Computational Fluid Mechanics and Heat Transfer Third Edition_19 docx

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 secondary 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 How- ever, although we use a few of Drake’s numbers directly in Table A.6, many of his other values have been superseded by more recent measure- ments.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 691 692 Appendix A: Some thermophysical properties of selected materials 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]orthe 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, c p for alumimum, iron, molydenum, and ti- tanium decreases by two orders of magnitude as temperature decreases from 200 K to 20 K. On the other hand, for most of these metals, c p changes more gradually for temperatures between 300 K and 800 K, vary- ing by tens of percent to a factor of two. At still higher temperatures, some of these metals (iron and titanium) show substantial spikes in c p , which are associated with solid-to-solid phase transitions. Table A.2 gives the same properties as Table A.1 (where they are avail- 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- 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 temperatures. 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, c p , 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%, c p 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 c p , 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/ρc p were allowed to stand. Densities for other substances came from [A.24] and a variety of other sources. A few values of ρ and c p 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 c p 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 694 Chapter A: Some thermophysical properties of selected materials 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%, c p has 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. J. Phys. Chem. Ref. Data, 19(3):763–808, 1990. 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. 696 Chapter A: Some thermophysical properties of selected materials [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.1 Properties of metallic solids Properties at 20 ◦ C Thermal Conductivity, k(W/m·K) ρc p kα Metal (kg/m 3 )(J/kg·K)(W/m·K)(10 −5 m 2 /s) −170 ◦ C −100 ◦ C0 ◦ C 100 ◦ C 200 ◦ C 300 ◦ C 400 ◦ C 600 ◦ C 800 ◦ C 1000 ◦ C Aluminums Pure 2,707 905 237 9.61 302 242 236 240 238 234 228 215 ≈95 (liq.) 99% pure 211 220 206 209 Duralumin 2,787 883 164 6.66 126 164 182 194 (≈4% Cu, 0.5% Mg) Alloy 6061-T6 2,700 896 167 6.90 166 172 177 180 Alloy 7075-T6 2,800 841 130 5.52 76 100 121 137 172 177 Chromium 7,190 453 90 2.77 158 120 95 88 85 82 77 69 64 62 Cupreous metals Pure Copper 8,954 384 398 11.57 483 420 401 391 389 384 378 366 352 336 DS-C15715 ∗ 8,900 ≈384 365 ≈10.7 367 355 345 335 320 Beryllium copper 8,250 420 103 2.97 117 (2.2% Be) Brass (30% Zn) 8,522 385 109 3.32 73 89 106 133 143 146 147 Bronze (25% Sn) § 8,666 343 26 0.86 Constantan 8,922 410 22 0.61 17 19 22 26 35 (40% Ni) German silver 8,618 394 25 0.73 18 19 24 31 40 45 48 (15% Ni, 22% Zn) Gold 19,320 129 318 12.76 327 324 319 313 306 299 293 279 264 249 Ferrous metals Pure iron 7,897 447 80 2.26 132 98 84 72 63 56 50 39 30 29.5 Cast iron (4% C) 7,272 420 52 1.70 Steels (C ≤ 1.5%) || AISI 1010 †† 7,830 434 64 1.88 70 65 61 55 50 45 36 29 0.5% carbon 7,833 465 54 1.47 55 52 48 45 42 35 31 29 1.0% carbon 7,801 473 43 1.17 43 43 42 40 36 33 29 28 1.5% carbon 7,753 486 36 0.97 36 36 36 35 33 31 28 28 ∗ Dispersion-strengthened copper (0.3% Al 2 O 3 by weight); strength comparable to stainless steel. § Conductivity data for this and other bronzes vary by a factor of about two. || k and α for carbon steels can vary greatly, owing to trace elements. †† 0.1% C, 0.42% Mn, 0.28% Si; hot-rolled. 698 Table A.1 Properties of metallic solids…continued. Properties at 20 ◦ C Thermal Conductivity, k(W/m·K) ρc p kα Metal (kg/m 3 )(J/kg·K)(W/m·K)(10 −5 m 2 /s) −170 ◦ C −100 ◦ C0 ◦ C 100 ◦ C 200 ◦ C 300 ◦ C 400 ◦ C 600 ◦ C 800 ◦ C 1000 ◦ C Stainless steels: AISI 304 8,000 400 13.80.41517 + 19 − 21 25 AISI 316 8,000 460 13.50.37 12 15 16 17 + 19 − 21 + 24 26 + AISI 347 8,000 420 15 0.44 13 16 + 18 − 19 20 23 26 28 AISI 410 7,700 460 25 0.725 + 26 27 27 + 28 + AISI 446 7,500 460 18 19 − 19 20 21 22 Lead 11,373 130 35 2.34 40 37 36 34 33 32 17 (liq.) 20 (liq.) Magnesium 1,746 1023 156 8.76 169 160 157 154 152 150 148 145 89 (liq.) Mercury † 32 30 7.8 (liq.) Molybdenum 10,220 251 138 5.38 175 146 139 135 131 127 123 116 109 103 Nickels Pure 8,906 445 91 2.30 156 114 94 83 74 67 64 69 73 78 Alumel §§ 8,600 532 30 32 35 38 Chromel P (10% Cr) 8,730 428 19 21 23 25 Inconel X-750 ¶ 8,510 442 11.60.23 8.8 10.6 11.3 13.0 14.7 16.0 18.3 21.8 25.3 29 Nichrome Þ 8,250 448 0.34 13 15 16 18 − Nichrome V ∗∗ 8,410 466 10 0.26 11 13 15 17 20 24 Platinum 21,450 133 71 2.50 78 73 72 72 72 73 74 77 80 84 Silicon ‡ 2,330 705.5 153 9.31 856 342 168 112 82 66 54 38 29 25 Silver 99.99 + % pure 10,524 236 427 17.19 449 431 428 422 417 409 401 386 370 176 99.9% pure 10,524 236 411 16.55 422 405 373 367 364 (liq.) Tin † 7,304 228 67 4.17 85 76 68 63 60 32 (liq.) 34 (liq.) 38 (liq.) Titanium Pure † 4,540 523 22 0.93 31 26 22 21 20 20 19 21 21 22 Ti-6%Al-4%V 4,430 580 7.10.28 7.8 8.8 10 12 − Tungsten 19,350 133 178 6.92 235 223 182 166 153 141 134 125 122 114 Uranium 18,700 116 28 1.29 22 24 27 29 31 33 36 41 46 Zinc 7,144 388 121 4.37 124 122 122 117 110 106 100 60 (liq.) † Polycrystalline form. §§ 2% Al, 2% Mn, 1% Si ¶ 73% Ni, 15% Cr, 6.75% Fe, 2.5% Ti, 0.85% Nb, 0.8% Al, 0.7% Mn, 0.3% Si. Þ 23% Fe, 16% Cr ∗∗ 20% Cr, 1.4% Si ‡ Single crystal form. 699 700 Appendix A: Some thermophysical properties of selected materials Table A.2 Properties of nonmetallic solids Temperature Density Specific Thermal Thermal Range Heat Conductivity Diffusivity Material ( ◦ C) ρ(kg/m 3 )c p (J/kg·K)k(W/m·K) α(m 2 /s) Aluminum oxide (Al 2 O 3 ) plasma sprayed coating 20 ≈ 4 HVOF sprayed coating 20 ≈ 14 polycrystalline (98% dense) 0 725 40 27 3900 779 36 1.19 × 10 −5 127 940 26 577 1200 10 1077 1270 6.1 1577 1350 5.6 single crystal (sapphire) 0 725 52 27 3980 779 46 1.48 × 10 −5 127 940 32 577 1180 13 Asbestos Cement board 20 1920 0.6 Fiber, densely packed 20 1930 0.8 Fiber, loosely packed 20 980 0.14 Asphalt 20–25 0.75 Beef (lean, fresh) 25 1070 3400 0.48 1.35 × 10 −7 Brick B & W, K-28 insulating 300 0.3 1000 0.4 Cement 10 720 0.34 Common 0–1000 0.7 Chrome 100 1.9 Facing 20 1.3 Firebrick, insulating 300 2000 960 0.15.4 × 10 −8 1000 0.2 Butter 20 920 2520 0.22 9.5 ×10 −6 Carbon Diamond (type IIb) 20 ≈3250 510 1350.08.1 × 10 −4 Graphites 20 ≈1730 ≈710 k varies with structure AGOT graphite ⊥ to extrusion axis 0 141 27 1700 800 138 500 1600 59.1  to extrusion axis 0 230 27 1700 800 220 500 1600 93.6 [...]... hsg latent heat of vaporization (J/kg), latent heat of fusion (J/kg), latent heat of sublimation (J/kg) hfg latent heat corrected for sensible heat F (t) time-dependent driving force (N) ˆ hi specific enthalpy of species i (J/kg) F1-2 radiation view factor for surface (1) seeing surface (2) h∗ F1-2 gray-body transfer factor from surface (1) to surface (2) heat transfer coefficient at zero mass transfer, ... more conversion factors and an extensive discussion of the S.I system and may be found in [B.1] The dimensions that are used consistently in the subject of heat transfer are length, mass, force, energy, temperature, and time We generally avoid using both force and mass dimensions in the same equation, since force is always expressible in dimensions of mass, length, and time, and vice versa We do not... cross-sectional area (m2 ) B radiosity (W/m2 ), or the function defined in Fig 8.14 Bm,i boundary condition b.l heat capacity rate (W/K) or electrical capacitance (s/ohm) or correction factor in Fig 7.17; heat capacity rate for hot and cold fluids (W/K) c, cp , cv specific heat, specific heat at constant pressure, specific heat at constant volume (J/kg·K) c molar concentration of a mixture (kmol/m3 ) or damping coefficient... Cement, Portland Clay Fireclay Sandy clay Coal Anthracite Brown coal Bituminous in situ Concrete Limestone gravel Sand : cement (3 : 1) Sand and gravel Corkboard (medium ρ) Egg white Glass Lead Plate Pyrex (borosilicate) Soda Window Glass wool Ice Ivory Kapok Lunar surface dust (high vacuum) Temperature Range (◦ C) 0 27 227 1027 0 27 227 1027 0–20 34 500–750 20 900 900 Density ρ (kg/m3 ) Specific Heat cp... time, and vice versa We do not make a practice of eliminating energy in terms of force times length because the accounting of work and heat is often kept separate in heat transfer problems The text makes occasional reference to electrical units; however, these are conventional and do not have counterparts in the English system, so no electrical units are discussed here We present conversion factors in... National Institute of Standards and Technology, Gaithersburg, MD, 1995 NIST Special Publication 811 May be downloaded from NIST’s web pages 1 Shortly after World War II, a group of staff physicists at Boeing Airplane Co answered angry demands by engineers that calculations be presented in English units with a report translated entirely into such dimensions as these Appendix B: Units and conversion factors... W/m2 = 104 × W/cm2 Heat transfer coefficient W/m2 K = 5.6786 × Btu/hr·ft2 ◦ F Length m = 10−10 × ångströms (Å) m = 0.0254 × inches m = 0.3048 × feet m = 201.168 × furlongs m = 1609.34 × miles m = 3.0857 × 1016 × parsecs kg = 0.45359 × lbm kg = 14.594 × slug Dimension Density Diffusivity (α, ν, D) Energy Energy per unit mass Flow rate Force Heat flux Mass SI kg/m 4.7195×10 Appendix B: Units and conversion factors... 1191 2860 0.331 0.97 1.14 118 0.00053 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 80, 000 W/m·K between 1.4 and 1.75 K and it might go as high as 340,000 W/m·K at 1.92 K These are the highest conductivities known (cf copper, silver, and diamond) Appendix A: Some thermophysical... tension 528 Total emittances 616 Lennard-Jones constants and molecular weights 618 Collision integrals 622 Molal specific volumes and latent heats 719 B Units and conversion factors The reader is certainly familiar with the Système International d’ Unités (the “S.I System”) and will probably make primary use of it in later work But the need to deal with English units will remain with us for many years... electric current density (amperes/m2 ) h, h, hrad local heat transfer coefficient (W/m2 K), or enthalpy (J/kg), or height (m), or Planck’s constant (6.6260755 × 10−34 J·s); average heat transfer coefficient (W/m2 K); radiation heat transfer coefficient (W/m2 K) ∗ Ji diffusional mole flux of species i (kmol/m2 ·s) k thermal conductivity (W/m2 K) kB Boltzmann’s constant, 1.3806503 × 10−23 J/K kT thermal diffusion . 23: 657–729, 199 4. [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, 197 7. [A.13] ASM Handbook. Metals Handbook. ASM, International, Materials Park, OH, 10th edition, 199 0. [A.14] R. A. Parsons, editor. 199 3 ASHRAE Handbook—Fundamentals. American Society of Heating, Refrigerating, and Air-Conditioning Engineers,. 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