O3) 39 Soda-lime glass 1.7 Silica (cryst. SiO2) 1.4
atomic vibrations
MetalsAluminum 247Steel 52 Tungsten 178 Gold 315
atomic vibrations and motion of free electrons
k (W/m-K)Energy Transfer
MechanismMaterial
www.csun.edu/~bavarian/Courses/MSE%20227/Lectures_Exam3/ch17-Thermal_Properties.ppt
Gases k
7
Chapman-Enskog Formula (for monatomic gases)- Model based on rigid, nonattracting spheres of mass m
Eucken Formula (for polyatomic gases)
(9.7-13)
(9.7-15)
8Not complete, see Page 738-739
9Not complete, see Page 740
Example
10
Estimate the thermal conductivity of Argon (Ar) at 100C and atmospheric pressure.
Compare your result with the observed value of 506 10-7 cal/cmsK.
Liquids k
11
Bridgmans Equation: - Derived assuming monatomic liquids, but also show
good agreement for polyatomic liquids
(9.8-3)
(9.8-4)
Example
12
The density of liquid CCl4 at 20 C and 1 atm is 1.595g/cm3, and its isothermal compressibility
is
90.710-6 atm-1. Please estimate its thermal conductivity.
Solids k
13
Usually measured experimentally due to dependence on various factors (crystallite size, degree of molecular orientation, void fraction, etc.)
Wiedemann-Franz-Lorenz Equation:
- ke: electrical conductivity- L: Lorenz number, 22 ~ 29 10-9 volt2/k2 at 0 C and increases
slowly with temperature.- Only for pure metal, because free electrons are the major heat
carriers in pure metals.
(9.9-1)
Composite Solids keff
14
For one solid phase dispersed in a second solid phase, or solids containing pores -> effective thermal conductivity
http://www.ruthtrumpold.id.au/designtech/pmwiki.php?n=Main.ClassifyingMaterials
Maxwell Equation: (9.6-1)
- Only for spherical inclusions- Assuming low volume fraction and
uniform sphere distribution (but okay)
See other correlations in the textbook.Find specific k information in the literature
(9.10-1)
Other Important Properties
15
Thermal diffusivity:
- has the same dimension as kinematic viscosity [L2/T]; - and occur in similar ways in the equations of change for momentum and energy transport
Prandtl number:
Peclet number: Pe = RePr
relative ease of momentum and energy transport
p
kc
Density
Heat capacity at constant pressure
Pr pc
k
rate of advection / rate of diffusion