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between these theoretical descriptors and empirical data. The high .... Thermal conductivity data follow the .... DIPPRÂ® 801 Thermophysical Property Database,.
In order to measure thermal conductivity of small samples (3.0 x 0.1 x 0.2 mm. 3. ) ... system. By subtraction, the parallel thermal conductance. (PTC) is calculated.
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Aug 22, 2007 - At low temperatures the correlation function shows a characteristic two-stage decay, a short-time ... In contrast, equilibrium molecular dynamics MD simulation6 ... thermal conductivity as the time integral of a current corre-.
I. Introduction. The temperatures used ... For the prediction of the thermal conductivity of powder beds up to high temperatures, a number of equations ..... Technology, edited by Landolt-Bornstein Editorial Staff, 6th ed., 1950-80; New Series.
The thermal conductivities of argon, krypton, and nitrogen were measured at 760 mm Hg in the temperature range 800-2000oK. Two thermal conductivity columns of different outside diameters were used in the experiments to provide an assessment of the convective heat transfer. In addition, potential leads were employed to minimize convection and end effects. The thermal conductivity values obtained were compared with existing data, with results of viscosity measurements, and with theoretical predictions.
FIG. 1. Schematic of conductivity column.
FIG. 2. Heat transfer from the filament in vacuum and in the presence of nitrogen (small column).
FIG. 3. Schematic of temperature variation along the filament between the potential leads.
where D is the inner diameter of the outer cylinder and Ra is the Rayleigh number defined as Ra= [(gp2~TV/7J2T)( Cp7J/A) ]T-r.
FIG. 4. Experimental results for argon (0, small column' /:::,. large column). Solid line, Eq. (11). "
FIG. 5. Experimental results for krypton (0, small column' /:::,. large column). Solid line, Eq. (11). "
TABLE I. Estimate of random errors (percent).
Ab is the thermal conductivity of the gas at the water bath temperature T b , Ag is the thermal conductivity of the Pyrex, d is the filament diameter, and w is the wall thickness of the Pyrex envelope (w= 0.158 cm). In the present experiments A' was found to be less than 0.0015. (dQxc/dThf was determined by numerical differentiation based on Stirling's interpolation formula. 30 Five points at 10°C temperature intervals were used for each derivative. Equation (9) is applicable only if temperature jump effects are negligible, which is the case when the Knudsen number (Kn denotes mean free path/filament diam) is less than "'0.002.31.32 In our experiments the Knudsen numbers were below this value, and therefore, it was unnecessary to correct for the temperature jump.
AN2=0.802X 10-5+0.155 X 1()--6T-0.100X lO-lOp.
FIG. 7. Thermal conductivity of argon. -, Present result [Eq. (11)]; 0, Collins and Menard 36 ; +, Desmond17 ; . , Lee and Bonilla37 ; 0, Saxena and Saxena12 ; \7, Smiley 36; 0, Timrot and Umanskii9 ; 6, Vargaftik and Zimina6 ; 0, Vines•.
Here T is in degrees Kelvin and A is in calories/second. centimeter· degrees Kelvin. The preceding equations synthesize the A values within an average absolute deviation of 0.4%. Polynomials of the type given above are used frequently to correlate thermal conductivity data. According to the Chapman-Enskog method of solution of the Boltzmann equation,33 A"",P/2/(Q(2.2)*u2).
FIG. 11. Comparison between measured and calculated thermal conductivities of argon (for Lennard-Jones 6--12: .jk= 124°K, 0'=3.413 A).
(12) where T is in degrees Kelvin. For argon a= 1.172X 10-6, b=0.1507, for krypton a=S.950XIO-7, b= 0.1684. The thermal conductivity values given by Eqs. (11) are compared to previous results4.6,9 ,12 ,17 ,35-37 in Figs. 7-9. For argon, below 15000 K all existing data agree within ",,3 %, and the present results fall within this spread.
FIG. 10. Comparison between experimental and theoretical volumes of f. 0, data; -, Lennard-Jones 6--12; - ' - , Mason and Monchick42 ; - - -, Eucken approximation; - - -, modified Eucken approximation.
FIG. 12. Comparison between measured and calculated thermal conductivities of krypton (for Lennard-Jones 6--12: .jk=19(rK, 0'=3.61 A).
FIG. 13. Comparison between measured and calculated thermal conductivities of nitrogen (for Lennard-Jones 6-12: ./k=91,S'K, 0"=3.681 A).
given in Table II. As can be seen, the agreement is quite good between the measured and calculated values. ACKNOWLEDGMENTS The authors wish to thank Mr. H. Ehya for his help in the experiments. The authors also wish to thank Professor J. Kestin, Professor S. C. Saxena, and Professor R. E. Sonntag for their careful reading of the manuscript and for their many valuable comments. This work was supported by the National Science Foundation under Grant No. KG-14006. 1 N. V. Tsederberg, The Thermal Conductivity of Gases and Liquids (Technology, Cambridge, Mass., 1965). 2 S. C. Saxena and J. M. Gandhi, J. Sci. Ind. Res. 26, 458 (1967) . a A. J. Rothman and L. A. Bromley, Ind. Eng. Chern. 47,899 (1955) . 4 R. G. Vines, J. Heat Transfer 82, 48 (1960). 5 N. C. Blais and J. B. Mann, J. Chern. Phys. 32, 1459 (1960). • N. B. Vargaftik and N. K. Zimina, Teplofiz. Vysokikh Temp. 2, 716 (1964) [High Temp. 2, 645 (1964)]. 7 N. B. Vargaftik and N. K. Zimina, Teplofiz. Vysokikh Temp. 2,838 (1964) [High Temp. 2, 782 (1964)]. 8 D. L. Timrot and A. S. Umanskii, Teplofiz. Vysokikh Temp. 3,381 (1965) [High Temp. 3, 345 (1965)]. 9 D. L. Timrot and A. S. Umanskii, Teplofiz. Vysokikh Temp. 4,289 (1966) [High Temp. 4, 285 (1966)]. 10 A. S. Umanskii and D. L. Timrot, in Thermal Conductivity, edited by C. Y. Ho and R. E. Taylor (Plenum, New York, 1969), p. 151. 11 V. K. Saxena and S. C. Saxena, J. Phys. D. 1, 1341 (1968). 12 V. K. Saxena and S. C. Saxena, Chern. Phys. Letters 2, 44 (1968) . 13 V. K. Saxena and S. C. Saxena, J. Chern. Phys. 48, 5662 (1968) . 14 S. C. Saxena, G. P. Gupta, and V. K. Saxena, Ref. 10, p. 125. 16 V. K. Saxena and S. C. Saxena, J. Chern. Phys. 51, 3361 (1969) . 16 S. C. Saxena and G. P. Gupta, Progr. Aeron. Astron. 23, 34 (1970). 17 R. Desmond, Ph.D. thesis, University of Minnesota, Minneapolis, Minn. 1968. 18 D. E. Poland, J. W. Green, and J. L. Margrave, Natl. Bur. Std. (U.S.) Monograph 30 (1961). 19 P. D. Foote, C. O. Fairchild, and T. R. Harrison, Natl. Bur. Std. (U.S.) Tech. Paper 170 (1921). 20 H. J. Kostowski and R. D. Lee, Natl. Bur. Std. (U.S.) Monograph 41 (1962). 21 C. J. Smithells, Tungsten (Chapman and Hall, London, 1952), 3rd ed., p. 177.
33 J. O. Hirschfelder, C. F. Curtis, and R. B. Byrd, Molecular Theory of Gases and Liquids (Wiley, New York, 1967).
34 The authors are grateful to Professor J. Kestin for suggesting this method of correlation. 35 E. F. Smiley, Ph.D. Thesis, The Catholic University of America, Washington, D.C., 1957. 36 D. J. Collins and W. A. Menard, J. Heat Transfer 88, 52 (1966) . 37 C. S. Lee and C. F. Bonilla, Proc. Conf. Thermal Conductivity, 7th, Nat!. Bur. Std., Gaithersburg, Md., 1967. 38 F. A. Guevara, B. B. McInteer, and W. E. Wageman, Phys. Fluids 12, 2493 (1969). 39 R. Dipippo and J. Kestin, Symp. Thermophys. Properties 4th, New York, 304 (1968). 40 M. Goldblatt, F. A. Guevara, and B. B. McInteer, Phys. .Fluids 13, 2873 (1970). 41 J. Hilsenrath et al., Nat!. Bur. Std. (U.S.) Circ. No. 564 (1955) . 42 E. A. Mason and L. Monchick, J. Chern. Phys. 36, 1622 (1962) . 431. Amdur and E. A. Mason, Phys. Fluids 1, 370 (1958). 44 J. O. Hirschfelder, J. Chern. Phys. 26 282 (1957). 45 J. H. Dymond and B. J. Alder, J. Chern. Phys. 51, 390 (1969).
(Received 8 March 1971) Two procedures by which atomic valence shell orbitals may be transferred between atoms have been studied numerically. The one procedure optimizes the overlap between transferred and true orbitals, and the second, the electronic energy calculated with the transferred orbitals. The two procedures give significantly different results. Both improve on the results obtained in a previous study.
It has been shown by straightforward calculations that the valence shell, Hartree-Fock orbitals of atoms which are congeners, are in some cases quite similar.! (We refer to this reference as I.) The degree to which these similarities might be optimized has not been studied. This paper presents the results obtained using two alternative methods of optimizing the transferability of valence shell orbitals. The words transfer, transferable, and transferability are used frequently in this paper with special meanings. When we write that we transfer an orbital between atoms A and B, we mean that we substitute some linear combination of the occupied A Hartree-Fock (HF) orbitals for one orbital in the set of occupied HF orbitals of B, and that this A orbital is orthonormalized with respect to the other orbitals in the B set. How the linear combination of A orbitals is chosen is discussed in Sec. II. The resultant set of orbitals is used to calculate various properties of atom B. If the calculated properties are identical to those found with the occupied HF orbitals of B, we say the A orbital is exactly transferable to B. We find at best only approximate transferability.

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