672 Design and Optimization of Thermal Systems TABLE B.5 (CONTINUED) Thermal Properties of Metals and Alloys Properties at 20nC Thermal Conductivity, k (W/m nC) Metal R (kg/m 3 ) c p (kJ/ kg nC) k (W/m nC) Ar 10 5 (m 2 /s) 100nC0nC 100nC 200nC 300nC 400nC 600nC 800nC 1000nC 1200nC Cr–Ni–Al; 6 Cr, 1.5 Al, 0.55 Si (Sicromal 8) 7,721 0.490 22 0.594 24 Cr, 2.5 Al, 0.55 Si (Sicromal 12) 7,673 0.494 19 0.501 Manganese steel, Mn = 0% 7,897 0.452 73 2.026 87 73 67 62 55 48 40 36 35 36 1% 7,865 0.46 50 1.388 2% 7,865 0.46 38 1.050 36 36 36 36 35 33 5% 7,849 0.46 22 0.637 10% 7,801 0.46 17 0.483 Tungsten steel, W = 0% 7,897 0.452 73 2.026 87 73 67 62 55 48 40 36 35 36 1% 7,913 0.448 66 1.858 2% 7,961 0.444 62 1.763 62 59 54 48 45 36 5% 8,073 0.435 54 1.525 10% 8,314 0.419 48 1.391 20% 8,826 0.389 43 1.249 Silicon steel, Si = 0% 7,897 0.452 73 2.026 87 73 67 62 55 48 40 36 35 36 1% 7,769 0.46 42 2% 7,673 0.46 31 5% 7,417 0.46 19 Copper Appendix B 673 Pure 8,954 0.3831 386 11.234 407 386 379 374 369 363 353 Aluminum bronze: 95 Cu, 5 Al 8,666 0.410 83 2.330 Bronze: 75 Cu, 25 Sn 8,666 0.343 26 0.859 Red brass: 85 Cu, 9 Sn, 6 Zn 8,714 0.385 61 1.804 59 71 Brass: 70 Cu, 30 Zn 8,522 0.385 111 3.412 88 128 144 147 German silver: 62 Cu, 15 Ni, 22 Zn 8,618 0.394 24.9 0.733 19.2 31 40 45 48 Constantan: 60 Cu, 40 Ni 8,922 0.410 22.7 0.612 21 22.2 26 Magnesium Pure 1,746 1.013 171 9.708 178 171 168 163 157 Mg–Al (electrolytic): 6–8 Al, 1–2 Zn 1,810 1.00 66 3.605 52 62 74 83 Mg–Mn: 2% Mn 1,778 1.00 114 6.382 93 111 125 130 Molybdenum 10,220 0.251 123 4.790 138 125 118 114 111 109 106 102 99 92 Nickel Pure (99.9%) 8,906 0.4459 90 2.266 104 93 83 73 64 59 Impure (99.2%) 8,906 0.444 69 1.747 69 64 59 55 52 55 62 67 69 Ni–Cr: 90 Ni 10 Cr 8,666 0.444 17 0.444 17.1 18.9 20.9 22.8 24.6 80 Ni, 20 Cr 8.314 0.444 12.6 0.343 12.3 13.8 15.6 17.1 18.9 22.5 (Continued) 674 Design and Optimization of Thermal Systems TABLE B.5 (CONTINUED) Thermal Properties of Metals and Alloys Properties at 20nC Thermal Conductivity, k (W/m nC) Metal R (kg/m 3 ) c p (kJ/ kg nC) k (W/m nC) Ar 10 5 (m 2 /s) 100nC0nC 100nC 200nC 300nC 400nC 600nC 800nC 1000nC 1200nC Silver Purest 10.524 0.2340 419 17.004 419 417 415 412 Pure (99.9%) 10.524 0.2340 407 16.563 419 410 415 374 362 360 Tin, pure 7,304 0.2265 64 3.884 74 65.9 59 57 Tungsten 19,350 0.1344 163 6.271 166 151 142 133 126 112 76 Zinc, pure 7,144 0.3843 112.2 4.106 114 112 109 406 100 93 Source: Data collected by R. Koch and R. M. Drake, as given in Eckert, E. R. G., and Drake, R. M. (1972) Analysis of Heat and Mass Transfer, McGraw-Hill, New York. Appendix B 675 TABLE B.6 Properties of Other Materials Description/ Composition Temperature, K Density, R, kg/m 3 Thermal Conductivity, k, W/m K Specific Heat, c p , J/kg K Asphalt 300 2115 0.062 920 Bakelite 300 1300 1.4 1465 Brick, refractory Carborundum 872 — 18.5 — 1672 — 11.0 — Chrome brick 473 3010 2.3 835 823 2.5 1173 2.0 Diatomaceous silica, red 478 — 0.25 — 1145 — 0.30 Fire clay, burnt 1600 K 773 2050 1.0 960 1073 — 1.1 1373 — 1.1 Fire clay, burnt 1725 K 773 2325 1.3 960 1073 1.4 1373 1.4 Fire clay brick 478 2645 1.0 960 922 1.5 1478 1.8 Magnesite 478 — 3.8 1130 922 — 2.8 1478 1.9 Clay 300 1460 1.3 880 Coal, anthracite 300 1350 0.26 1260 Concrete (stone mix) 300 2300 1.4 880 Cotton 300 80 0.06 1300 Foodstuffs Banana (75.7% water content) 300 980 0.481 3350 Apple, red (75% water content) 300 840 0.513 3600 Cake, batter 300 720 0.223 — Cake, fully baked 300 280 0.121 — Chicken meat, white 198 — 1.60 — (74.4% water content) 233 — 1.49 253 1.35 263 1.20 273 0.476 283 0.480 293 0.489 (Continued) 676 Design and Optimization of Thermal Systems TABLE B.6 (CONTINUED) Properties of Other Materials Description/ Composition Temperature, K Density, R, kg/m 3 Thermal Conductivity, k, W/m K Specific Heat, c p , J/kg K Glass Plate (soda lime) 300 2500 1.4 750 Pyrex 300 2225 1.4 835 Ice 273 920 1.88 2040 253 — 2.03 1945 Leather (sole) 300 998 0.159 — Paper 300 930 0.180 1340 Parafn 300 900 0.240 2890 Rock Granite, Barre 300 2630 2.79 775 Limestone, Salem 300 2320 2.15 810 Marble, Halston 300 2680 2.80 830 Quartzite, Sioux 300 2640 5.38 1105 Sandstone, Berea 300 2150 2.90 745 Rubber, vulcanized Soft 300 1100 0.13 2010 Hard 300 1190 0.16 — Sand 300 1515 0.27 800 Soil 300 2050 0.52 1840 Snow 273 110 0.049 — 500 0.190 — Teon 300 2200 0.35 — 400 0.45 — Tissue, human Skin 300 — 0.37 — Fat layer (adipose) 300 — 0.2 — Muscle 300 — 0.41 — Wood, cross gain Balsa 300 140 0.055 — Cypress 300 465 0.097 — Fir 300 415 0.11 2720 Oak 300 545 0.17 2385 Yellow pine 300 640 0.15 2805 White pine 300 435 0.11 — Wood, radial Oak 300 545 0.19 2385 Fir 300 420 0.14 2720 Source: Incropera, F.P., and Dewitt, D. P., (1990) Fundamentals of Heat and Mass Transfer, 3rd ed., Wiley, New York. Copyright © 1990. Used with permission of John Wiley & Sons, Inc. Appendix B 677 TABLE B.7 Emissivities E n of the Radiation in the Direction of the Normal to the Surface and E of the Total Hemispherical Radiation for Various Materials for the Temperature T†‡ Surface T, nC E n E Gold, polished 130 0.018 400 0.022 Silver 20 0.020 Copper, polished 20 0.030 Lightly oxidized 20 0.037 Scraped 20 0.070 Black oxidized 20 0.78 Oxidized 131 0.76 0.725 Aluminum, bright rolled 170 0.039 0.049 500 0.050 Aluminum paint 100 0.20–0.40 Silumin, cast polished 150 0.186 Nickel, bright matte 100 0.041 0.046 Polished 100 0.045 0.053 Manganin, bright rolled 118 0.048 0.057 Chrome, polished 150 0.058 0.071 Iron, bright etched 150 0.128 0.158 Bright abrased 20 0.24 Red rusted 20 0.61 Hot rolled 20 0.77 130 0.60 Hot cast 100 0.80 Heavily rusted 20 0.85 Heat-resistant oxidized 80 0.613 200 0.639 Zinc, gray oxidized 20 0.23–0.28 Lead, gray oxidized 20 0.28 Bismuth, bright 80 0.340 0.366 Corundum, emery rough 80 0.855 0.84 Clay, red 70 0.91 0.86 Lacquer, white 100 0.925 Red lead 100 0.93 Enamel, lacquer 20 0.85–0.95 Lacquer, black matte 80 0.970 Bakelite lacquer 80 0.935 Brick, mortar, plaster 20 0.93 Porcelain 20 0.92–0.94 Glass 90 0.940 0.876 (Continued) 678 Design and Optimization of Thermal Systems TABLE B.7 (CONTINUED) Emissivities E n of the Radiation in the Direction of the Normal to the Surface and E of the Total Hemispherical Radiation for Various Materials for the Temperature T†‡ Surface T, nC E n E Ice, smooth, water 0 0.966 0.918 Rough crystals 0 0.985 Waterglass 20 0.96 Paper 95 0.92 0.89 Wood, beech 70 0.935 0.91 Tarpaper 20 0.93 †: From measurements by E. Schmidt and E. Eckert. ‡: For metals, the emissivities rise with rising temperature, but for nonmetallic substances (metal oxides, organic substances) this rule is sometimes not correct. Where the exact measurements are not given, take for bright metal surfaces an average ratio E/E n = 1.2 and for other substances with smooth surfaces E/E n = 0.95; for rough surfaces use E/E n = 0.98. Source: Eckert, E.R.G., and Drake, R.M., (1972) Analysis of Heat and Mass Transfer, McGraw-Hill, New York. 679 Appendix C Interest Tables C.1: 4 percent compound interest rate C.2: 10 percent compound interest rate C.3: 16 percent compound interest rate A NOTE ON INTEREST TABLES Thesetablesareprovidedasaconvenientreferenceforcheckingcalculationson economicanalysis.Someadditionalfactorsarealsointroduced.Forotherinterest rates and compounding frequencies (these tables are for annual compounding), the formulas given in Chapter 6 may be used and other references cited in the chapter may be consulted. TABLE C.1 4 Percent Compound Interest Rate Single Payment Uniform Annual Series Compound- Amount Factor Present- Worth Factor Series Present-Worth Factor Capital- Recovery Factor (1 i) n 1/(1 i) n [(1 i) n − 1]/[i(1 i) n ][i(1 i) n ]/[(1 i) n − 1] P to FF to PS to PP to S n F/P P/F P/S S/P 1 1.0400E 00 9.6154E-01 9.6154E-01 1.0400E 00 2 1.0816E 00 9.2456E-01 1.8861E 00 5.3020E-01 3 1.1249E 00 8.8900E-01 2.7751E 00 3.6035E-01 4 1.1699E 00 8.5480E-01 3.6299E 00 2.7549E-01 5 1.2167E 00 8.2193E-01 4.4518E 00 2.2463E-01 6 1.2653E 00 7.9031E-01 5.2421E 00 1.9076E-01 7 1.3159E 00 7.5992E-01 6.0021E 00 1.6661E-01 8 1.3686E 00 7.3069E-01 6.7327E 00 1.4853E-01 9 1.4233E 00 7.0259E-01 7.4353E 00 1.3449E-01 10 1.4802E 00 6.7556E-01 8.1109E 00 1.2329E-01 11 1.5395E 00 6.4958E-01 8.7605E 00 1.1415E-01 12 1.6010E 00 6.2460E-01 9.3851E 00 1.0655E-01 (Continued ) 680 Design and Optimization of Thermal Systems TABLE C.1 (CONTINUED) 4 Percent Compound Interest Rate Single Payment Uniform Annual Series Compound- Amount Factor Present- Worth Factor Series Present-Worth Factor Capital- Recovery Factor (1 i) n 1/(1 i) n [(1 i) n − 1]/[i(1 i) n ][i(1 i) n ]/[(1 i) n − 1] P to FF to PS to PP to S n F/P P/F P/S S/P 13 1.6651E 00 6.0057E-01 9.9856E 00 1.0014E-01 14 1.7317E 00 5.7748E-01 1.0563E 01 9.4669E-02 15 1.8009E 00 5.5526E-01 1.1118E 01 8.9941E-02 16 1.8730E 00 5.3391E-01 1.1652E 01 8.5820E-02 18 2.0258E 00 4.9363E-01 1.2659E 01 7.8993E-02 20 2.1911E 00 4.5639E-01 1.3590E 01 7.3582E-02 25 2.6658E 00 3.7512E-01 1.5622E 01 6.4012E-02 30 3.2434E 00 3.0832E-01 1.7292E 01 5.7830E-02 35 3.9461E 00 2.5342E-01 1.8665E 01 5.3577E-02 40 4.8010E 00 2.0829E-01 1.9793E 01 5.0523E-02 45 5.8412E 00 1.7120E-01 2.0720E 01 4.8262E-02 50 7.1067E 00 1.4071E-01 2.1482E 01 4.6550E-02 Reproduced with permission from Jelen, F. C., ed. (1970) Cost and Optimization Engineering, McGraw-Hill, New York. Uniform Gradient Series Depreciation Series Capitalized- Cost Factor Present- Worth Factor Sum-of-Digits Present-Worth Factor Straight-Line Present-Worth Factor [(1 i ) n ]/[(1 i) n − 1] [(P/S) − (nP/F)]/i [n − (P/S)]/[0.5n(n 1)i ] 1/[ni(K/P)] P to KC to P n K/P P/C 1 2.6000E 01 0.0000E 00 9.6154E-01 9.6154E-01 2 1.3255E 01 9.2456E-01 9.4921E-01 9.4305E-01 3 9.0087E 00 2.7025E 00 9.3712E-01 9.2503E-01 4 6.8873E 00 5.2670E 00 9.2526E-01 9.0747E-01 5 5.6157E 00 8.5547E 00 9.1363E-01 8.9036E-01 6 4.7690E 00 1.2506E 01 9.0222E-01 8.7369E-01 7 4.1652E 00 1.7066E 01 8.9102E-01 8.5744E-01 8 3.7132E 00 2.2181E 01 8.8004E-01 8.4159E-01 9 3.3623E 00 2.7801E 01 8.6926E-01 8.2615E-01 (Continued ) Appendix C 681 Uniform Gradient Series Depreciation Series Capitalized- Cost Factor Present- Worth Factor Sum-of-Digits Present-Worth Factor Straight-Line Present-Worth Factor [(1 i ) n ]/[(1 i) n − 1] [(P/S) − (nP/F)]/i [n − (P/S)]/[0.5n(n 1)i ] 1/[ni(K/P)] P to KC to P n K/P P/C 10 3.0823E 00 3.3881E 01 8.5868E-01 8.1109E-01 11 2.8537E 00 4.0377E 01 8.4830E-01 7.9641E-01 12 2.6683E 00 4.7248E 01 8.3812E-01 7.8209E-01 13 2.5036E 00 5.4455E 01 8.2812E-01 7.6813E-01 14 2.3667E 00 6.1962E 01 8.1830E-01 7.5451E-01 15 2.2485E 00 6.9735E 01 8.0867E-01 7.4123E-01 16 2.1455E 00 7.7744E 01 7.9921E-01 7.2827E-01 18 1.9748E 00 9.4350E 01 7.8080E-01 7.0329E-01 20 1.8395E 00 1.1156E 02 7.6306E-01 6.7952E-01 25 1.6003E 00 1.5610E 02 7.2138E-01 6.2488E-01 30 1.4458E 00 2.0106E 02 6.8322E-01 5.7640E-01 35 1.3394E 00 2.4488E 02 6.4823E-01 5.3327E-01 40 1.2631E 00 2.8653E 02 6.1607E-01 4.9482E-01 45 1.2066E 00 3.2540E 02 5.8647E-01 4.6045E-01 50 1.1638E 00 3.6116E 02 5.5917E-01 4.2964E-01 TABLE C.2 10 Percent Compound Interest Rate Single Payment Uniform Annual Series Compound- Amount Factor Present- Worth Factor Series Present-Worth Factor Capital- Recovery Factor (1 i) n 1/(1 i) n [(1 i) n − 1]/[i(1 i) n ][i(1 i) n ]/[(1 i) n − 1] P to FF to PS to PP to S n F/P P/F P/S S/P 1 1.1000E 00 9.0909E-01 9.0909E-01 1.1000E 00 2 1.2100E 00 8.2645E-01 1.7355E 00 5.7619E-01 3 1.3310E 00 7.5131E-01 2.4869E 00 4.0211E-01 4 1.4641E 00 6.8301E-01 3.1699E 00 3.1547E-01 5 1.6105E 00 6.2092E-01 3.7908E 00 2.6380E-01 6 1.7716E 00 5.6447E-01 4.3553E 00 2.2961E-01 7 1.9487E 00 5.1316E-01 4.8684E 00 2.0541E-01 8 2.1436E 00 4.6651E-01 5.3349E 00 1.8744E-01 (Continued ) [...]... 2.8583E 01 3. 0 632 E 01 3. 4284E 01 3. 6423E 01 3. 7 633 E 01 3. 8 299 E 01 3. 8660E 01 3. 8852E 01 6.6103E-01 6 .34 79E-01 6.1020E-01 5.8713E-01 5.6547E-01 5.4510E-01 5.2 594 E-01 5.0789E-01 4 .90 86E-01 4.7479E-01 4.4525E-01 4.1878E-01 3. 635 2E-01 3. 2020E-01 2.8556E-01 2.5 737 E-01 2 .34 05E-01 2.1448E-01 5.7 694 E-01 5.4 295 E-01 5.1184E-01 4. 833 2E-01 4.5715E-01 4 .33 09E-01 4.1 095 E-01 3. 90 54E-01 3. 7170E-01 3. 5428E-01 3. 232 1E-01... 4. 595 0E 00 5.5 599 E 00 6.7275E 00 1.0 835 E 01 1.7449E 01 2.8102E 01 4.5259E 01 7.2 890 E 01 1.1 7 39 E 02 4.2410E-01 3. 8554E-01 3. 5049E-01 3. 1863E-01 2. 896 6E-01 2. 633 3E-01 2 . 39 39E-01 2.1763E-01 1. 798 6E-01 1.4864E-01 9. 2 296 E-02 5. 730 9E-02 3. 5584E-02 2.2 095 E-02 1 .37 19E-02 8.5186E- 03 [(1 i )n − 1]/[i(1 S to P P/S i )n] [i(1 5.7 590 E 00 6.1446E 00 6. 495 1E 00 6.8 137 E 00 7.1 034 E 00 7 .36 67E 00 7.6061E 00 7.8 237 E 00 8.2014E... 01 9. 4889E 01 7.4 030 E-01 7.2022E-01 7.0 099 E-01 6.8257E-01 6.6 491 E-01 6.4 798 E-01 6 .31 74E-01 6.1616E-01 6.0120E-01 5. 730 2E-01 5.4 697 E-01 4. 899 4E-01 4.4243E-01 4.0247E-01 3. 6855E-01 3. 394 9E-01 3. 1 4 39 E-01 6.6687E-01 6 . 39 89E-01 6.1446E-01 5 .90 46E-00 5.6781E-00 5.4641E-01 5.2619E-01 5.0707E-01 4.8 898 E-01 4.5563E-01 4.2568E-01 3. 630 8E-01 3. 1423E-01 2.7555E-01 2.4448E-01 2. 191 7E-01 1 .9 830 E-01 TABLE C .3 16 Percent... 6.2 296 E-01 4.4526E-01 3. 5 738 E-01 3. 0541E-01 2.7 1 39 E-01 2.4761E-01 (Continued ) 684 Design and Optimization of Thermal Systems TABLE C .3 16 Percent Compound Interest Rate Single Payment CompoundPresentAmount Worth Factor Factor n (1 i )n P to F F/P 8 9 10 11 12 13 14 15 16 18 20 25 30 35 40 45 50 3. 2784E 00 3. 8 030 E 00 4.4114E 00 5.1173E 00 5. 93 6 0E 00 6.8858E 00 7 .98 75E 00 9. 2655E 00 1.0748E 01 1.4463E... 1. 036 9E 00 1.0226E 00 1.0 1 39 E 00 1.0086E 00 [(1 PresentWorth Factor [(P/S) − (nP/F)]/i Depreciation Series Sum -of- Digits Straight-Line Present-Worth Present-Worth Factor Factor 1/[ni(K/P)] [n − (P/S)]/[0.5n(n 1)i ] C to P P/C 1.6029E 01 1 .94 21E 01 2.2 891 E 01 2. 6 39 6E 01 2 .99 01E 01 3. 337 7E 01 3. 6800E 01 4.0152E 01 4 .34 16E 01 4 .96 40E 01 5.5407E 01 6.7 696 E 01 7.7077E 01 8 . 39 87E 01 8. 895 3E 01 9. 2454E 01 9. 4889E... 0. 592 — — 0. 497 — 0.505 0.460 0.416 0 .35 6 — — 0.558 — 0.554 0.562 0.568 0.580 — 0.446 — 0.478 0.5 19 0.452 0.482 0.440 — 0.571 — 0.565 0.556 0.568 0.556 0.562 0.2 13 0.401 — 0.518 0.522 0.488 0.4 49 0.428 0. 636 0.581 — 0.560 0.562 0.568 0.570 0.574 C2: NL 2.0 C1 Nu D |N L 10 C 2 Nu D|N L 1 1 2 3 4 5 6 7 8 9 0.64 0.68 0.80 0.75 0.87 0. 83 0 .90 0. 89 0 .92 0 .92 0 .94 0 .95 0 .96 0 .97 0 .98 0 .98 0 .99 0 .99 SL and. .. 00 7.8 237 E 00 8.2014E 00 8.5 136 E 00 9. 0770E 00 9. 4269E 00 9. 6442E 00 9. 7 791 E 00 9. 8628E 00 9. 9148E 00 i )n]/[(1 i )n − 1] P to S S/P 1. 736 4E-01 1.6275E-01 1. 5 39 6E-01 1.4676E-01 1.4078E-01 1 .35 75E-01 1 .31 47E-01 1.2782E-01 1.2 193 E-01 1.1746E-01 1.1017E-01 1.0608E-01 1. 036 9E-01 1.0226E-01 1.0 1 39 E-01 1.0086E-01 Reproduced with permission from Jelen, F C., ed ( 197 0) Cost and Optimization Engineering, McGraw-Hill,... 0.86 0.84 0 .90 0. 89 0 .92 0 .92 0 .95 0 .95 0 .97 0 .97 0 .98 0 .98 0 .99 0 .99 Source: Incropera, F P., and Dewitt, D P ( 199 6) Fundamentals of Heat and Mass Transfer, 6th ed., Wiley, New York Copyright © 199 6 Used with permission of John Wiley & Sons, Inc TABLE D.4 Summary of Forced Convection Correlations for Flow in a Circular Tube Correlation f Conditions Laminar, fully developed 64/ReD NuD 4 .36 Laminar, fully... 7. 431 6E-01 2.0245E 00 3. 6814E 00 5.5858E 00 7. 638 0E 00 8.6207E-01 8.2243E-01 7.8553E-01 7.5114E-01 7. 190 4E-01 6. 890 7E-01 8.6207E-01 8.0262E-01 7.4863E-01 6 .99 55E-01 6.5486E-01 6.1412E-01 Appendix C 685 Uniform Gradient Series CapitalizedCost Factor n i )n]/[(1 i)n − 1] P to K K/P 7 8 9 10 11 12 13 14 15 16 18 20 25 30 35 40 45 50 1.5476E 00 1. 438 9E 00 1 .35 68E 00 1.2 93 1 E 00 1.2429E 00 1.2026E 00 1.1 699 E... 8.8154E-01 8.5525E-01 8 .30 13E-01 8.0614E-01 7. 832 1E-01 7.6128E-01 9. 090 9E-01 8.6777E-01 8.2 895 E-01 7 .92 47E-01 7.5816E-01 7.2588E-01 6 .95 49E-01 Appendix C 6 83 Uniform Gradient Series CapitalizedCost Factor n i )n]/[(1 i )n − 1] P to K K/P 8 9 10 11 12 13 14 15 16 18 20 25 30 35 40 45 50 1.8744E 00 1. 736 4E 00 1.6275E 00 1. 5 39 6E 00 1.4676E 00 1.4078E 00 1 .35 75E 00 1 .31 47E 00 1.2782E 00 1.2 193 E 00 1.1746E 00 . = 0% 7, 897 0.452 73 2.026 87 73 67 62 55 48 40 36 35 36 1% 7,7 69 0.46 42 2% 7,6 73 0.46 31 5% 7,417 0.46 19 Copper Appendix B 6 73 Pure 8 ,95 4 0 .38 31 38 6 11. 234 407 38 6 37 9 37 4 36 9 36 3 35 3 Aluminum. 4. 93 6 3E-01 1.2659E 01 7. 899 3E-02 20 2. 191 1E 00 4.5 6 39 E-01 1 .35 90 E 01 7 .35 82E-02 25 2.6658E 00 3. 7512E-01 1.5622E 01 6.4012E-02 30 3. 2 434 E 00 3. 0 832 E-01 1.7 292 E 01 5.7 830 E-02 35 3. 94 61E 00 2. 534 2E-01. 3. 1423E-01 35 1. 036 9E 00 8 . 39 87E 01 4.0247E-01 2.7555E-01 40 1.0226E 00 8. 895 3E 01 3. 6855E-01 2.4448E-01 45 1.0 1 39 E 00 9. 2454E 01 3. 394 9E-01 2. 191 7E-01 50 1.0086E 00 9. 4889E 01 3. 1 4 39 E-01 1 .9 830 E-01 TABLE