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“FrontMatter.” The CRC Handbook of Thermal Engineering Ed Frank Kreith Boca Raton: CRC Press LLC, 2000 Library of Congress Cataloging-in-Publication Data The CRC handbook of thermal engineering / edited by Frank Kreith p cm (The mechanical engineering handbook series) Includes bibliographical references and index ISBN 0-8493-9581-X (alk paper) Heat engineering Handbooks, manuals, etc I Kreith, Frank TJ260.C69 1999 621.402—dc21 II Series 99-38340 CIP This book contains information obtained from authentic and highly regarded sources Reprinted material is quoted with permission, and sources are indicated A wide variety of references are listed Reasonable efforts have been made to publish reliable data and information, but the author and the publisher cannot assume responsibility for the validity of all materials or for the consequences of their use Neither this book nor any part may be reproduced or transmitted in any form or by any means, electronic or mechanical, including photocopying, microfilming, and recording, or by any information storage or retrieval system, without prior permission in writing from the publisher All rights reserved Authorization to photocopy items for internal or personal use, or the personal or internal use of specific clients, may be granted by CRC Press LLC, provided that $.50 per page photocopied is paid directly to Copyright Clearance Center, 222 Rosewood Drive, Danvers, MA 01923 USA The fee code for users of the Transactional Reporting Service is ISBN 0-8493-9581-X/00/$0.00+$.50 The fee is subject to change without notice For organizations that have been granted a photocopy license by the CCC, a separate system of payment has been arranged The consent of CRC Press LLC does not extend to copying for general distribution, for promotion, for creating new works, or for resale Specific permission must be obtained in writing from CRC Press LLC for such copying Direct all inquiries to CRC Press LLC, 2000 Corporate Blvd., N.W., Boca Raton, Florida 33431 Trademark Notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation, without intent to infringe © 2000 by CRC Press LLC No claim to original U.S Government works International Standard Book Number 0-8493-9581-X Library of Congress Card Number 99-38340 Printed in the United States of America Printed on acid-free paper Acknowledgment This book is dedicated to professionals in the field of thermal engineering I want to express my appreciation for the assistance rendered by members of the Editorial Advisory Board, as well as the lead authors of the various sections I would also like to acknowledge the assistance of the many reviewers who provided constructive criticism on various parts of this handbook during its development Their reviews were in the form of written comments as well as telephone calls and e-mails I cannot remember all the people who assisted as reviewers, and rather than mention a few and leave out others, I am thanking them as a group There are, of course, some special individuals without whose dedication and assistance this book would not have been possible They include my editorial assistant, Bev Weiler, and the editors at CRC — Norm Stanton, Bob Stern, and Maggie Mogck My wife, Marion, helped keep track of the files and assisted with other important facets of this handbook But the existence of the handbook and its high quality is clearly the work of the individual authors, and I want to express my deep appreciation to each and every one of them for their contribution I hope that the handbook will serve as a useful reference on all topics of interest to thermal engineers in their professional lives But during the planning stages of the book, certain choices had to be made to limit its scope I realize, however, that the field of thermal engineering is ever-changing and growing I would, therefore, like to invite engineers who will use this book to give me their input on topics that should be included in the next edition I would also like to invite readers and users of the handbook to send me any corrections, errors, or omissions they discover, in order that these can be corrected in the next printing Frank Kreith Boulder, Colorado fkreith@aol.com Introduction Industrial research today is conducted in a changing, hectic, and highly competitive global environment Until about 25 years ago, the R&D conducted in the U.S and the technologies based upon it were internationally dominant But in the last 20 years, strong global competition has emerged and the pace at which high technology products are introduced has increased Consequently, the lifetime of a new technology has shortened and the economic benefits of being first in the marketplace have forced an emphasis on short-term goals for industrial development To be successful in the international marketplace, corporations must have access to the latest developments and most recent experimental data as rapidly as possible In addition to the increased pace of industrial R&D, many American companies have manufacturing facilities, as well as product development activities in other countries Furthermore, the restructuring of many companies has led to an excessive burden of debt and to curtailment of in-house industrial research All of these developments make it imperative for industry to have access to the latest information in a convenient form as rapidly as possible The goal of this handbook is to provide this type of up-to-date information for engineers involved in the field of thermal engineering This handbook is not designed to compete with traditional handbooks of heat transfer that stress fundamental principles, analytical approaches to thermal problems, and elegant solutions of traditional problems in the thermal sciences The goal of this handbook is to provide information on specific topics of current interest in a convenient form that is accessible to the average engineer in industry The handbook contains in the first three chapters sufficient background information to refresh the reader's memory of the basic principles necessary to understand specific applications The bulk of the book, however, is devoted to applications in thermal design and analysis for technologies of current interest, as well as to computer solutions of heat transfer and thermal engineering problems The applications treated in the book have been selected on the basis of their current relevance to the development of new products in diverse fields such as food processing, energy conservation, bioengineering, desalination, measurement techniques in fluid flow and heat transfer, and other specific topics Each application section stands on its own, but reference is made to the basic introductory material as necessary The introductory material is presented in such a manner that it can be referred to and used by several authors of application sections For the convenience of the reader, each author has been requested to use the same nomenclature in order to help the reader in the transition from material in some of the basic chapters to the application chapters But wherever necessary, authors have defined special symbols in their chapters A special feature of this handbook is an introduction to the use of the Second Law rather than the First Law of Thermodynamics in analysis, optimization, and economics This approach has been widely used in Europe and Asia for many years, but has not yet penetrated engineering education and usage in the U.S The Second Law approach will be found particularly helpful in analyzing and optimizing thermal systems for the generation and/or conservation of energy © 2000 by CRC Press LLC The material for this handbook has been peer reviewed and carefully proofread However, in a project of this magnitude with authors from varying backgrounds and different countries, it is unavoidable that errors and/or omissions occur As the editor, I would, therefore, like to invite the professional engineers who use this book to give me their feedback on topics that should be included in the next edition I would also greatly appreciate it if any readers who find an error would contact me by e-mail in order for the manuscript to be corrected in the next printing Since CRC Press expects to update the book frequently, both in hard copy and on CD-ROM, errors will be corrected and topics of interest will be added promptly Frank Kreith fkreith@aol.com Boulder, CO © 2000 by CRC Press LLC Nomenclature Unit Symbol a a A b c C C · C D e e E E Eλ f f′ F FT F1-2 g gc G G h Quantity Velocity of sound Acceleration Area: Ac, cross-sectional area; Ap, projected area of a body normal to the direction of flow; Aq, area through which rate of heat flow is q; Ag, surface area; Ao, outside surface area; Ai, inside surface area; Af, fin surface area Breadth or width Specific heat; cp, specific heat at constant pressure; cv, specific heat at constant volume Constant or Coefficient; CD, total drag coefficient; Cf, skin friction coefficient; Cfx, local value of Cf — at distance x, from leading edge; Cf , average value of Cf Thermal capacity · Hourly heat capacity rate; Cc , hourly heat capacity rate of colder fluid in a heat · exchanger; Ch, hourly heat capacity of hotter fluid; C*, ratio of heat capacity rates in heat exchangers Diameter, DH, hydraulic diameter; Do, outside diameter; Di, inside diameter Base of natural or Napierian logarithm Total energy per unit mass Total energy Emissive power of a radiating body; Eb, emissive power of a blackbody Monochromatic emissive power per micron at wavelength λ Darcy friction factor for flow through a pipe or duct Friction coefficient for flow over banks of tubes Force; FB, buoyant force Temperature factor Geometric shape factor for radiation from one blackbody to another Acceleration due to gravity Dimensional conversion factor Mass velocity or flow rate per unit area Irradiation incident on unit surface in unit time Enthalpy per unit mass © 2000 by CRC Press LLC SI English Dimensions (MLtT) m/s m/s2 m2 ft/s ft/s2 ft2 L t–1 L t–2 L2 m J/kg K ft Btu/lbm °R L L2 t–2 T–1 none none — J/K W/K Btu/°F Btu/hr°F M L2 t–2 T–1 M L2 t–1 T–1 m ft L none J/kg J W/m2 none Btu/lbm L2 t–2 Btu Btu/hr·ft2 — — M L2 t–2 M t–2 W/m µm Btu/hr·ft2 micron M t–2 L–1 none none — none N none none none lb none none — M L t–2 — — m/s2 1.0 kg·m/N·s2 kg/s·m2 W/m2 J/kg ft/s2 32.2 ft·lbm/lb·s2 lbm/hr·ft2 Btu/hr·ft2 Btu/lbm L t–2 M L–2 t–1 M L–2 t–1 L2 t–2 Unit Symbol h hfg H i I I Iλ J k K K log ln l L Lf · m m M · M n n NPSH N p P q q qٞ q″ Q r R Quantity SI – Local heat transfer coefficient; h, average heat – – – transfer coefficient h = hc + hr ; hb , heat transfer coefficient of a boiling liquid; hc , local – convection heat transfer coefficient; hc , average – heat transfer coefficient; hr , average heat transfer coefficient for radiation Latent heat of condensation or evaporation Head, elevation of hydraulic grade line Angle between sun direction and surface normal Moment of inertia Intensity of radiation Intensity per unit wavelength Radiosity Thermal conductivity; ks, thermal conductivity of a solid; kf, thermal conductivity of a fluid; kg, thermal conductivity of a gas Thermal conductance; kk, thermal conductance for conduction heat transfer; kc, thermal convection conductance; Kr, thermal conduction for radiation heat transfer Bulk modulus of elasticity Logarithm to the base 10 Logarithm to the base e Length, general or characteristic length of a body Lift Latent heat of solidification Mass flow rate Mass Molecular weight Momentum per unit time Manning roughness factor Number of moles Net positive suction head Number in general; number of tubes, etc Static pressure; pc, critical pressure; pA, partial pressure of component A Wetted perimeter or height of weir Discharge per unit width Rate of heat flow; qk, rate of heat flow by conduction; qr, rate of heat flow by radiation; qc, rate of heat flow by convection; qb, rate of heat flow by nucleate boiling Rate of heat generation per unit volume Rate of heat generation per unit area (heat flux) Quantity of heat Radius; rH, hydraulic radius; ri, inner radius; ro, outer radius Thermal resistance; Rc, thermal resistance to convection heat transfer; Rk, thermal resistance to conduction heat transfer; Rf, to radiation heat transfer © 2000 by CRC Press LLC English Dimensions (MLtT) W/m2·K Btu/hr·ft2·°F M t–3 T–1 J/kg m rad m4 W/sr W/sr·µm W/m2 W/m·K Btu/lbm ft deg ft4 Btu/hr unit solid angle Btu/hr·sr micron Btu/hr·ft2 Btu/hr·ft°F L2 t–2 L — L4 M L2 t–3 M L t–3 M L–2 t–1 M L–2 t–1 T–1 W/K Btu/hr·ft°F M t–1 T–1 Pa none none m N J/kg kg/s kg gm/gm mole N none none m none N/m2 lb/ft2 none none ft lb Btu/lbm lbm/s lbm lbm/lb mole lb none none ft none psi or lb/ft2 or atm M L–1 t–2 — — L M L t–2 L2 t–2 M t–1 M — MLt–2 — — L — M L–1 t–2 m m2/s W ft ft2/s Btu/hr L L2 t–1 M L2 t–3 W/m3 W/m2 J m Btu/hr·ft3 Btu/hr·ft2 Btu ft M L–1 t–3 M t–3 M L2 t–3 L K/W hr°F/Btu L T M–1 Unit Symbol Re R s S SL ST t T u u u* U U U∞ v v V · V Ws · W x x y z Z English Dimensions (MLtT) Quantity SI Electrical resistance Perfect gas constant Entropy per unit mass Entropy Distance between centerlines of tubes in adjacent longitudinal rows Distance between centerlines of tubes in adjacent transverse rows Time Temperature; Tb, temperature of bulk of fluid; Tf, mean film temperature; Ts, surface temperature, To, temperature of fluid far removed from heat source or sink; Tm, mean bulk temperature of fluid flowing in a duct; TM, temperature of saturated vapor; Tsl, temperature of a saturated liquid; Tfr, freezing temperature; Tt, liquid temperature; Tas, adiabatic wall temperature Internal energy per unit mass Velocity in x direction; u′, instantaneous – fluctuating x component of velocity; u, average velocity Shear stress velocity Internal energy Overall heat transfer coefficient Free-stream velocity Specific volume Velocity in y direction; v′, instantaneous fluctuating y component of velocity Volume Volumetric flow rate Shaft work Rate of work output or power Coordinate or distance from the leading edge; xc, critical distance from the leading edge where flow becomes turbulent Quality Coordinate or distance from a solid boundary measured in direction normal to surface Coordinate Ratio of hourly heat capacity rates in heat exchangers ohm 8.314 J/K·kg mole J/kg·K J/K m ohm 1545 ft·lbf/lb·mole°F ft·lb/lbm·°R ft·lb/°R ft — L2 t–2 T–1 L2t–2T–1 ML2t–2T–1 L m ft L s K or °C hr or s °F or R t T J/kg m/s Btu/lbm L2 t–2 ft/s or ft/hr L t–1 m/s J W/m2K m/s m3/kg m/s ft/s Btu Btu/hr·ft2°F ft/s ft3/lbm ft/s or ft/hr Lt–1 ML2t–2 M t–3 T–1 L t–1 L3 M–1 L t–1 m3 m3/s m·N W m ft3 ft3/s ft·lb Btu/hr ft L3 L3 t–1 ML2t–2 M L2 t–3 L percent m percent ft none L m none ft none L — none none — m2/s 1/K 1/K none m2 ft2/s 1/R 1/R none ft2 L2 t–1 T–1 T–1 — L2t–1 Greek Symbols α α β βk γ Γ Absorptivity for radiation, αλ, monochromatic absorptivity at wavelength λ Thermal diffusivity = k/ρc Temperature coefficient of volume expansion Temperature coefficient of thermal conductivity Specific heat ratio, cp /cv Circulation © 2000 by CRC Press LLC Unit Symbol Γ Γc δ ∆ ε ⑀ ⑀ ⑀H ⑀M ζ η λ µ ν νf Φ ρ τ τ σ σ φ ψ ω ω Quantity Body force per unit mass Mass rate of flow of condensate per unit breadth · = m/πD for a vertical tube Boundary-layer thickness; δh, hydrodynamic boundary-layer thickness; δth, thermal boundary-layer thickness Difference between values Heat exchanger effectiveness Roughness height Emissivity for radiation; ⑀λ, monochromatic emissivity at wavelength λ; ⑀φ, emissivity in direction φ Thermal eddy diffusivity Momentum eddy diffusivity Ratio of thermal to hydrodynamic boundarylayer thickness, δh/δth Efficiency; ηf, fin efficiency Wavelength; λmax, wavelength at which monochromatic emissive power Ebλ is a maximum Absolute viscosity Kinematic viscosity, µ/ρ Frequency of radiation Velocity potential Mass density, 1/v; ρ1, density of liquid; ρv, density of vapor Shearing stress, τs, shearing stress at surface; τw, shear at wall of a tube or a duct Transmissivity for radiation Stefan-Boltzmann constant Surface tension Angle Stokes’ stream function Angular velocity Solid angle Dimensionless Numbers Bi Ec Eu Fo Fr Gz Gr Ja Kn M Nu Pe Biot number Eckert number Euler number Fourier modulus Froude number Graetz number Grahsof number Jakob number Knudsen number Mach number Average Nusselt number; NuD, average diameter Nusselt number; Nux, local Nusselt number Peclet number © 2000 by CRC Press LLC SI English Dimensions (MLtT) N/kg kg/s·m lb/lbm lbm/hr·ft L t–2 M L–2 t–1 m ft L none none m none none ft — — L m2/s m2/s — ft2/s ft2/s — L2 t–1 L2 t–1 — none µm none micron — L N·s/m2 m2/s 1/s m2/s kg/m3 lb/ft·s ft2/s 1/s ft2/s lbmft3 M L–1 t–1 L2 t–1 t–1 L2 t–1 M L–3 N/m2 lb/ft2 M L–1 t–2 none W/m2K4 N/m rad m3/s 1/s sr none Btu/hr ft2R4 lb/ft rad ft3/s 1/s steradian — M t–3 T–4 M t–2 — L3 t–1 t–1 — A-32 TABLE A.8 (continued) Ideal Gas Properties of Air Part b English Units © 2000 by CRC Press LLC A-33 TABLE A.8 (continued) Ideal Gas Properties of Air Source: Adapted from M.J Moran and H.N Shapiro, Fundamentals of Engineering Thermodynamics, 3rd ed., Wiley, New York, 1995, as based on J.H Keenan and J Kaye, Gas Tables, Wiley, New York, 1945 © 2000 by CRC Press LLC Table A.9 Equations forGas Properties Appendix B Properties of Liquids B-35 TABLE B.1 Properties of Liquid Water* Symbols and Units: ρ = density, lbm/ft3 For g/cm3 multiply by 0.016018 For kg/m3 multiply by 16.018 cp = specific heat, Btu/lbm·deg R = cal/g·K For J/kg·K multiply by 4186.8 µ = viscosity For lbf·sec/ft2 = slugs/sec·ft, multiply by 10–7 For lbm·sec·ft multiply by 10–7 and by 32.174 For g/sec·cm (poises) multiply by 10–7 and by 478.80 For N·sec/m2 multiply by 10–7 and by 478.880 k = thermal conductivity, Btu/hr·ft·deg R For W/m·K multiply by 1.7307 B Appendix B Properties of Liquids © 2000 by CRC Press LLC B-36 TABLE B.2 Physical and Thermal Properties of Common Liquids Part a SI Units (At 1.0 Atm Pressure (0.101 325 MN/m2), 300 K, except as noted.) © 2000 by CRC Press LLC C-37 Appendix C Properties of Solids TABLE C.1 Properties of Common Solids* © 2000 by CRC Press LLC C Appendix C Properties of Solids C-38 TABLE C.2 Miscellaneous Properties of Metals and Alloys Part a Pure Metals At Room Temperature C © 2000 by CRC Press LLC C-39 TABLE C.2 Miscellaneous Properties of Metals and Alloys Part b Commercial Metals and Alloys © 2000 by CRC Press LLC D Appendix D SI Units D-40 Appendix D SI Units and Conversion Factors Greek Alphabet Greek Letter Α Β Γ ∆ Ε Ζ Η Θ Ι Κ Λ Μ α β γ δ ε ζ η θ ϑ ι κ λ µ Greek Name English Equivalent Alpha Beta Gamma Delta Epsilon Zeta Eta Theta Iota Kappa Lambda Mu a b g d e z e th i k l m Greek Letter Ν Ξ Ο Π Ρ Σ Τ Υ Φ Χ Ψ Ω ν ξ ο π ρ σ ς τ υ φ ϕ χ ψ ω Greek Name English Equivalent Nu Xi Omicron Pi Rho Sigma Tau Upsilon Phi Chi Psi Omega n x o p r s t u ph ch ps o International System of Units (SI) The International System of units (SI) was adopted by the 11th General Conference on Weights and Measures (CGPM) in 1960 It is a coherent system of units built from seven SI base units, one for each of the seven dimensionally independent base quantities: the meter, kilogram, second, ampere, kelvin, mole, and candela, for the dimensions length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity, respectively The definitions of the SI base units are given below The SI derived units are expressed as products of powers of the base units, analogous to the corresponding relations between physical quantities but with numerical factors equal to unity In the International System there is only one SI unit for each physical quantity This is either the appropriate SI base unit itself or the appropriate SI derived unit However, any of the approved decimal prefixes, called SI prefixes, may be used to construct decimal multiples or submultiples of SI units It is recommended that only SI units be used in science and technology (with SI prefixes where appropriate) Where there are special reasons for making an exception to this rule, it is recommended always to define the units used in terms of SI units This section is based on information supplied by IUPAC Definitions of SI Base Units Meter: The meter is the length of path traveled by light in vacuum during a time interval of 1/299 792 458 of a second (17th CGPM, 1983) Kilogram: The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram (3rd CGPM, 1901) Second: The second is the duration of 192 631 770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom (13th CGPM, 1967) Ampere: The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed meter apart in vacuum, would produce between these conductors a force equal to × 10–7 newton per meter of length (9th CGPM, 1958) Kelvin: The kelvin, unit of thermodynamic temperature, is the fraction 1/273.16 of the thermodynamic temperature of the triple point of water (13th CGPM, 1967) Mole: The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon-12 When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, or other particles, or specified groups of such particles (14th CGPM, 1971) Examples of the use of the mole: â 2000 by CRC Press LLC D-41 ã • • • • • • 1 1 1 mol mol mol mol mol mol mol of of of of of of of H2 contains about 6.022 × 1023 H2 molecules, or 12.044 × 1023 H atoms HgCl has a mass of 236.04 g Hg2Cl2 has a mass of 472.08 g Hg 2+ has a mass of 401.18 g and a charge of 192.97 kC Fe0.91 S has a mass of 82.88 g e– has a mass of 548.60 µg and a charge of –96.49 kC photons whose frequency is 1014 Hz has energy of about 39.90 kJ Candela: The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540 × 1012 Hz and that has a radiant intensity in that direction of (1/683) watt per steradian (16th CGPM, 1979) Names and Symbols for the SI Base Units Physical Quantity Name of SI Unit Symbol for SI Unit Length Mass Time Electric current Thermodynamic temperature Amount of substance Luminous intensity meter kilogram second ampere kelvin mole candela m kg s A K mol cd SI Derived Units with Special Names and Symbols Physical Quantity Frequencya Force Pressure, stress Energy, work, heat Power, radiant flux Electric charge Electric potential, electromotive force Electric resistance Electric conductance Electric capacitance Magnetic flux density Magnetic flux Inductance Celsius temperatureb Luminous flux Illuminance Activity (radioactive) Absorbed dose (or radiation) Dose equivalent (dose equivalent index) Plane angle Solid angle a b Name of SI Unit Symbol for SI Unit Expression in Terms of SI Base Units hertz newton pascal joule watt coulomb volt ohm siemens farad tesla weber henry degree Celsius lumen lux becquerel gray sievert radian steradian Hz N Pa J W C V Ω S F T Wb H °C lm lx Bq Gy Sv rad sr s–1 m · kg · s–2 N · m–2 = m–1 · kg · s–2 N · m = m2 · kg · s–2 J · s–1 = m2 · kg · s–3 A·s J · C–1 = m2 · kg · s–3 · A–1 V · A–1 = m2 · kg · s–3 · A–2 Ω–1 = m–2 · kg–1 · s4 · A2 C · V–1 = m–2 · kg–1 · s4 · A2 V · s · m–2 = kg · s–2 · A–1 V · s = m2 · kg · s–2 · A–1 V · A–1 · s = m2 · kg · s–2 · A–2 K cd · sr cd · sr · m–2 s–1 J · kg–1 = m2 · s–2 J · kg–1 = m2 · s–2 = m · m–1 = m2 · m–2 For radial (circular) frequency and for angular velocity the unit rad s–1, or simply s–1, should be used, and this may not be simplified to Hz The unit Hz should be used only for frequency in the sense of cycles per second The Celsius temperature θ is defined by the equation q/°C = T/K = 237.15 The SI unit of Celsius temperature interval is the degree Celsius, °C, which is equal to the kelvin, K °C should be treated as a single symbol, with no space between the ° sign and the letter C (The symbol °K, and the symbol °, should no longer be used.) © 2000 by CRC Press LLC D-42 Units in Use Together with the SI These units are not part of the SI, but it is recognized that they will continue to be used in appropriate contexts SI prefixes may be attached to some of these units, such as milliliter, ml; millibar, mbar; megaelectronvolt, MeV; and kilotonne, kt Physical Quantity Name of Unit Symbol for Unit Value in SI Units Time Time Time Plane angle Plane angle Plane angle Length Area Volume Mass Pressure Energy Mass minute hour day degree minute second angstroma barn liter tonne bara electronvoltb unified atomic mass unitb,c h d ° ′ ″ Å b l, L t bar eV (= e × V) u (= ma(12C)/12) 60 s 3600 s 86 400 s (π/180) rad (π/10 800) rad (π/648 000) rad 10–10 m 10–28 m2 dm3 = 10–3 m3 Mg = 103 kg 105 Pa = 105 N · m–2 ≈ 1.60218 × 10–19 J ≈ 1.66054 × 10–27 kg a b c The angstrom and the bar are approved by CIPM for “temporary use with SI units,” until CIPM makes a further recommendation However, they should not be introduced where they are not used at present The values of these units in terms of the corresponding SI units are not exact, since they depend on the values of the physical constants e (for the electronvolt) and NA (for the unified atomic mass unit), which are determined by experiment The unified atomic mass unit is also sometimes called the dalton, with symbol Da, although the name and symbol have not been approved by CGPM Conversion Constants and Multipliers Recommended Decimal Multiples and Submultiples Multiple or Submultiple 18 10 1015 1012 109 106 103 102 10 Prefix exa peta tera giga mega kilo hecto deca Symbol Multiple or Submultiple –1 E P T G M k h da 10 10–2 10–3 10–6 10–9 10–12 10–15 10–18 Prefix Symbol deci centi milli micro nano pico femto atto d c m µ (Greek mu) n p f a Conversion Factors — Metric to English To Obtain Inches Feet Yards Miles Ounces Pounds © 2000 by CRC Press LLC Multiply Centimeters Meters Meters Kilometers Grams Kilograms By 0.393 700 787 3.280 839 895 1.093 613 298 0.621 371 192 3.527 396 195 × 10–2 2.204 622 622 D-43 To Obtain Multiply By Gallons (U.S liquid) Fluid ounces Square inches Square feet Square yards Cubic inches Cubic feet Cubic yards Liters Milliliters (cc) Square centimeters Square meters Square meters Milliliters (cc) Cubic meters Cubic meters 0.264 172 052 3.381 402 270 × 10–2 0.155 000 310 10.763 910 42 1.195 990 046 6.102 374 409 × 10–2 35.314 666 72 1.307 950 619 Conversion Factors — English to Metric To Obtain Multiply Bya Microns Centimeters Meters Meters Kilometers Grams Kilograms Liters Millimeters (cc) Square centimeters Square meters Square meters Milliliters (cc) Cubic meters Cubic meters Mils Inches Feet Yards Miles Ounces Pounds Gallons (U.S liquid) Fluid ounces Square inches Square feet Square yards Cubic inches Cubic feet Cubic yards 25.4 2.54 0.3048 0.9144 1.609 344 28.349 523 13 0.453 592 37 3.785 411 784 29.573 529 56 6.451 0.092 903 04 0.836 127 36 16.387 064 2.831 684 659 × 10–2 0.764 554 858 a Boldface numbers are exact; others are given to ten significant figures where so indicated by the multiplier factor Conversion Factors — General To Obtain Multiply Atmospheres Atmospheres Atmospheres Btu Btu Cubic feet Degree (angle) Ergs Feet Feet of water @ 4°C Foot-pounds Foot-pounds Foot-pounds per minute Horsepower Inches of mercury @ 0°C Joules Joules Kilowatts Kilowatts Kilowatts Feet of water @ 4°C Inches of mercury @ 0°C Pounds per square inch Foot-pounds Joules Cords Radians Foot-pounds Miles Atmospheres Horsepower-hours Kilowatt-hours Horsepower Foot-pounds per second Pounds per square inch Btu Foot-pounds Btu per minute Foot-pounds per minute Horsepower © 2000 by CRC Press LLC Bya 2.950 × 10–2 3.342 × 10–2 6.804 × 10–2 1.285 × 10–3 9.480 × 10–4 128 57.2958 1.356 × 10–7 5280 33.90 1.98 × 106 2.655 × 106 3.3 × 104 1.818 × 10–3 2.036 1054.8 1.355 82 1.758 × 10–2 2.26 × 10–5 0.745712 D-44 To Obtain Knots Miles Nautical miles Radians Square feet Watts a Bya Multiply Miles per hour Feet Miles Degrees Acres Btu per minute 0.868 976 24 1.894 × 10–4 0.868 976 24 1.745 × 10–2 43 560 17.5796 Boldface numbers are exact; others are given to ten significant figures where so indicated by the multiplier factor Temperature Factors °F = (°C) + 32 Fahrenheit temperature = 1.8(temperature in kelvins) − 459.67 °C = 9[(°F) − 32] Celsius temperature = temperature in kelvins − 273.15 Fahrenheit temperature = 1.8(Celsius temperature) + 32 Conversion of Temperatures From To Fahrenheit Celcius Kelvin Rankine © 2000 by CRC Press LLC From tC = t F − 32 1.8 t − 32 Tk = F + 273.15 1.8 TR = tF + 459.67 To Celsius Fahrenheit Kelvin tF = (tc × 1.8) + 32 TK = tc + 273.15 Rankine Celsius Rankine TR = (tc + 273.15) × 18 tc = TK – 273.15 TR = Tk × 1.8 Fahrenheit Kelvin tF = TR – 459.67 Kelvin Rankine TK = TR 1.8 D-46 © 2000 by CRC Press LLC ... goal of this handbook is to provide this type of up-to-date information for engineers involved in the field of thermal engineering This handbook is not designed to compete with traditional handbooks... thermal conductivity of a solid; kf, thermal conductivity of a fluid; kg, thermal conductivity of a gas Thermal conductance; kk, thermal conductance for conduction heat transfer; kc, thermal convection...Library of Congress Cataloging-in-Publication Data The CRC handbook of thermal engineering / edited by Frank Kreith p cm (The mechanical engineering handbook series) Includes