Computational Fluid Mechanics and Heat Transfer Third Edition_19 docx

Some thermophysical propertiesof selected materials A primary source of thermophysical properties is a document in which the experimentalist who obtained the data reports the details and

A Some thermophysical properties

of selected materials

A primary source of thermophysical properties is a document in which

the experimentalist who obtained the data reports the details and results

of his or her measurements The term secondary source generally refers

to a document, based on primary sources, that presents other peoples’

data and does so critically This appendix is neither a primary nor a

sec-ondary source, since it has been assembled from a variety of secsec-ondary

and even tertiary sources.

We attempted to cross-check the data against different sources, and

this often led to contradictory values Such contradictions are usually

the result of differences between the experimental samples that are

re-ported or of differences in the accuracy of experiments themselves We

resolved such differences by judging the source, by reducing the

num-ber of significant figures to accommodate the conflict, or by omitting the

substance from the table The resulting numbers will suffice for most

calculations However, the reader who needs high accuracy should be

sure of the physical constitution of the material and then should seek

out one of the relevant secondary data sources.

The format of these tables is quite close to that established by R M.

Drake, Jr., in his excellent appendix on thermophysical data [A.1]

How-ever, although we use a few of Drake’s numbers directly in Table A.6,

many of his other values have been superseded by more recent

measure-ments One secondary source from which many of the data here were

obtained was the Purdue University series Thermophysical Properties of

Matter [ A.2] The Purdue series is the result of an enormous

property-gathering effort carried out under the direction of Y S Touloukian and

several coworkers The various volumes in the series are dated since

691

1970, and addenda were issued throughout the following decade In more recent years, IUPAC, NIST, and other agencies have been developing critically reviewed, standard reference data for various substances, some

of which are contained in [A.3, A.4, A.5, A.6, A.7, A.8, A.9, A.10, A.11].

We have taken many data for fluids from those publications A third

secondary source that we have used is the G E Heat Transfer Data

Book [ A.12].

Numbers that did not come directly from [A.1], [A.2], [A.12] or the sources of standard reference data were obtained from a variety of man- ufacturers’ tables, handbooks, and other technical literature While we have not documented all these diverse sources and the various compro- mises that were made in quoting them, specific citations are given below for the bulk of the data in these tables.

Table A.1 gives the density, specific heat, thermal conductivity, and thermal diffusivity for various metallic solids These values were ob- tained from volumes 1 and 4 of [A.2] or from [A.3] whenever it was pos- sible to find them there Most thermal conductivity values in the table

have been rounded off to two significant figures The reason is that k

is sensitive to very minor variations in physical structure that cannot be detailed fully here Notice, for example, the significant differences be- tween pure silver and 99.9% pure silver, or between pure aluminum and 99% pure aluminum Additional information on the characteristics and

use of these metals can be found in the ASM Metals Handbook [A.13].

The effect of temperature on thermal conductivity is shown for most

of the metals in Table A.1 The specific heat capacity is shown only at

20◦C For most materials, the heat capacity is much lower at cryogenic

temperatures For example, cp for alumimum, iron, molydenum, and tanium decreases by two orders of magnitude as temperature decreases

ti-from 200 K to 20 K On the other hand, for most of these metals, cp

changes more gradually for temperatures between 300 K and 800 K, ing by tens of percent to a factor of two At still higher temperatures,

vary-some of these metals (iron and titanium) show substantial spikes in cp, which are associated with solid-to-solid phase transitions.

Table A.2 gives the same properties as Table A.1 (where they are able) but for nonmetallic substances Volumes 2 and 5 of [A.2] and also [A.3] provided many of the data here, and they revealed even greater vari-

avail-ations in k than the metallic data did For the various sands reported,

k varied by a factor of 500, and for the various graphites by a factor of

50, for example The sensitivity of k to small variations in the packing of

fibrous materials or to the water content of hygroscopic materials forced

Appendix A: Some thermophysical properties of selected materials 693

us to restrict many of the k values to a single significant figure The

ef-fect of water content is illustrated for soils Additional data for many

building materials can be found in [A.14].

The data for polymers come mainly from their manufacturers’ data

and are substantially less reliable than, say, those given in Table A.1

for metals The values quoted are mainly those for room temperature.

In processing operations, however, most of these materials are taken

to temperatures of several hundred degrees Celsius, at which they flow

more easily The specific heat capacity may double from room

tempera-ture to such temperatempera-tures These polymers are also produced in a variety

of modified forms; and in many applications they may be loaded with

significant portions of reinforcing fillers (e.g., 10 to 40% by weight glass

fiber) The fillers, in particular, can have a significant effect on thermal

properties.

Table A.3 gives ρ, cp, k, α, ν, Pr, and β for several liquids Data

for water are from [A.4] and [A.15]; they are in agreement with IAPWS

recommendations through 1998 Data for ammonia are from [A.5, A.16,

A.17], data for carbon dioxide are from [A.6, A.7, A.8], and data for oxygen

are from [A.9, A.10] Data for HFC-134a, HCFC-22, and nitrogen are from

[A.11] and [A.18] For these liquids, ρ has uncertainties less than 0.2%, cp

has uncertainties of 1–2%, while µ and k have typical uncertainties of 2–

5% Uncertainties may be higher near the critical point Thermodynamic

data for methanol follow [A.19], while most viscosity data follow [A.20].

Data for mercury follow [A.3] and [A.21] Sources of olive oil data include

[A.20, A.22, A.23], and those for Freon 12 include [A.14] Volumes 3, 6,

10, and 11 of [A.2] gave many of the other values of cp, k, and µ = ρν,

and occasional independently measured values of α Additional values

came from [A.24] Values of α that disagreed only slightly with k/ρcp

were allowed to stand Densities for other substances came from [A.24]

and a variety of other sources A few values of ρ and cp were taken

from [A.25].

Table A.5 provides thermophysical data for saturated vapors The

sources and the uncertainties are as described for gases in the next

para-graph.

Table A.6 gives thermophysical properties for gases at 1 atmosphere

pressure The values were drawn from a variety of sources: air data

are from [A.26, A.27], except for ρ and cp above 850 K which came

from [A.28]; argon data are from [A.29, A.30, A.31]; ammonia data were

taken from [A.5, A.16, A.17]; carbon dioxide properties are from [A.6,

A.7, A.8]; carbon monoxide properties are from [A.18]; helium data are

from [A.32, A.33, A.34]; nitrogen data came from [A.35]; oxygen data are from [A.9, A.10]; water data were taken from [A.4] and [A.15] (in agreement with IAPWS recommendations through 1998); and a few high- temperature hydrogen data are from [A.24] with the remainding hydro- gen data drawn from [A.1] Uncertainties in these data vary among the

gases; typically, ρ has uncertainties of 0.02–0.2%, cphas uncertainties of

0.2–2%, µ has uncertainties of 0.3–3%, and k has uncertainties of 2–5%.

The uncertainties are generally lower in the dilute gas region and higher near the saturation line or the critical point The values for hydrogen and for low temperature helium have somewhat larger uncertainties.

Table A.7 lists values for some fundamental physical constants, as given in [A.36] Table A.8 points out physical data that are listed in other parts of this book.

References

[A.1] E R G Eckert and R M Drake, Jr Analysis of Heat and Mass

Transfer McGraw-Hill Book Company, New York, 1972.

[A.2] Y S Touloukian Thermophysical Properties of Matter vols 1–6,

10, and 11 Purdue University, West Lafayette, IN, 1970 to 1975 [A.3] C Y Ho, R W Powell, and P E Liley Thermal conductivity of the

elements: A comprehensive review J Phys Chem Ref Data, 3,

1974 Published in book format as Supplement No 1 to the cited volume.

[A.4] C.A Meyer, R B McClintock, G J Silvestri, and R.C Spencer ASME

Steam Tables American Society of Mechanical Engineers, New

York, NY, 6th edition, 1993.

[A.5] A Fenghour, W A Wakeham, V Vesovic, J T R Watson, J Millat,

and E Vogel The viscosity of ammonia J Phys Chem Ref Data,

24(5):1649–1667, 1995.

[A.6] A Fenghour, W A Wakeham, and V Vesovic The viscosity of

carbon dioxide J Phys Chem Ref Data, 27(1):31–44, 1998.

[A.7] V Vesovic, W A Wakeham, G A Olchowy, J V Sengers, J T R Watson, and J Millat The transport properties of carbon dioxide.

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References 695

[A.8] R Span and W Wagner A new equation of state for carbon

diox-ide covering the fluid region from the triple-point temperature to

1100 K at pressures up to 800 MPa J Phys Chem Ref Data, 25

(6):1509–1596, 1996.

[A.9] A Laesecke, R Krauss, K Stephan, and W Wagner Transport

properties of fluid oxygen J Phys Chem Ref Data, 19(5):1089–

1122, 1990.

[A.10] R B Stewart, R T Jacobsen, and W Wagner Thermodynamic

properties of oxygen from the triple point to 300 K with pressures

to 80 MPa J Phys Chem Ref Data, 20(5):917–1021, 1991.

[A.11] R Tillner-Roth and H D Baehr An international

stan-dard formulation of the thermodynamic properties of

1,1,1,2-tetrafluoroethane (HFC-134a) covering temperatures from 170 K

to 455 K at pressures up to 70 MPa J Phys Chem Ref Data, 23:

657–729, 1994.

[A.12] R H Norris, F F Buckland, N D Fitzroy, R H Roecker, and D A.

Kaminski, editors Heat Transfer Data Book General Electric Co.,

Schenectady, NY, 1977.

[A.13] ASM Handbook Committee Metals Handbook ASM, International,

Materials Park, OH, 10th edition, 1990.

[A.14] R A Parsons, editor 1993 ASHRAE Handbook—Fundamentals.

American Society of Heating, Refrigerating, and Air-Conditioning

Engineers, Inc., Altanta, 1993.

[A.15] A H Harvey, A P Peskin, and S A Klein NIST/ASME Steam

Prop-erties National Institute of Standards and Technology,

Gaithers-burg, MD, March 2000 NIST Standard Reference Database 10,

Version 2.2.

[A.16] R Tufeu, D Y Ivanov, Y Garrabos, and B Le Neindre Thermal

con-ductivity of ammonia in a large temperature and pressure range

including the critical region Ber Bunsenges Phys Chem., 88:422–

427, 1984.

[A.17] R Tillner-Roth, F Harms-Watzenberg, and H D Baehr Eine neue

Fundamentalgleichung fuer Ammoniak DKV-Tagungsbericht, 20:

167–181, 1993.

[A.18] E W Lemmon, A P Peskin, M O McLinden, and D G Friend

Ther-modynamic and Transport Properties of Pure Fluids — NIST Pure Fluids National Institute of Standards and Technology, Gaithers-

burg, MD, September 2000 NIST Standard Reference Database Number 12, Version 5 Property values are based upon the most accurate standard reference formulations then available.

[A.19] K M deReuck and R J B Craven Methanol: International

Ther-modynamic Tables of the Fluid State-12 Blackwell Scientific

Pub-lications, Oxford, 1993 Developed under the sponsorship of the International Union of Pure and Applied Chemistry (IUPAC).

[A.20] D S Viswanath and G Natarajan Data Book on the Viscosity of

Liquids Hemisphere Publishing Corp., New York, 1989.

[A.21] N B Vargaftik, Y K Vinogradov, and V S Yargin Handbook of

Physical Properties of Liquids and Gases Begell House, Inc., New

York, 3rd edition, 1996.

[A.22] D Dadarlat, J Gibkes, D Bicanic, and A Pasca Photopyroelectric

(PPE) measurement of thermal parameters in food products J.

Food Engr., 30:155–162, 1996.

[A.23] H Abramovic and C Klofutar The temperature dependence of

dynamic viscosity for some vegetable oils Acta Chim Slov., 45(1):

69–77, 1998.

[A.24] N B Vargaftik Tables on the Thermophysical Properties of Liquids

and Gases Hemisphere Publishing Corp., Washington, D.C., 2nd

edition, 1975.

[A.25] E W Lemmon, M O McLinden, and D G Friend

Thermophys-ical properties of fluid systems In W G Mallard and P J

Lin-strom, editors, NIST Chemistry WebBook, NIST Standard Reference

Database Number 69 National Institute of Standards and

Technol-ogy, Gaithersburg, MD, 2000 http://webbook.nist.gov.

[A.26] K Kadoya, N Matsunaga, and A Nagashima Viscosity and thermal

conductivity of dry air in the gaseous phase J Phys Chem Ref.

Data, 14(4):947–970, 1985.

[A.27] R.T Jacobsen, S.G Penoncello, S.W Breyerlein, W.P Clark, and E.W.

Lemmon A thermodynamic property formulation for air Fluid

Phase Equilibria, 79:113–124, 1992.

References 697

[A.28] E.W Lemmon, R.T Jacobsen, S.G Penoncello, and D G Friend.

Thermodynamic properties of air and mixtures of nitrogen, argon,

and oxygen from 60 to 2000 K at pressures to 2000 MPa J Phys.

Chem Ref Data, 29(3):331–385, 2000.

[A.29] Ch Tegeler, R Span, and W Wagner A new equation of state for

argon covering the fluid region for temperatures from the melting

line to 700 K at pressures up to 1000 MPa J Phys Chem Ref Data,

28(3):779–850, 1999.

[A.30] B A Younglove and H J M Hanley The viscosity and thermal

con-ductivity coefficients of gaseous and liquid argon J Phys Chem.

Ref Data, 15(4):1323–1337, 1986.

[A.31] R A Perkins, D G Friend, H M Roder, and C A Nieto de Castro.

Thermal conductivity surface of argon: A fresh analysis Intl J.

Thermophys., 12(6):965–984, 1991.

[A.32] R D McCarty and V D Arp A new wide range equation of state

for helium Adv Cryo Eng., 35:1465–1475, 1990.

[A.33] E Bich, J Millat, and E Vogel The viscosity and thermal

conduc-tivity of pure monatomic gases from their normal boiling point

up to 5000 K in the limit of zero density and at 0.101325 MPa J.

Phys Chem Ref Data, 19(6):1289–1305, 1990.

[A.34] V D Arp, R D McCarty, and D G Friend Thermophysical

prop-erties of helium-4 from 0.8 to 1500 K with pressures to 2000 MPa.

Technical Note 1334, National Institute of Standards and

Technol-ogy, Boulder, CO, 1998.

[A.35] B A Younglove Thermophysical properties of fluids: Argon,

ethylene, parahydrogen, nitrogen, nitrogen trifluoride, and

oxy-gen J Phys Chem Ref Data, 11, 1982 Published in book format

as Supplement No 1 to the cited volume.

[A.36] P J Mohr and B N Taylor CODATA recommended values of the

fundamental physical constants: 1998 J Phys Chem Ref Data,

28(6):1713–1852, 1999.

Table A.2 Properties of nonmetallic solids

Appendix A: Some thermophysical properties of selected materials 701

TableA.2…continued.

Appendix A: Some thermophysical properties of selected materials 703

Table A.3 Thermophysical properties of saturated liquids

Appendix A: Some thermophysical properties of selected materials 705

Helium I and Helium II

• k for He I is about 0.020 W/m·K near the λ-transition (≈ 2.17 K).

• k for He II below the λ-transition is hard to measure It appears to be about

1.92 K These are the highest conductivities known (cf copper, silver, and diamond)

TableA.3: saturated liquids…continued

Appendix A: Some thermophysical properties of selected materials 707

TableA.3: saturated liquids…continued

Temperature

Oils (some approximate viscosities)

Appendix A: Some thermophysical properties of selected materials 709