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Convection Heat Transfer
Convection Heat Transfer Heat transfer from a solid to the surrounding fluid Consider fluid motion Recall flow of water in a pipe Thermal Boundary Layer • A temperature profile similar to velocity profile. Temperature of pipe surface is kept constant. At the end of the thermal entry region, the boundary layer extends to the center of the pipe. Therefore, two boundary layers: hydrodynamic boundary layer and a thermal boundary layer. Analytical treatment is beyond the scope of this course. Instead we will use an empirical approach. Drawback of empirical approach: need to collect large amount of data. Reynolds Number: Nusselt Number: it is the dimensionless form of convective heat transfer coefficient. Consider a layer of fluid as shown If the fluid is stationary, then And Dividing Replacing l with a more general term for dimension, called the characteristic dimension, dc, we get hd N ≡ c Nu k Nusselt number is the enhancement in the rate of heat transfer caused by convection over the conduction mode. If NNu =1, then there is no improvement of heat transfer by convection over conduction. On the other hand, if NNu =10, then rate of convective heat transfer is 10 times the rate of heat transfer if the fluid was stagnant. Prandtl Number: It describes the thickness of the hydrodynamic boundary layer compared with the thermal boundary layer. It is the ratio between the molecular diffusivity of momentum to the molecular diffusivity of heat. kinematic viscosity υ N == Pr thermal diffusivity α μcp N = Pr k If NPr =1 then the thickness of the hydrodynamic and thermal boundary layers will be the same. -
Laws of Similarity in Fluid Mechanics 21
Laws of similarity in fluid mechanics B. Weigand1 & V. Simon2 1Institut für Thermodynamik der Luft- und Raumfahrt (ITLR), Universität Stuttgart, Germany. 2Isringhausen GmbH & Co KG, Lemgo, Germany. Abstract All processes, in nature as well as in technical systems, can be described by fundamental equations—the conservation equations. These equations can be derived using conservation princi- ples and have to be solved for the situation under consideration. This can be done without explicitly investigating the dimensions of the quantities involved. However, an important consideration in all equations used in fluid mechanics and thermodynamics is dimensional homogeneity. One can use the idea of dimensional consistency in order to group variables together into dimensionless parameters which are less numerous than the original variables. This method is known as dimen- sional analysis. This paper starts with a discussion on dimensions and about the pi theorem of Buckingham. This theorem relates the number of quantities with dimensions to the number of dimensionless groups needed to describe a situation. After establishing this basic relationship between quantities with dimensions and dimensionless groups, the conservation equations for processes in fluid mechanics (Cauchy and Navier–Stokes equations, continuity equation, energy equation) are explained. By non-dimensionalizing these equations, certain dimensionless groups appear (e.g. Reynolds number, Froude number, Grashof number, Weber number, Prandtl number). The physical significance and importance of these groups are explained and the simplifications of the underlying equations for large or small dimensionless parameters are described. Finally, some examples for selected processes in nature and engineering are given to illustrate the method. 1 Introduction If we compare a small leaf with a large one, or a child with its parents, we have the feeling that a ‘similarity’ of some sort exists. -
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. -
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. -
Chapter 5 Dimensional Analysis and Similarity
Chapter 5 Dimensional Analysis and Similarity Motivation. In this chapter we discuss the planning, presentation, and interpretation of experimental data. We shall try to convince you that such data are best presented in dimensionless form. Experiments which might result in tables of output, or even mul- tiple volumes of tables, might be reduced to a single set of curves—or even a single curve—when suitably nondimensionalized. The technique for doing this is dimensional analysis. Chapter 3 presented gross control-volume balances of mass, momentum, and en- ergy which led to estimates of global parameters: mass flow, force, torque, total heat transfer. Chapter 4 presented infinitesimal balances which led to the basic partial dif- ferential equations of fluid flow and some particular solutions. These two chapters cov- ered analytical techniques, which are limited to fairly simple geometries and well- defined boundary conditions. Probably one-third of fluid-flow problems can be attacked in this analytical or theoretical manner. The other two-thirds of all fluid problems are too complex, both geometrically and physically, to be solved analytically. They must be tested by experiment. Their behav- ior is reported as experimental data. Such data are much more useful if they are ex- pressed in compact, economic form. Graphs are especially useful, since tabulated data cannot be absorbed, nor can the trends and rates of change be observed, by most en- gineering eyes. These are the motivations for dimensional analysis. The technique is traditional in fluid mechanics and is useful in all engineering and physical sciences, with notable uses also seen in the biological and social sciences. -
International Conference Euler's Equations: 250 Years on Program
International Conference Euler’s Equations: 250 Years On Program of Lectures and Discussions (Dated: June 14, 2007) Schedule of the meeting Tuesday 19 June Wednesday 20 June Thursday 21 June Friday 22 June 08:30-08:40 Opening remarks 08:30-09:20 08:30-09:20 G. Eyink 08:30-09:20 F. Busse 08:40-09:10 E. Knobloch O. Darrigol/U. Frisch 09:30-10:00 P. Constantin 09:30-10:00 Ph. Cardin 09:20-10:10 J. Gibbon 09:20-09:50 M. Eckert 10:00-10:30 T. Hou 10:00-10:30 J.-F. Pinton 10:20-10:50 Y. Brenier 09:50-10:30 Coffee break 10:30-11:00 Coffee break 10:30-11:00 Coffee break 10:50-11:20 Coffee break 10:30-11:20 P. Perrier 11:00-11:30 K. Ohkitani 11:00-11:30 Discussion D 11:20-11:50 K. Sreenivasan 11:20-12:30 Poster session II 11:30-12:00 P. Monkewitz 11:30-12:30 Discussion C 12:00-12:30 C.F. Barenghi 12:00-12:30 G.J.F. van Heijst 12:30-14:00 Lunch break 12:30-14:00 Lunch break 12:30-14:00 Lunch break 12:30-14:00 Lunch break 14:00-14:50 I. Procaccia 14:00-14:30 G. Gallavotti 14:00-14:50 M. Ghil 14:00-14:30 N. Mordant 14:50-15:20 L. Biferale 14:40-15:10 L. Saint Raymond 14:50-15:20 A. Nusser 14:30-15:00 J. -
Teaching Students to Model Neural Circuits and Neural Networks Using an Electronic Spreadsheet Simulator
Behavior Research Methods, Instruments, & Computers 1985, 17(2),339-344 SESSION XI TEACHING APPLICATIONS OF MICROCOMPUTERS N. John Castellan, Presider Teaching students to model neural circuits and neural networks using an electronic spreadsheet simulator THOMAS T. HEWETT Drexel University, Philadelphia. Pennsylvania An electronic spreadsheet simulator can be used to enable students to conduct simulated micro electrode recording experiments. In addition, it can be used both to let students explore the oper ation of models of hypothetical neural networks and to let them design and develop their own neural models. A recent paper (Smith et al., 1984) described the educa demand. This calculation cycle often involves recalcula tional goals of student ownership of a personal microcom tion of new values for previously entered formulas that puter at Drexel University. In a later paper, Hewett and depend upon still other values that may have been changed Perkey (1984) argued that many computer programs in during or since the last calculation cycle. The typical tended for instructional purposes are impractical or of little spreadsheet simulator also offers a number of program use when each student has a personal machine. However, ming language capabilities, including the ability to required student access to a personal computer creates new manipulate strings and to do iterative calculations. In ad opportunities for the use of microcomputer applications dition, built-in functions can be combined to produce a programs. One obvious, but nontrivial, example is the im limited plotting capability, thereby providing both a pact of the word processor on what is considered accept graphical and a numerical method for illustrating relational able written work, from lab reports to term papers. -
What Is PC MOUSE????
PC MOUSE FACT SHEET September 1983 What is PC MOUSE???? PC Mouse is a small hand-held pointing and selecting device used to move the cursor on your screen. As you slide PC Mouse on the mouse pad, the cursor moves correspondingly. Three buttons on top of mouse allow you to activate functions by the use of pop-up menus. PC Mouse software with pop-up menus has been created for some of your favorite software programs: Lotus 1 -2-3™, Personal Editor™, VisiCalc®, WordStar®, Volkswriter™ and Multiplan™. The pop-up menus are transparent to the underlying program, and no modification to your existing software is required. Pop-up menus allow you to select and execute commands at the press of a button. No longer do you have to memorize commands. Even if you are an expert typist, moving around in spreadsheets and wordprocessors will be faster and easier than ever before. PC Mouse interfaces through an RS-232 asynchronous communication port. Since there are no moving parts, no maintenance or cleaning is required. PC Mouse software is compatible with PC-DOS 1.10 and 2.00. Only 10K of memory and disk space are used by the mouse driver. ""—signifies manufacturers' trademark -"'—signifies manufacturers' registered trademark APPLICATION: With the help of the function buttons/pop-up menus, PC Mouse can be used to do word processing, spreadsheets and graphics. PC MOUSE PACKAGE INCLUDES: HARDWARE Optical mouse and pad, RS-232 interface box and cable, and a power supply. SOFTWARE Pop-up menu software Version 2.0 provides pop-up menus for Lotus 1 -2-3, Personal Editor, VisiCalc, WordStar, Volkswriter, and Multiplan. -
Leonhard Euler - Wikipedia, the Free Encyclopedia Page 1 of 14
Leonhard Euler - Wikipedia, the free encyclopedia Page 1 of 14 Leonhard Euler From Wikipedia, the free encyclopedia Leonhard Euler ( German pronunciation: [l]; English Leonhard Euler approximation, "Oiler" [1] 15 April 1707 – 18 September 1783) was a pioneering Swiss mathematician and physicist. He made important discoveries in fields as diverse as infinitesimal calculus and graph theory. He also introduced much of the modern mathematical terminology and notation, particularly for mathematical analysis, such as the notion of a mathematical function.[2] He is also renowned for his work in mechanics, fluid dynamics, optics, and astronomy. Euler spent most of his adult life in St. Petersburg, Russia, and in Berlin, Prussia. He is considered to be the preeminent mathematician of the 18th century, and one of the greatest of all time. He is also one of the most prolific mathematicians ever; his collected works fill 60–80 quarto volumes. [3] A statement attributed to Pierre-Simon Laplace expresses Euler's influence on mathematics: "Read Euler, read Euler, he is our teacher in all things," which has also been translated as "Read Portrait by Emanuel Handmann 1756(?) Euler, read Euler, he is the master of us all." [4] Born 15 April 1707 Euler was featured on the sixth series of the Swiss 10- Basel, Switzerland franc banknote and on numerous Swiss, German, and Died Russian postage stamps. The asteroid 2002 Euler was 18 September 1783 (aged 76) named in his honor. He is also commemorated by the [OS: 7 September 1783] Lutheran Church on their Calendar of Saints on 24 St. Petersburg, Russia May – he was a devout Christian (and believer in Residence Prussia, Russia biblical inerrancy) who wrote apologetics and argued Switzerland [5] forcefully against the prominent atheists of his time. -
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: -
Package 'Gnumeric'
Package ‘gnumeric’ March 9, 2017 Version 0.7-8 Date 2017-03-09 Title Read Data from Files Readable by 'gnumeric' Author Karoly Antal <[email protected]>. Maintainer Karoly Antal <[email protected]> Depends R (>= 2.8.1), XML Imports utils Description Read data files readable by 'gnumeric' into 'R'. Can read whole sheet or a range, from several file formats, including the native format of 'gnumeric'. Reading is done by using 'ssconvert' (a file converter utility included in the 'gnumeric' distribution <http://projects.gnome.org/gnumeric/>) to convert the requested part to CSV. From 'gnumeric' files (but not other formats) can list sheet names and sheet sizes or read all sheets. License GPL (>= 2) Repository CRAN Date/Publication 2017-03-09 13:20:28 NeedsCompilation no R topics documented: read.gnumeric.sheet . .2 read.gnumeric.sheet.info . .6 read.gnumeric.sheets . .7 Index 9 1 2 read.gnumeric.sheet read.gnumeric.sheet Read data from a gnumeric (or MS Excel, Openoffice Calc, Xbase, Quatro Pro, Paradox, HTML, etc) spreadsheet or database file using ssconvert from the gnumeric distribution Description Read data from a sheet of a gnumeric (or other common spreadsheet or database) file to a data.frame. Requires an external program, ‘ssconvert’ (normally installed with gnumeric in ‘PATH’. (Gnumeric home page is http://projects.gnome.org/gnumeric/) (Note: last gnumeric release for windows is 1.12.17 from 2014) Calls ‘ssconvert’ to convert the input to CSV. ‘ssconvert’ can read several file formats (see Details below). Note: During conversion to CSV ‘ssconvert’ also evaluates formulas (e.g. ‘=sum(A1:A3)’) in cells, and emits the result instead of the formula. -
Forced Convection Heat Transfer Convection Is the Mechanism of Heat Transfer Through a Fluid in the Presence of Bulk Fluid Motion
Forced Convection Heat Transfer Convection is the mechanism of heat transfer through a fluid in the presence of bulk fluid motion. Convection is classified as natural (or free) and forced convection depending on how the fluid motion is initiated. In natural convection, any fluid motion is caused by natural means such as the buoyancy effect, i.e. the rise of warmer fluid and fall the cooler fluid. Whereas in forced convection, the fluid is forced to flow over a surface or in a tube by external means such as a pump or fan. Mechanism of Forced Convection Convection heat transfer is complicated since it involves fluid motion as well as heat conduction. The fluid motion enhances heat transfer (the higher the velocity the higher the heat transfer rate). The rate of convection heat transfer is expressed by Newton’s law of cooling: q hT T W / m 2 conv s Qconv hATs T W The convective heat transfer coefficient h strongly depends on the fluid properties and roughness of the solid surface, and the type of the fluid flow (laminar or turbulent). V∞ V∞ T∞ Zero velocity Qconv at the surface. Qcond Solid hot surface, Ts Fig. 1: Forced convection. It is assumed that the velocity of the fluid is zero at the wall, this assumption is called no‐ slip condition. As a result, the heat transfer from the solid surface to the fluid layer adjacent to the surface is by pure conduction, since the fluid is motionless. Thus, M. Bahrami ENSC 388 (F09) Forced Convection Heat Transfer 1 T T k fluid y qconv qcond k fluid y0 2 y h W / m .K y0 T T s qconv hTs T The convection heat transfer coefficient, in general, varies along the flow direction.