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