DOCSLIB.ORG

Heat Transfer to Liquid Sodium in the Thermal Entrance Region

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Heat Transfer to Liquid Sodium in the Thermal Entrance Region UNIVERSITE LIBRE DE BRUXELLES FACULTE DES SCIENCES APPLIQUEES CENTRE O'ETUDE DE L'ENERGIE NUCLEAIRE STUDIECENTRUM VOOR KERNENERGIE HEAT TRANSFER TO LIQUID SODIUM IN THE THERMAL ENTRANCE REGION UN, RMSII Mai 1101 Dlsstrtatfei artstatta •• wit dt J'titiHIti rfi iratft tft . •tctiar M SclMCtt ApMltjMtt. UNIVERSITE LIBRE DE BRUXELLES FACULTE DES SCIENCES APPLIQUEES Institut de Mécanique Service de Métrologie Appliquée Nucléaire CENTRE D'ETUDE DE L'ENERGIE NUCLEAIRE STUDIECENTRUM VOOR KERNENERGIE Département Technologie h Energie HEAT TRANSFER TO LIQUID SODIUM IN THE THERMAL ENTRANCE REGION QIU, Reuse» Mai 1981 Dissertation présentée ei vie de l'obtention da trade de Docteur en Sciences Appliques. , >* Le travail, obget de oe mimoire, a 6ti effectuS aous la direction de la Faculti dee Saienaea Appliquiea de I'VniveraitS Libre de Bruxelle8 et r&alis6 au department Technologic et Energie du Centre d'Etude de I'Energie NucUaire d MDL. Je tiena d remeroier vivement lea direeteur8 Messieurs les Professsurs A. JAUMOTTE et J. DEVCOGET pour lea suggestions utilea, lea discussions fructueuaea et lea encouragements incessants. ties remerciement8 vont 4galement & Monsieur J. PLANQUART, Chef du d&gartewenty pour le support effioaae et lea enoouragementa prodiguis tout au long de won travail. Toute ma reaormaiaaanae A Meaeieura G. VAXMASSEHHOVE, J. DEKEYSER et B. ARIEN ainei qu'd. toue ceux du d&partement qui ont3 par leur travail et leur aoutien3 contribuer & la realisation du montage, & la pourauite des essais et a la dactylographie du document. GrSae a la collaboration de toua3 j'ai pu terminer ce travail dans lea dilaia courts qui m'Staient fia&a, notamsnt du fait de la durie limitie de mm sijour en Belgique. QIU, Beneen. CONTENTS List of Figures Nomenclature I Introduction ' II Literature Review 4 2.1. Theoretical Studies 5 2.2. Experimental Studies 28 III General Investigation about Heat Transfer in the Thermal 41 Entrance Region 3.1. Characteristics of Liquid Sodium 42 3.2. Behaviors in the Thermal Entrance Region 44 3.3. Thermal Entrance Length 50 3.4. Influence of Reynolds Number on Heat Transfer in the 53 Thermal Entrance Region 3.5. Influence of Prandtl Number on Heat Transfer in the 60 Thermal Entrance Region 3.6. Influence of Velocity Development on tfeat Transfer in 66 the Thermal Entrance Region 3.7. Hydrodynamic Entrance Length 70 3.8. Effect of Axial Conduction 71 3.9. Natural Convection Effect on Heat Transfer in the 79 Thermal Entrance Region 3.10. Influence of Radius Ratio 86 3.11. Influence of Circumferential Variation of Heat Flux on 87 Heat Transfer in the Thermal Entrance Region 3.12. Effects of Wetting, Oxide Film and Gas Entrainment 89 Document typed and printed at CEN/SCR - MOL. II IV Theoretical Analysis of Turbulent Heat Transfer to Liquid 95 Sodium in the Thermal Entrance Region 4.1. Turbulent Energy Equation 96 4.2. Turbulent Heat Transfer to Liquid Solium in the Thermal 10] Entrance Regions of Annulus and Rod Bundles 4.3. Velocity Profiles in the Annular Channel 127 4.4. Eddy Diffusivities 140 4.5. Ratio of the Eddy Diffusivity for Heat Transfer to the 148 Eddy Diffusivity for Momentum Transfer 4.6. Radius of Maximum Local Velocity Point 150 4.7. Friction Velocity 154 4.8. Analytical Results of Heat Transfer in the Thermal 158 Entrance Region of Annulus 4.9. Turbulent Heat Transfer in the Thermal Entrance Region 162 of Circular Tube 4.10. Turbulent Heat Transfer in the Thermal Entrance Region 165 of Parallel-Plate Channel 4.11. Heat Transfer in Annulus and Rod Bundles with Variable |69 Heat Flux 4.12. Asymptotic Solution for the Initial Portion of Thermal 173 Entrance Region 4.13. Comparison with the Results Neglecting Thermal Developing 181 Effect 4.14. Time-Dependent Temperature Evolution 186 Ill Experimental Investigation of Turbulent Heat Transfer to Liquid 191 Sodium in the Thermal Entrance Region of Annulus 5.1. Purposes of Experiments 192 5.2. Related Characteristics of the Core of Fast Reactor 192 5.3. Definition of Experimental Conditions 193 5.3.1. Definition of the diameters of channel 5.3.2. Definition of the heating element length 5.3.3. Definition of the length of the section for stabilization of flow 5.3.4. Definition of the inlet teaperature of the test section 5.3.5. Definition of the flowrate in the test section 5.4. Description of the Experimental System 196 5.4.1. Description of sodium loop 5.4.2. Description of test section 5.4.3. Measurement system 5.5. Preliminary Experiments 210 5.5.1. Purposes of preliminary experiments 5.5.2. Verification of the readings of thermocouples 5.5.3. Determination of heat less 5.5.4. Determination of stabilization time 5.6. Procedure of Main Experiments 212 5.7. Data Reduction 213 5.7.1. Bulk temperature 5.7.2. Wall temperature 5.7.3. Heat loss 5.7.4. Leak flowrate 5.7.5. Parameters representing the results 5.7.6. Estimation of teaperature measurement errors produced by the lead wires of thermocouples 5.7.7. Correction for the influence of thermocouple station 5.8. Time-dependent Temperature Evolution in the Channel of Liquid 229 Sodium 5.8.1. Experimental apparatus 5.8.2. Experimental procedures IV 5.9. Results of Experiments. 232 5.9.1. Results of the main experiments 5.9.2. Results of the time-dependent temperature experiments 5.10. Error Analysis 236 VI. Discussion and Conclusions. 239 6.1. Comparison of Theoretical and Experimental Results 240 6.2. Comparison of Fully Developed Values of the Nusselt Number 240 6.3. Conclusions. 241 BIBLIOGRAPHY 243 APPENDIX 262 FIGURES 268 LIST OF FIGURES 3.1.-1 Fully developed temperature distribution during turbulent heat transfer 3.2.-1 Boundary layer growth 3.2.-2 Coordinates for parallel-plate channel 3.3.-1 Variation of thermal entrance lengths 3.4.-1 Effect of Reynolds number (for Pr=0.006) 3.4.-2 Effect of Prandtl number (for Re=5xlO4, Y2/Yi=2) 3.4.-3 Effect of Reynolds number (for Pr=0.006, "Y2/Yx=2) 3.4.-4 Effect of Reynolds number (for Pr=0.74, y2/ j=2) 3.5.-1 Effect of Prandtl number for pipe (for Re=104) 3.5.-2 Effect of Prandtl number for parallel plates (for Re=104) 3.5.-3 Effect of Prandtl number (for Re=5xlO4, Y2/Vi=2) 3.5.-4 Variation of thermal entrance length 3.6.-1 Effect of velocity development 3.8.-1 Effect of axial conduction (for various Pe) 3.8.-2 Effect of axial conduction (for various Re) 3.8.-3 Effect of axial conduction (for various Pr) 3.9.-1 Effect of natural convection 4.2.-1 Annular cell 4.2.-2 Annular channel 4.2.-3 Differential element for energy balance 4.3.-1 Shear stress nomenclature 4.3.-2 Variation of heat flux 4.3.-3 Comparison of results with difterent velocity profiles 4.5.-1 Comparison of results with different values I|I = 4.8.-1 Effect of Reynolds number (for Pr=0.0054t Y2/Yi 2) 4.8.-2 Effect of Reynolds number (for Pr=0.0054, Y2/Yi=2) 4.8.-3 Effect of Reynolds number (for Pr=0.0054, Y2»Yi=2) 4.8.-4 Temperature profiles (for Re=6.000, Y2/"Yi=2) 4.8.-5 Temperature profiles (for Re=8.000, Y2/Yi=2) 4.8.-6 Temperature profiles (for Re=2xlO4, Y2/Yi=2) 4.8.-7 Temperature profiles (for Re=4xlO4, Y2/Vi=2) 4.8.-8 Temperature profiles (for Re=6xlO4, Y2/Yi=2) 4 4.8.-9 Temperature profiles (for Re=8xlO , Y2/Yi=2) 4.8.-10 Temperature profiles (for Re=105, Y2/Yi=2) 4.8.-11 Temperature profiles (for Re=2xlOs, Y2/'Yi=2) 4.8.-12 Temperature profiles (for Re=5xlO5, Y2/Yi=2) 4.8.-13 Effect of Reynolds number (for Pr=0.0054, Y2/Yi=l-5) 4.8.-14 Effect of Reynolds number (for Pr=0.0054, Y2/Yi=l-5) 4.8.-15 Effect of Reynolds number (for Pr=0.0054, Y2/ i=l-5) 4.8.-16 Temperature profiles (for Re=6.000, Y2/Yi=l-5) 4.8.-17 Temperature profiles (for Re=104, Y2/Yi=l-5) 4.8.-18 Temperature profiles (for Re=4xlO4, Y2/Yi=l-5) 4.8.-19 Temperature profiles (for Re=10s, Y2/Yi=l»5) 4.8.-20 Temperature profiles (for Re=5xlO5, Y2/Yi=l-5) 4.8.-21 Variation of thermal entrance length with Re 4.8.-22 Effect of Prandtl number (for Re=5xl04, Y2/Yi=2) 4.8.-23 Effect of Prandtl number (for Re=5xlO4, Y2/Yi=l-5) 4.8.-24 Effect of radius ratio (for Re=5xlO4, Pr=C.OO52) 4.8.-25 Comparison of results 4.8.-26 Comparison of fully developed Nusselt number 4.11.-1 Variation of Nu for the annulus 4.11.-2 Variation of Nu with element length (for Re=5xlO4) 4.11.-3 Variation of Nu with element length (for Re=104) 4.11.-4 Effect of pitch to diameter ratio (for L=100De) 4.11.-5 Effect of pitch to diameter ratio (for L=30De) 4.11.-6 Effect of amplitude (for L=20De) 4.11.-7 Effect of amplitude (for I=100De) 4.11.-8 Axial temperature distribution 4.12.-1 Comparison of temperature profiles 4.12.-2 Comparison of Nusselt numbers 4.13.-1 Comparison of temperature profiles 5.4.-1 Na2 loop flow sheet 5.4.-2 Test section 5.4.-3 Cross section of test section 5.4.-4 Block diagram of measurement system 5.7.-1 Nomenclature of test section 5.9.-1 Temperature profiles (Pr - 0.0059, Re « 6,000) 5.9.-2 Temperature profiles (Pr - 0.0059, Re - 8,000} 5.9.-3 Temperature profiles (Pr - 0.0054, Re » 2 x 104) 5.9.-4 Temperature profiles (Pr • 0.0054, Re - 5 x 104) 5.9.-5 Temperature profiles (Pr - 0.0054, Re - 6 x 104) 5.9.-6 Variation of Nusselt number with Re (Pr * 0.0059, Re « 6,000 - 10 ) 5.9.-7 Variation of Nusselt number with Re (Pr * 0.0059, Re - 2 x 10 - 5.5 x 104) 5.9.-8 Variation of Nusselt number with Re (Pr - 0.0054, Re - 6,000 - JO4) 5.9.-9 Variation of Nusselt number with Re (Pr - 0.0054, Re « 2 x 104 - 6 x 104) 5.9.-10 Variation of Nusselt number with Pr (Re - 104) 5.9.-11 Variation of Nusselt number with Pr (Re • 5 x 104) 5.9.-12 Effect of heat flux 5.9.-13 Wall temperature distribution 5.9.-14 Comparison of Nusselt numbers 5.9.-15 Comparison of temperature profiles 5.9.-16 Temperature evolution for a period T » 60 sec.
Load more

Recommended publications
  • Static Mixing Spacers for Spiral Wound Modules
    Desalination and Water Purification Research and Development Program Report No. 161 Static Mixing Spacers for Spiral Wound Modules U.S. Department of the Interior Bureau of Reclamation Technical Service Center Denver, Colorado November 2012 Form Approved REPORT DOCUMENTATION PAGE OMB No. 0704-0188 The public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing the burden, to Department of Defense, Washington Headquarters Services, Directorate for Information Operations and Reports (0704-0188), 1215 Jefferson Davis Highway, Suite 1204, Arlington, VA 22202-4302. Respondents should be aware that notwithstanding any other provision of law, no person shall be subject to any penalty for failing to comply with a collection of information if it does not display a currently valid OMB control number.PLEASE DO NOT RETURN YOUR FORM TO THE ABOVE ADDRESS. 1. REPORT DATE (DD-MM-YYYY) 2. REPORT TYPE 3. DATES COVERED (From - To) November 2012 Final 2010-2012 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER Static Mixing Spacers for Spiral Wound Modules Agreement No.R10AP81213 5b. GRANT NUMBER 5c. PROGRAM ELEMENT NUMBER 6. AUTHOR(S) 5d. PROJECT NUMBER Glenn Lipscomb 5e. TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER Chemical Engineering Task Identification Number University of Toledo Task IV: Expanding Scientific 3048 Nitschke Hall (MS 305) Understanding of Desalination Processes 1610 N Westwood Ave Subtask: Increase of rates of mass transfer Toledo, OH 43607 to membrane or to heat transfer surfaces.
    [Show full text]
  • Experimental Heat Transfer and Friction Factor of Fe3o4 Magnetic Nanofluids Flow in a Tube Under Laminar Flow at High Prandtl Numbers
    International Journal of Heat and Technology Vol. 38, No. 2, June, 2020, pp. 301-313 Journal homepage: http://iieta.org/journals/ijht Experimental Heat Transfer and Friction Factor of Fe3O4 Magnetic Nanofluids Flow in a Tube under Laminar Flow at High Prandtl Numbers Lingala Syam Sundar1*, Hailu Misganaw Abebaw2, Manoj K. Singh3, António M.B. Pereira1, António C.M. Sousa1 1 Centre for Mechanical Technology and Automation (TEMA–UA), Department of Mechanical Engineering, University of Aveiro, Aveiro 3810-131, Portugal 2 Department of Mechanical Engineering, University of Gondar, Gondar, Ethiopia 3 Department of Physics – School of Engineering and Technology (SOET), Central University of Haryana, Haryana 123031, India Corresponding Author Email: [email protected] https://doi.org/10.18280/ijht.380204 ABSTRACT Received: 15 February 2020 The work is focused on the estimation of convective heat transfer and friction factor of Accepted: 23 April 2020 vacuum pump oil/Fe3O4 magnetic nanofluids flow in a tube under laminar flow at high Prandtl numbers experimentally. The thermophysical properties also studied Keywords: experimentally at different particle concentrations and temperatures. The Fe3O4 heat transfer enhancement, friction factor, nanoparticles were synthesized using the chemical reaction method and characterized using laminar flow, high Prandtl number, magnetic X-ray powder diffraction (XRD) and vibrating sample magnetometer (VSM) techniques. nanofluid The experiments were conducted at mass flow rate from 0.04 kg/s to 0.208 kg/s, volume concentration from 0.05% to 0.5%, Prandtl numbers from 440 to 2534 and Graetz numbers from 500 to 3000. The results reveal that, the thermal conductivity and viscosity enhancements are 9% and 1.75-times for 0.5 vol.
    [Show full text]
  • Exact Solution of Boundary Value Problem Describing the Convective Heat Transfer in Fully-Developed Laminar Flow Through a Circular Conduit
    Songklanakarin J. Sci. Technol. 40 (4), 840-853, Jul - Aug. 2018 Original Article Exact solution of boundary value problem describing the convective heat transfer in fully-developed laminar flow through a circular conduit Ali Belhocine1* and Wan Zaidi Wan Omar2 1Faculty of Mechanical Engineering, University of Sciences and the Technology of Oran, L. P. 1505 El – Mnaouer, Oran, 31000 Algeria 2Faculty of Mechanical Engineering, Universiti Teknologi Malaysia, UTM Skudai, Johor, 81310 Malaysia Received: 17 September 2016; Revised: 2 March 2017; Accepted: 8 May 2017 Abstract This paper proposes anexact solution in terms of an infinite series to the classical Graetz problem represented by a nonlinear partial differential equation considering two space variables, two boundary conditions and one initial condition. The mathematical derivation is based on the method of separation of variables whose several stages are elaborated to reach the solution of the Graetz problem. MATLAB was used to compute the eigenvalues of the differential equation as well as the coefficient series. However, both the Nusselt number as an infinite series solution and the Graetz number are based on the heat transfer coefficient and the heat flux from the wall to the fluid. In addition, the analytical solution was compared to the numerical values obtained by the same author using a FORTRAN program, showing that the orthogonal collocation method gave better results. It is important to note that the analytical solution is in good agreement with published numerical data. Keywords:
    [Show full text]
  • Heat Transfer Data
    Appendix A HEAT TRANSFER DATA This appendix contains data for use with problems in the text. Data have been gathered from various primary sources and text compilations as listed in the references. Emphasis is on presentation of the data in a manner suitable for computerized database manipulation. Properties of solids at room temperature are provided in a common framework. Parameters can be compared directly. Upon entrance into a database program, data can be sorted, for example, by rank order of thermal conductivity. Gases, liquids, and liquid metals are treated in a common way. Attention is given to providing properties at common temperatures (although some materials are provided with more detail than others). In addition, where numbers are multiplied by a factor of a power of 10 for display (as with viscosity) that same power is used for all materials for ease of comparison. For gases, coefficients of expansion are taken as the reciprocal of absolute temper­ ature in degrees kelvin. For liquids, actual values are used. For liquid metals, the first temperature entry corresponds to the melting point. The reader should note that there can be considerable variation in properties for classes of materials, especially for commercial products that may vary in composition from vendor to vendor, and natural materials (e.g., soil) for which variation in composition is expected. In addition, the reader may note some variations in quoted properties of common materials in different compilations. Thus, at the time the reader enters into serious profes­ sional work, he or she may find it advantageous to verify that data used correspond to the specific materials being used and are up to date.
    [Show full text]
  • Similitude of Forced Convection Heat Transfer of Dowtherm a and of Li2bef4 Molten Salt in Cylindrical Tubes
    Similitude of forced convection heat transfer of Dowtherm A and of Li2BeF4 molten salt in cylindrical tubes By Dajie Sun A thesis submitted in partial satisfaction of the requirements for the degree of Master of Science in Nuclear Engineering in the Graduate Division of the University of California, Berkeley Committee in charge: Prof. Per Peterson, Chair Prof. Karl van Bibber Prof. Jasmina Vujic Summer 2017 The University of California Berkeley Department of Nuclear Engineering Content Symbols ......................................................................................................................................................................................... ii Abstract .......................................................................................................................................................................................... 1 Chapter 1 Introduction ............................................................................................................................................................. 1 Chapter 2 Description of Experiments ................................................................................................................................ 4 Chapter 3 Theoretical model for data reduction ............................................................................................................. 7 Chapter 4 Fitting Method .......................................................................................................................................................
    [Show full text]
  • On Dimensionless Numbers
    chemical engineering research and design 8 6 (2008) 835–868 Contents lists available at ScienceDirect Chemical Engineering Research and Design journal homepage: www.elsevier.com/locate/cherd Review On dimensionless numbers M.C. Ruzicka ∗ Department of Multiphase Reactors, Institute of Chemical Process Fundamentals, Czech Academy of Sciences, Rozvojova 135, 16502 Prague, Czech Republic This contribution is dedicated to Kamil Admiral´ Wichterle, a professor of chemical engineering, who admitted to feel a bit lost in the jungle of the dimensionless numbers, in our seminar at “Za Plıhalovic´ ohradou” abstract The goal is to provide a little review on dimensionless numbers, commonly encountered in chemical engineering. Both their sources are considered: dimensional analysis and scaling of governing equations with boundary con- ditions. The numbers produced by scaling of equation are presented for transport of momentum, heat and mass. Momentum transport is considered in both single-phase and multi-phase flows. The numbers obtained are assigned the physical meaning, and their mutual relations are highlighted. Certain drawbacks of building correlations based on dimensionless numbers are pointed out. © 2008 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved. Keywords: Dimensionless numbers; Dimensional analysis; Scaling of equations; Scaling of boundary conditions; Single-phase flow; Multi-phase flow; Correlations Contents 1. Introduction .................................................................................................................
    [Show full text]
  • The Graetz–Nusselt Problem Extended to Continuum Flows With
    J. Fluid Mech. (2015), vol. 764, R3, doi:10.1017/jfm.2014.733 The Graetz–Nusselt problem extended to continuum flows with finite slip A. Sander Haase1, S. Jonathan Chapman2, Peichun Amy Tsai1, Detlef Lohse3 and Rob G. H. Lammertink1, † 1Soft matter, Fluidics and Interfaces, MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands 2Mathematical Institute, University of Oxford, 24-29 St Giles, Oxford OX1 3LB, UK 3Physics of Fluids, MESA+ Institute for Nanotechnology, University of Twente, PO Box 217, 7500 AE Enschede, The Netherlands (Received 13 October 2014; revised 10 December 2014; accepted 12 December 2014) Graetz and Nusselt studied heat transfer between a developed laminar fluid flow and a tube at constant wall temperature. Here, we extend the Graetz–Nusselt problem to dense fluid flows with partial wall slip. Its limits correspond to the classical problems for no-slip and no-shear flow. The amount of heat transfer is expressed by the local Nusselt number Nux, which is defined as the ratio of convective to conductive radial heat transfer. In the thermally developing regime, Nux scales with the ratio of position β x x=L to Graetz number Gz, i.e. Nux .x=Gz/− . Here, L is the length of the heatedQ D or cooled tube section. The Graetz/ numberQ Gz corresponds to the ratio of axial advective to radial diffusive heat transport. In the case of no slip, the scaling exponent β equals 1=3. For no-shear flow, β 1=2. The results show that for partial slip, where the ratio of slip length b to tube radiusD R ranges from zero to infinity, β transitions 4 0 from 1=3 to 1=2 when 10− < b=R < 10 .
    [Show full text]
  • Use of Dimensionless Numbers in Analyzing Melt Flow and Melt Cooling Processes
    USE OF DIMENSIONLESS NUMBERS IN ANALYZING MELT FLOW AND MELT COOLING PROCESSES NATTI S. RAO RANGANATH SHASTRI Plastics Solutions International CIATEO Ghent, NY 12075, USA San Luis Potosi, Mexiko Email: [email protected] Email:[email protected] ABSTRACT Dimensionless analysis is a powerful tool in analyzing the transient heat transfer and flow processes accompanying melt flow in an injection mold or cooling in blown film,to quote a couple of examples. However, because of the nature of non-Newtonian polymer melt flow the dimensionless numbers used to describe flow and heat transfer processes of Newtonian fluids have to be modified for polymer melts. This paper describes how an easily applicable equation for the cooling of melt in a spiral flow in injection molds has been derived on the basis of modified dimensionless numbers and verified by experiments. Analyzing the air gap dynamics in extrusion coating is another application of dimensional analysis. PREDICTING FLOW LENGTH IN INJECTION MOLDS Injection molding is widely used to make articles out of plastics for various applications. One of the criteria for the selection of the resin to make a given part is whether the melt is an easy flowing type or whether it exhibits a significantly viscous behavior. To determine the flowability of the polymer melt the spiral test, which consists of injecting the melt into a spiral shaped mold shown in Figure 1, is used. The length of the spiral serves as a measure of the ease of flow of the melt in the mold, and enables mold and part design suited to material flow.
    [Show full text]
  • The Dimnum Package
    The dimnum package Miguel R. Clemente [email protected] v1.0.1 from 2021/04/05 Note: Prandtl number is redefined from the amsmath package. 1 Introduction This package simplifies the calling of Dimensionless Numbers in math or text mode. In Table 1 you can find all available Dimensionless Numbers. 2 Usage A Dimensionless number is composed of four items: the command, the symbol, the name, its identifier. You can call a Dimensionless Number in three distinct ways: by its symbol { using the command (i.e. \Ar { Ar). by its name (short version) { appending [s] to the command (i.e. \Bi[s] { Biot). by its name and identifier (long version) { appending [l] to the command (i.e. \Kn[l] { Knudsen number). Symbol, short and long versions, all work in math or text mode without the need of further commands. 1 Besides the comprehensive list of included Dimensionless Numbers, this pack- age also introduces a command to create new Dimensionless Numbers. Creating a Dimensionless Number is achieved by using \newdimnum{\command}{symbol}{name}{identifier} for example, to add the Morton number we write \newdimnum{\Mo}{Mo}{Morton}{number} The identifier can be left empty, such as in the case of Drag Coefficient \newdimnum{Cd}{\ensuremath{C_d}}{Drag Coefficient}{} in this example we also introduce an important command. When the Dimension- less Number symbol is always expressed in math mode { either by definition or the use of subscripts or superscripts { we add \ensuremath{} to encompass the symbol, ensuring a proper representation of the Dimensionless Number. You can add your own Dimensionless Numbers to your projects.
    [Show full text]
  • SASO-ISO-80000-11-2020-E.Pdf
    SASO ISO 80000-11:2020 ISO 80000-11:2019 Quantities and units - Part 11: Characteristic numbers ICS 01.060 Saudi Standards, Metrology and Quality Org (SASO) ----------------------------------------------------------------------------------------------------------- this document is a draft saudi standard circulated for comment. it is, therefore subject to change and may not be referred to as a saudi standard until approved by the boardDRAFT of directors. Foreword The Saudi Standards ,Metrology and Quality Organization (SASO)has adopted the International standard No. ISO 80000-11:2019 “Quantities and units — Part 11: Characteristic numbers” issued by (ISO). The text of this international standard has been translated into Arabic so as to be approved as a Saudi standard. DRAFT DRAFT SAUDI STANDADR SASO ISO 80000-11: 2020 Introduction Characteristic numbers are physical quantities of unit one, although commonly and erroneously called “dimensionless” quantities. They are used in the studies of natural and technical processes, and (can) present information about the behaviour of the process, or reveal similarities between different processes. Characteristic numbers often are described as ratios of forces in equilibrium; in some cases, however, they are ratios of energy or work, although noted as forces in the literature; sometimes they are the ratio of characteristic times. Characteristic numbers can be defined by the same equation but carry different names if they are concerned with different kinds of processes. Characteristic numbers can be expressed as products or fractions of other characteristic numbers if these are valid for the same kind of process. So, the clauses in this document are arranged according to some groups of processes. As the amount of characteristic numbers is tremendous, and their use in technology and science is not uniform, only a small amount of them is given in this document, where their inclusion depends on their common use.
    [Show full text]
  • Thermo-Hydrodynamics of Developing Flow in a Rectangular Mini-Channel Array
    THERMO-HYDRODYNAMICS OF DEVELOPING FLOW IN A RECTANGULAR MINI-CHANNEL ARRAY Gaurav Agarwal Manoj Kumar Moharana Sameer Khandekar Dept. of Mechanical Engineering Dept. of Mechanical Engineering Dept. of Mechanical Engineering Indian Institute of Technology Kanpur Indian Institute of Technology Kanpur Indian Institute of Technology Kanpur Kanpur (UP) 208016, India Kanpur (UP) 208016, India Kanpur (UP) 208016, India [email protected] [email protected] [email protected] ABSTRACT T Temperature (K) u Velocity (m/s) Thermo-hydrodynamic performance of hydrodynamically and thermally developing single-phase flow in an array of w Width of channel (m) rectangular mini-channels has been experimentally Xh Hydrodynamic entry length (m) investigated. The array consists of fifteen rectangular parallel Xth Thermal entry length (m) mini-channels of width 1.1±0.02 mm, depth 0.772±0.005 mm Greek symbols (hydraulic diameter 0.907 mm), inter-channel pitch of 2.0 mm, Height/width (aspect) ratio of rectangular channels machined on a copper plate of 8.0 mm thickness and having Mass density (kg/m3) an overall length of 50 mm. Deionized water used as the μ Dynamic viscosity (Ns/m2) working fluid, flows horizontally and the test section is heated Surface roughness parameter (m) directly using a thin mica insulated, surface-mountable, stripe Wall thermal conductivity (W/mK) heater (constant heat flux boundary condition). Reynolds number between 200 and 3200 at an inlet pressure of about Non-dimensional Numbers 1.1 bar, are examined. The laminar-to-turbulent transition is Gz Graetz number found to occur at Re 1100 for average channel roughness of Nu Nusselt Number 3.3 m.
    [Show full text]
  • Flow Phenomena, Heat and Mass Transfer in Microchannel Reactors
    LAPPEENRANTA UNIVERSITY OF TECHNOLOGY Faculty of Technology The Degree Program of Chemical Technology Master’s Thesis Flow phenomena, heat and mass transfer in microchannel reactors Examiners: Professor Ilkka Turunen D.Sc. Jukka Koskinen Supervisors: M.Sc. Isto Eilos M.Sc. Steven Gust D.Sc. Azita Soleymani Lappeenranta 12.09.2007 Warin Ratchananusorn Liesharjunkatu 5 C10 53850 Lappeenranta Finland Tel. +358 50 9365742 Acknowledgement I am exceptionally grateful to Professor Ilkka Turunen for giving me an opportunity to complete this Master’s Thesis with Neste Oil Oyj and for his valuable advice. I would like to thank Jukka Koskinen, Isto Eilos, and Steven Gust for their suggestions during my stay at Neste Oil Oyj. Also, I would like to thank Azita Soleymani who greatly helps me on the simulation work. Without her guidance, I would not have been able to complete my Master’s Thesis. Finally, I would like to thank to my family and all my friends who help me get through two years of study. ABSTRACT Lappeenranta University of Technology Faculty of Technology Author: Warin Ratchananusorn Title: Flow phenomena, heat and mass transfer in microchannel reactors Year: 2007 The studies of flow phenomena, heat and mass transfer in microchannel reactors are beneficial to estimate and evaluate the ability of microchannel reactors to be operated for a given process reaction such as Fischer-Tropsch synthesis. The flow phenomena, for example, the flow regimes and flow patterns in microchannel reactors for both single phase and multiphase flow are affected by the configuration of the flow channel. The reviews of the previous works about the analysis of related parameters that affect the flow phenomena are shown in this report.
    [Show full text]