John H. Lienhard IV, John H. Lienhard V. A Heat Transfer Textbook (776116), страница 101
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If a 20 g ice cubeis rectangular and has a top surface area of 8 cm2 , find thetemperature of the ice cube and estimate the time required forit to sublimate completely. Assume that no heat is transferredthrough the ice cube tray. For ice, take hsg = 2.837 × 106 J/kg,and for water vapor in air, take Sc = 0.63. The vapor pressureof ice is given in Example 11.6.Chapter 11: An introduction to mass transfer68611.54Bikram yoga is a strenuous yoga done in a room at 38 to 41◦ Cwith relative humidity from 20 to 50%. People doing this yogawill generate body heat Q̇b of 300 to 600 W, which must beremoved to avoid heat stroke. Calculate the rate at which one’sbody can cool under these conditions and compare it to therate of heat generation.The body sweats more as its need to cool increases, but theamount of sweat evaporated on the skin depends on air temperature and humidity.
Sweating cannot exceed about 2 L/h,of which only about half evaporates (the rest will simply drip).Assume that sweating skin has a temperature of 36◦ C and anemissivity of 0.95, and that an average body surface area isAb = 1.8 m2 . Assume that the walls in the yoga studio areat the air temperature. Ignore the thermal effects of clothing.Convection to a person active in still air can be estimated fromthe following equation [11.31]:0.39Q̇b2h = (5.7 W/m K)− 0.8(58.1 W/m2 ) AbNote that at high humidity and temperature, some people become overheated and must stop exercising.References[11.1] W. C. Reynolds. Energy, from Nature to Man.
McGraw-Hill BookCompany, New York, 1974.[11.2] S. Chapman and T. G. Cowling. The Mathematical Theory ofNonuniform Gases. Cambridge University Press, New York, 2ndedition, 1964.[11.3] R. K. Ghai, H. Ertl, and F. A. L. Dullien. Liquid diffusion of nonelectrolytes: Part 1. AIChE J., 19(5):881–900, 1973.[11.4] R. C. Reid, J. M.
Prausnitz, and B. E. Poling. The Properties of Gasesand Liquids. McGraw-Hill Book Company, New York, 4th edition,1987.[11.5] P. W. Atkins. Physical Chemistry. W. H. Freeman and Co., NewYork, 3rd edition, 1986.References[11.6] D. R. Poirier and G. H. Geiger. Transport Phenomena in MaterialsProcessing. The Minerals, Metals & Materials Society, Warrendale,Pennsylvania, 1994.[11.7] T. R. Marrero and E.
A. Mason. Gaseous diffusion coefficients.J. Phys. Chem. Ref. Data, 1:3–118, 1972.[11.8] J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird. Molecular Theoryof Gases and Liquids. John Wiley & Sons, Inc., New York, 1964.[11.9] C. L. Tien and J. H. Lienhard. Statistical Thermodynamics. Hemisphere Publishing Corp., Washington, D.C., rev. edition, 1978.[11.10] R. A. Svehla. Estimated viscosities and thermal conductivities ofgases at high temperatures. NASA TR R-132, 1962. (Nat. Tech.Inf. Svcs.
N63-22862).[11.11] C. R. Wilke and C. Y. Lee. Estimation of diffusion coefficients forgases and vapors. Ind. Engr. Chem., 47:1253, 1955.[11.12] J. O. Hirschfelder, R. B. Bird, and E. L. Spotz. The transport properties for non-polar gases. J. Chem. Phys., 16(10):968–981, 1948.[11.13] J. Millat, J. H. Dymond, and C. A.
Nieto de Castro. TransportProperties of Fluids: Their Correlation, Prediction and Estimation.Cambridge University Press, Cambridge, UK, 1996.[11.14] G. E. Childs and H. J. M. Hanley. Applicability of dilute gas transport property tables to real gases. Cryogenics, 8:94–97, 1968.[11.15] C. Cercignani. Rarefied Gas Dynamics. Cambridge UniversityPress, Cambridge, UK, 2000.[11.16] A. Einstein. Investigations of the Theory Brownian Movement.Dover Publications, Inc., New York, 1956. (This book is a collection of Einstein’s original papers on the subject, which werepublished between 1905 and 1908.).[11.17] W. Sutherland.A dynamical theory of diffusion for nonelectrolytes and the molecular mass of albumin. Phil.
Mag., Ser.6, 9(54):781–785, 1905.[11.18] H. Lamb. Hydrodynamics. Dover Publications, Inc., New York,6th edition, 1945.687688Chapter 11: An introduction to mass transfer[11.19] J. C. M. Li and P. Chang. Self-diffusion coefficient and viscosity inliquids. J. Chem. Phys., 23(3):518–520, 1955.[11.20] S.
Glasstone, K. J. Laidler, and H. Eyring. The Theory of RateProcesses. McGraw-Hill Book Company, New York, 1941.[11.21] C. J. King, L. Hsueh, and K-W. Mao. Liquid phase diffusion ofnonelectrolytes at high dilution. J. Chem. Engr. Data, 10(4):348–350, 1965.[11.22] C. R. Wilke. A viscosity equation for gas mixtures. J. Chem. Phys.,18(4):517–519, 1950.[11.23] E.
A. Mason and S. C. Saxena. Approximate formula for the thermal conductivity of gas mixtures. Phys. Fluids, 1(5):361–369,1958.[11.24] J. M. Prausnitz, R. N. Lichtenthaler, and E. G. de Azevedo. Molecular Thermodynamics of Fluid-Phase Equilibria. Prentice-Hall, Englewood Cliffs, N.J., 2nd edition, 1986.[11.25] R. C. Weast, editor. Handbook of Chemistry and Physics.
ChemicalRubber Co., Cleveland, Ohio, 56th edition, 1976.[11.26] D. S. Wilkinson. Mass Transfer in Solids and Fluids. CambridgeUniversity Press, Cambridge, 2000.[11.27] W. K. Lewis. The evaporation of a liquid into a gas. Mech. Engr.,44(7):445–446, 1922.[11.28] T. H. Chilton and A. P. Colburn.
Mass transfer (absorption) coefficients: Prediction from data on heat transfer and fluid friction.Ind. Eng. Chem., 26:1183–1187, 1934.[11.29] A. F. Mills. The use of the diffusion velocity in conservation equations for multicomponent gas mixtures. Int. J. Heat. Mass Transfer, 41(13):1955–1968, 1998.[11.30] A. F. Mills. Mass Transfer. Prentice-Hall, Inc., Upper Saddle River,2001.[11.31] American Society of Heating, Refrigerating, and Air-ConditioningEngineers, Inc. 2001 ASHRAE Handbook—Fundamentals. Altanta,2001.Part VIAppendices689A.Some thermophysical propertiesof selected materialsA primary source of thermophysical properties is a document in whichthe experimentalist who obtained the data reports the details and resultsof his or her measurements. The term secondary source generally refersto a document, based on primary sources, that presents other peoples’data and does so critically.
This appendix is neither a primary nor a secondary source, since it has been assembled from a variety of secondaryand even tertiary sources.We attempted to cross-check the data against different sources, andthis often led to contradictory values. Such contradictions are usuallythe result of differences between the experimental samples that are reported or of differences in the accuracy of experiments themselves. Weresolved such differences by judging the source, by reducing the number of significant figures to accommodate the conflict, or by omitting thesubstance from the table. The resulting numbers will suffice for mostcalculations. However, the reader who needs high accuracy should besure of the physical constitution of the material and then should seekout 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]. However, 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 measurements. One secondary source from which many of the data here wereobtained was the Purdue University series Thermophysical Properties ofMatter [A.2]. The Purdue series is the result of an enormous propertygathering effort carried out under the direction of Y. S. Touloukian andseveral coworkers. The various volumes in the series are dated since691692Appendix A: Some thermophysical properties of selected materials1970, and addenda were issued throughout the following decade.
Inmore recent years, IUPAC, NIST, and other agencies have been developingcritically reviewed, standard reference data for various substances, someof 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 thirdsecondary source that we have used is the G. E. Heat Transfer DataBook [A.12].Numbers that did not come directly from [A.1], [A.2], [A.12] or thesources of standard reference data were obtained from a variety of manufacturers’ tables, handbooks, and other technical literature. While wehave not documented all these diverse sources and the various compromises that were made in quoting them, specific citations are given belowfor the bulk of the data in these tables.Table A.1 gives the density, specific heat, thermal conductivity, andthermal diffusivity for various metallic solids.
These values were obtained from volumes 1 and 4 of [A.2] or from [A.3] whenever it was possible to find them there. Most thermal conductivity values in the tablehave been rounded off to two significant figures. The reason is that kis sensitive to very minor variations in physical structure that cannot bedetailed fully here. Notice, for example, the significant differences between pure silver and 99.9% pure silver, or between pure aluminum and99% pure aluminum.
Additional information on the characteristics anduse of these metals can be found in the ASM Metals Handbook [A.13].The effect of temperature on thermal conductivity is shown for mostof the metals in Table A.1. The specific heat capacity is shown only at20◦ C. For most materials, the heat capacity is much lower at cryogenictemperatures. For example, cp for alumimum, iron, molydenum, and titanium decreases by two orders of magnitude as temperature decreasesfrom 200 K to 20 K. On the other hand, for most of these metals, cpchanges more gradually for temperatures between 300 K and 800 K, varying by tens of percent to a factor of two.
At still higher temperatures,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 available) but for nonmetallic substances.
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