Renewable Energy ResourcesRenewable Energy Resources is a numerate and quantitative text covering subjectsof proventechnical andeconomicimportanceworldwide. Energysupplies fromrenewables (such as solar, thermal, photovoltaic, wind, hydro, biofuels, wave, tidal,oceanandgeothermalsources)areessentialcomponentsofeverynationsenergystrategy, not least because of concerns for the environment and for sustainability.In the years between the first and this second edition, renewable energy has comeof age: it makes good sense, good government and good business.This second edition maintains the books basis on fundamentals, whilst includ-ingexperiencegainedfromtherapidgrowthofrenewableenergytechnologiesassecure national resources and for climate change mitigation, more extensively illus-trated with case studies and worked problems. The presentation has been improvedthroughout, along with a new chapter on economics and institutional factors. Eachchapter begins with fundamental theory from a scientific perspective, then considersapplied engineering examples and developments, and includes a set of problems andsolutions and a bibliography of printed and web-based material for further study.Common symbols and cross referencing apply throughout, essential data are tabu-lated in appendices. Sections on social and environmental aspects have been addedto each technology chapter.RenewableEnergyResourcessupportsmulti-disciplinarymasterdegreesinsci-enceandengineering, andspecialistmodulesinfirstdegrees. Practisingscientistsand engineers who have not had a comprehensive training in renewable energy willfind this book a useful introductory text and a reference book.John Twidell has considerable experience in renewable energy as an academic pro-fessor, a board member of wind and solar professional associations, a journal editorand contractor with the European Commission. As well as holding posts in the UK,he has worked in Sudan and Fiji.TonyWeirisapolicyadvisertotheAustraliangovernment, specialisingintheinterfacebetweentechnologyandpolicy,coveringsubjectssuchasenergysupplyanddemand,climatechangeandinnovationinbusiness.HewasformerlySeniorEnergy Officer at the South Pacific Forum Secretariat in Fiji, and has lectured andresearched in physics and policy studies at universities of the UK, Australia and thePacific.Also available from Taylor & FrancisEvaluation of the Built Environment forSustainabilityV. Bentivegna, P.S. Brandon and P. Lombardi Hb: 0-419-21990-0Spon PressGeothermal Energy for Developing CountriesD. Chandrasekharam and J. BundschuhHb: 9058095223Spon PressBuilding Energy Management Systems, 2nd edG. LevermoreHb: 0-419-26140-0Pb: 0-419-22590-0Spon PressCutting the Cost of Cold: Affordable Warmthfor Healthier HomesF. Nicol and J. RudgePb: 0-419-25050-6Spon PressInformation and ordering detailsFor price availability and ordering visit our website www.sponpress.comAlternatively our books are available from all good bookshops.RenewableEnergyResourcesSecond editionJohn Twidell and Tony WeirFirst published 1986by E&FN Spon LtdSecond edition published 2006by Taylor & Francis2 Park Square, Milton Park, Abingdon, Oxon OX14 4RNSimultaneously published in the USA and Canadaby Taylor & Francis270 Madison Ave, New York, NY 10016, USATaylor & Francis is an imprint of the Taylor & Francis Group 1986, 2006 John W. Twidell and Anthony D. WeirAll rights reserved. No part of this book may be reprinted orreproduced or utilised in any form or by any electronic, mechanical, orother means, now known or hereafter invented, including photocopyingand recording, or in any information storage or retrieval system, withoutpermission in writing from the publishers.The publisher makes no representation, express or implied, with regardto the accuracy of the information contained in this book and cannotaccept any legal responsibility or liability for any errors oromissions that may be made.British Library Cataloguing in Publication DataA catalogue record for this book is availablefrom the British LibraryLibrary of Congress Cataloging in Publication DataTwidell, John.Renewable energy resources / John Twidell andAnthony Weir. 2nd ed.p. cm.Includes bibliographical references and index.ISBN 0419253203 (hardback) ISBN 0419253300 (pbk.)1. Renewable energy sources. I. Weir, Anthony D. II. Title.TJ808.T95 2005621.042dc222005015300ISBN10: 0419253203 ISBN13: 9780419253204 HardbackISBN10: 0419253300 ISBN13: 9780419253303 PaperbackThis edition published in the Taylor & Francis e-Library, 2006.To purchase your own copy of this or any of Taylor & Francis or Routledgescollection of thousands of eBooks please go to www.eBookstore.tandf.co.uk.ContentsPreface xiList of symbols xvii1 Principles of renewable energy 11.1Introduction11.2Energyandsustainabledevelopment 21.3Fundamentals 71.4Scientificprinciplesofrenewableenergy121.5Technical implications 161.6Social implications 22Problems 24Bibliography252 Essentials of fluid dynamics 292.1Introduction292.2Conservationofenergy:Bernoullisequation302.3Conservationof momentum322.4Viscosity332.5Turbulence 342.6Frictioninpipeflow352.7Lift and drag forces: fluid and turbine machinery39Problems 41Bibliography443 Heat transfer 453.1Introduction453.2Heatcircuitanalysisandterminology463.3Conduction49vi Contents3.4Convection513.5Radiativeheat transfer 613.6Propertiesoftransparent materials 733.7Heattransferbymasstransport 743.8Multimodetransferandcircuitanalysis 77Problems 80Bibliography824 Solar radiation 854.1Introduction854.2Extraterrestrial solarradiation864.3Componentsof radiation874.4GeometryoftheEarthandSun894.5Geometryofcollectorandthesolarbeam934.6EffectsoftheEarthsatmosphere 984.7Measurementsofsolarradiation1044.8Estimationof solarradiation107Problems 110Bibliography1125 Solar water heating 1155.1Introduction1155.2Calculationofheatbalance:generalremarks 1185.3Uncovered solar water heaters progressive analysis 1195.4Improvedsolarwaterheaters 1235.5Systemswithseparatestorage 1295.6Selectivesurfaces 1345.7Evacuatedcollectors 1375.8Social andenvironmental aspects 140Problems 141Bibliography1456 Buildings and other solar thermal applications 1466.1Introduction1466.2Air heaters 1476.3Energy-efficient buildings 1496.4Cropdriers 1576.5Space cooling1616.6Water desalination162Contents vii6.7 Solar ponds 1646.8 Solar concentrators 1666.9 Solarthermal electricpowersystems 1706.10Social andenvironmental aspects 173Problems 175Bibliography1797 Photovoltaic generation 1827.1 Introduction1827.2 Thesiliconpnjunction1847.3 Photonabsorptionatthejunction1937.4 Solarradiationabsorption1977.5 Maximisingcell efficiency2007.6 Solarcell construction2087.7 Typesandadaptationsofphotovoltaics 2107.8 Photovoltaiccircuitproperties 2207.9 Applicationsandsystems 2247.10Social andenvironmental aspects 229Problems 233Bibliography2348 Hydro-power 2378.1 Introduction2378.2 Principles 2408.3 Assessingtheresourceforsmallinstallations 2408.4 Animpulseturbine 2448.5 Reactionturbines 2498.6 Hydroelectricsystems 2528.7 Thehydraulicrampump2558.8 Social andenvironmental aspects 257Problems 258Bibliography2619 Power from the wind 2639.1 Introduction2639.2 Turbinetypesandterms 2689.3 Linearmomentumandbasictheory2739.4 Dynamicmatching2839.5 Bladeelement theory288viii Contents9.6 Characteristicsof thewind2909.7 Powerextractionbyaturbine 3059.8 Electricitygeneration3079.9 Mechanical power 3169.10Socialandenvironmentalconsiderations 318Problems 319Bibliography32210 The photosynthetic process 32410.1 Introduction32410.2 Trophiclevel photosynthesis 32610.3 Photosynthesisattheplantlevel 33010.4 Thermodynamicconsiderations 33610.5 Photophysics 33810.6 Molecularlevel photosynthesis 34310.7 Appliedphotosynthesis 348Problems 349Bibliography35011 Biomass and biofuels 35111.1 Introduction35111.2 Biofuel classification35411.3 Biomassproductionforenergyfarming35711.4 Direct combustionforheat 36511.5 Pyrolysis(destructivedistillation) 37011.6 Furtherthermochemical processes 37411.7 Alcoholicfermentation37511.8 Anaerobicdigestionforbiogas 37911.9 Wastes andresidues 38711.10Vegetableoilsandbiodiesel 38811.11Social andenvironmental aspects 389Problems 395Bibliography39712 Wave power 40012.1 Introduction40012.2 Wavemotion40212.3 Waveenergyandpower 40612.4 Wavepatterns 41212.5 Devices 418Contents ix12.6Social andenvironmental aspects 422Problems 424Bibliography42713 Tidal power 42913.1Introduction42913.2Thecauseof tides 43113.3Enhancement of tides 43813.4Tidal current/streampower 44213.5Tidal rangepower 44313.6Worldrangepowersites 44713.7Social and environmental aspects of tidal range power 449Problems 450Bibliography45114 Ocean thermal energy conversion (OTEC) 45314.1Introduction45314.2Principles 45414.3Heat exchangers 45814.4Pumpingrequirements 46414.5Otherpractical considerations 46514.6Environmental impact 468Problems 469Bibliography46915 Geothermal energy 47115.1Introduction47115.2Geophysics 47215.3Dryrockandhotaquiferanalysis 47515.4HarnessingGeothermal Resources 48115.5Social andenvironmental aspects 483Problems 487Bibliography48716 Energy systems, storage and transmission 48916.1The importance of energy storage and distribution48916.2Biological storage 49016.3Chemical storage 49016.4Heat storage 49516.5Electricalstorage:batteriesandaccumulators 49916.6Fuel cells 506x Contents16.7 Mechanical storage 50716.8 Distributionof energy50916.9 Electrical power 51316.10Social andenvironmental aspects 520Problems 521Bibliography52417 Institutional and economic factors 52617.1 Introduction52617.2 Socio-political factors 52617.3 Economics 53017.4 Somepolicytools 53417.5 Quantifyingchoice 53617.6 Thewayahead545Problems 550Bibliography550Appendix A Units and conversions 553Appendix B Data 558Appendix C Some heat transfer formulas 564Solution guide to problems 568Index 581PrefaceOur aimRenewable Energy Resources is a numerate and quantitative text coveringsubjects of proven technical and economic importance worldwide. Energysupply from renewables is an essential component of every nations strat-egy, especiallywhenthereis responsibilityfor theenvironment andforsustainability.Thisbookconsidersthetimelessprinciplesof renewableenergytech-nologies, yet seekstodemonstratemodernapplicationandcasestudies.Renewable Energy Resources supports multi-disciplinary master degrees inscience and engineering, and also specialist modules in science and engineer-ing first degrees. Moreover, since many practising scientists and engineerswill not have had a general training in renewable energy, the book has wideruse beyond colleges and universities. Each chapter begins with fundamentaltheoryfromaphysical scienceperspective, thenconsidersappliedexam-plesanddevelopments,andfinallyconcludeswithasetofproblemsandsolutions. The whole book is structured to share common material and torelate aspects together. After each chapter, reading and web-based materialis indicated for further study. Therefore the book is intended both for basicstudy and for application. Throughout the book and in the appendices, weinclude essential and useful reference material.The subjectRenewableenergysuppliesareofeverincreasingenvironmentalandeco-nomic importance in all countries. A wide range of renewable energy tech-nologies are established commercially and recognised as growth industriesbymostgovernments. Worldagencies, suchastheUnitedNations, havelarge programmes to encourage the technology. In this book we stress thescientific understanding and analysis of renewable energy, since we believethese are distinctive and require specialist attention. The subject is not easy,mainly because of the spread of disciplines involved, which is why we aimto unify the approach within one book.xii PrefaceThisbookbridgesthegapbetweendescriptivereviewsandspecialisedengineering treatises on particular aspects. It centres on demonstrating howfundamental physical processes govern renewable energy resources and theirapplication.Althoughtheapplicationsarebeingupdatedcontinually,thefundamental principles remain the same and we are confident that this newedition will continue to provide a useful platform for those advancing thesubject and its industries. We have been encouraged in this approach by theever increasing commercial importance of renewable energy technologies.Why a second edition?Intherelativelyfewyears betweenthefirst edition, withfivereprintedrevisions, andthissecondedition, renewableenergyhascomeofage; itsusemakesgoodsense, goodgovernmentandgoodbusiness. Frombeing(apart fromhydro-power) small-scalecuriosities promotedbyidealists,renewables have become mainstream technologies, produced and operatedby companies competing in an increasingly open market where consumersand politicians are very conscious of sustainability issues.In recognition of the social, political and institutional factors which con-tinuetodrivethischange, thisneweditionincludesanewfinal chapteron institutional and economic factors. The new chapter also discusses anddemonstrates sometools for evaluatingtheincreasinglyfavourableeco-nomics of renewable energy systems. There is also a substantial new sectioninChapter1showinghowrenewableenergyisakeycomponentofsus-tainable development, an ideal which has become much more explicit sincethe first edition. Each technology chapter now includes a brief concludingsection on its social and environmental impacts.Thebookmaintainsthesamegeneral format asthefirst edition, butmanyimprovementsandupdateshavebeenmade. Inparticularwewishtorelatetothevibrantdevelopmentsintheindividual renewableenergytechnologies, and to the related commercial growth. We have improved thepresentationofthefundamentalsthroughout,inthelightofourteachingexperience.Althoughthebookcontinuestofocusonfundamentalphysi-cal principles, which have not changed, we have updated the technologicalapplicationsandtheirrelativeemphasestoreflectmarketexperience.Forelectricitygeneration, wind-power andphotovoltaics havehaddramaticgrowth over the last two decades, both in terms of installed capacity andin sophistication of the industries. In all aspects of renewable energy, com-positematerialsandmicroelectroniccontrolhavetransformedtraditionaltechnologies, including hydro-power and the use of biomass.Extra problems have been added at the end of each chapter, with hintsand guidance for all solutions as an appendix. We continue to emphasisesimplified, order-of-magnitude, calculations of the potential outputs of thevarioustechnologies. Suchcalculationsareespeciallyuseful inindicatingPreface xiiithe potential applicability of a technology for a particular site. However weappreciatethatspecialistsincreasinglyusecomputermodellingofwhole,complexsystems; inourviewsuchmodellingisessential but onlyafterinitial calculation as presented here.ReadershipWe expect our readers to have a basic understanding of science and tech-nology, especially of physical science and mathematics. It is not necessaryto read or refer to chapters consecutively, as each aspect of the subject istreated,inthe main,as independentofthe other aspects.However,somecommon elements, especially heat transfer, will have to be studied seriouslyif the reader is to progress to any depth of understanding in solar energy.Thedisciplinesbehindaproperunderstandingandapplicationofrenew-able energy also include environmental science, chemistry and engineering,with social science vital for dissemination. We are aware that readers withaphysicalsciencebackgroundwillusuallybeunfamiliarwithlifescienceand agricultural science, but we stress the importance of these subjects withobvious application for biofuels and for developments akin to photosynthe-sis. We ourselves see renewable energy as within human-inclusive ecology,both now and for a sustainable future.OurselvesWewouldlikeourreaderstoenjoythesubject of renewableenergy, aswedo, andtobestimulatedtoapplytheenergysourcesforthebenefitof their societies. Our own interest and commitment has evolved from theworkinbothhemispheresandinarangeof countries. Wefirst taught,andthereforelearnt,renewableenergyattheUniversityofStrathclydeinGlasgow (JWT) and the University of the South Pacific in Fiji (ADW andJWT). So teaching, together with research and application in Scotland andthe South Pacific, has been a strong influence for this book. Since the firsteditionwehavemadeseparatecareersinuniversitiesandingovernmentservice, whilst experiencing the remarkable, but predicable, growth in rele-vance of renewable energy. One of us (JWT) became Director of the EnergyStudies Unit, in the Faculty of Engineering at the University of StrathclydeinGlasgow,Scotland,andthenacceptedtheChairinRenewableEnergyattheAMSETCentre,DeMontfortUniversity,Leicester,England.Heiseditor of the academic journal Wind Engineering, has been a Council andBoardmemberoftheBritishWindEnergyAssociationandtheUKSolarEnergy Society, and has supervised many postgraduates for their disserta-tions. The AMSET Centre is nowa private company, for research, educationandtraininginrenewables; support isgiventoMSccoursesat ReadingUniversity, Oxford University and City University, and there are Europeanxiv PrefaceUnionfunded research programmes. TW was for several years the SeniorEnergy Officer of the South Pacific Forum Secretariat, where he manageda substantial program of renewable energy pilot projects. He then workedfor the Australian Government as an adviser on climate change, and lateron new economy issues.We do not see the world as divided sharply between developed industri-alised countries and developing countries of the Third World. Renewablesare essential for both, and indeed provide one way for the separating con-ceptstobecomeirrelevant. Thisismeaningful touspersonally, sincewewishourownenergiestobedirectedforajust andsustainablesociety,increasingly free of poverty and the threat of cataclysmic war. We sincerelybelievethedevelopmentandapplicationofrenewableenergytechnologywill favour these aspirations. Our readers may not share these views, andthis fortunately does not affect the content of the book. One thing they willhave to share, however, is contact with the outdoors. Renewable energy isdrawnfromtheenvironment,andpractitionersmustputontheirrubberboots or their sun hat and move from the closed environment of buildingsto the outside. This is no great hardship however; the natural environmentis the joy and fulfilment of renewables.Suggestions for using the book in teachingHowabookis usedinteachingdepends mainlyonhowmuchtimeisdevotedtoitssubject. Forexample, thebookoriginatedfromshortandone-semester courses to senior undergraduates in Physics at the Universityof the SouthPacific andthe Universityof Strathclyde, namelyEnergyResources and Distribution, Renewable Energy and Physics and Ecology.When completed and with regular revisions, the book has been mostly usedworldwide for MSc degrees in engineering and science, including those onrenewableenergy andonenergyandtheenvironment. Wehavealsotaught other lecture and laboratory courses, and have found many of thesubjectsandtechnologiesinrenewableenergycanbeincorporatedwithgreat benefit into conventional teaching.This book deliberately contains more material than could be covered inone specialist course. This enables the instructor and readers to concentrateonthoseparticularenergytechnologiesappropriateintheirsituation.Toassistinthisselection,eachchapterstartswithapreliminaryoutlineandestimate of each technologys resource and geographical variation, and endswith a discussion of its social and environmental aspects.The chapters are broadly grouped into similar areas. Chapter 1 (Principlesof Renewable Energy) introduces renewable energy supplies in general, andin particular the characteristics that distinguish their application from thatfor fossil or nuclear fuels. Chapter 2 (Fluid Mechanics) and Chapter 3 (HeatTransfer) are background material for later chapters. They contain nothingPreface xvthat asenior student inmechanical engineeringwill not alreadyknow.Chapters 47deal withvarious aspects of direct solar energy. Readersinterested in this area are advised to start with the early sections of Chapter 5(Solar Water Heating) or Chapter 7 (Photovoltaics), and review Chapters 3and 4 as required. Chapters 8 (Hydro), 9 (Wind), 12 (Waves) and 13 (Tides)present applications of fluid mechanics. Again the reader is advised to startwithanapplicationschapter,andreviewtheelementsfromChapter2asrequired. Chapters 10 and 11 deal with biomass as an energy source andhowtheenergyisstoredandmaybeused.Chapters14(OTEC)and15(Geothermal) treat sources that are, like those in Chapters 12 (wave) and 13(tidal), important only in fairly limited geographical areas. Chapter 16, likeChapter1, treatsmattersofimportancetoall renewableenergysources,namely the storage and distribution of energy and the integration of energysourcesintoenergysystems. Chapter17, oninstitutional andeconomicfactors bearing on renewable energy, recognises that science and engineeringare not the only factors for implementing technologies and developments.Appendices A (units), B (data) and C (heat transfer formulas) are referred toeither implicitly or explicitly throughout the book. We keep to a commonset of symbols throughout, as listed in the front. Bibliographies include bothspecific and general references of conventional publications and of websites;theinternet isparticularlyvaluableforseekingapplications. Suggestionsfor further reading and problems (mostly numerical in nature) are includedwithmostchapters.Answerguidanceisprovidedattheendofthebookfor most of the problems.AcknowledgementsAs authors we bear responsibility for all interpretations, opinions and errorsin this work. However, many have helped us, and we express our gratitudeto them. The first edition acknowledged the many students, colleagues andcontacts that had helped and encouraged us at that stage. For this secondedition, enormously more information and experience has been available,especially from major international and national R&D and from commer-cial experience, with significant information available on the internet. Weacknowledgethehelpandinformationwehavegainedfrommanysuchsources, with specific acknowledgement indicated by conventional referenc-ing and listing in the bibliographies. We welcome communications from ourreaders, especially when they point out mistakes and possible improvement.Muchof TWs workonthis secondeditionwas donewhilehewasonleaveat theInternational Global ChangeInstituteof theUniversityofWaikato,NewZealand,in2004.Hegratefullyacknowledgestheaca-demic hospitality of Neil Ericksen and colleagues, and the continuing sup-port of the [Australian Government] Department of Industry Tourism andxvi PrefaceResources. JWTis especiallygrateful for thecomments andideas fromstudents of his courses.And last, but not least, we have to thank a succession of editors at SponPress and Taylor & Francis and our families for their patience and encour-agement. Our children were young at the first edition, but had nearly all lefthomeatthesecond;thethirdeditionwillbefortheirfuturegenerations.John Twidell MA DPhil A.D. (Tony) Weir BSc PhDAMSET Centre, Horninghold CanberraLeicestershire, LE16 8DH, UK AustraliaandVisiting Professor in Renewable EnergyUniversity of Reading, UKemail -info.renewable@tandf.co.uk>see -www.amset.com>List of symbolsSymbol Main use Other use or commentCapitalsA Area (m2) Acceptor; ideality factorAM Air-mass-ratioC Thermal capacitance ( J K1) Electrical capacitance (l); constantCPPower coefficientCrConcentration ratioC!Torque coefficientu Distance (m) Diameter (of pipe or blade)L Energy ( J)LFFermi levelLgBand gap (eV)LKKinetic energy ( J)EMF Electromotive force (V)l Force (N) Faraday constant (Cmol1)l/|jRadiation exchange factor (|toj)C Solar irradiance (Wm2) Gravitational constant (Nm2kg2);Temperature gradient (Km1);Gibbs energyCb, Cd, ChIrradiance (beam, diffuse, onhorizontal)H Enthalpy (J) Head(pressureheight) of fluid(m);wave crest height (m); insolation( J m2day1); heat of reaction (AH)l Electric current (A) Moment of inertia (kg m2)j Current density (Am2)K Extinction coefficient (m1) Clearness index (KT); constantL Distance, length (m) Diffusion length (m); litre (103m3)N Mass (kg) Molecular weightN Concentration (m3) Hours of daylightN0Avogadro numberP Power (W)P/Power per unit length(Wm1)PS Photosystem(Continued)Symbol Main use Other use or comment0 Volume flow rate (m3s1) Thermal resistance (KW1) Radius (m); electrical resistance (H);reduction level; tidal range (m); gasconstant (0);mThermal resistance (masstransfer)nThermal resistance(conduction)rThermal resistance (radiation)vThermal resistance(convection)RFD Radiant flux density (Wm2)S Surface area (m2) entropySvSurface recombinationvelocity (ms1)STP Standard temperature andpressure7 Temperature (K) Period (s1)U Potential energy ( J) Heat loss coefficient (Wm2K1)\ Volume (m3) Electrical potential (V)W Width (m) Energy density (Jm3)X Characteristic dimension (m) Concentration ratioScript capitals (Non-dimensional numberscharacterising fluid flow) Rayleigh number Grashof number Nusselt number Prandtl number Reynolds number Shape number (of turbine)Lower casea Amplitude (m) Wind interference factor; radius (m)h Wind profile exponent Width (m)c Specific heat capacity( J kg1K1)Speed of light (ms1); phase velocityof wave (ms1); chord length (m);Weibull speed factor (ms1)d Distance (m) Diameter (m); depth (m); zero planedisplacement (wind) (m)e Electron charge (C) Base of natural logarithms (2.718)[ Frequency of cycles(Hz =s1)Pipe friction coefficient; fraction;force per unit length (Nm1)g Acceleration due to gravity(ms2)h Heat transfer coefficient(Wm2K1)Vertical displacement (m); Planckconstant ( Js)Symbol Main use Other use or comment|1k Thermal conductivity(Wm1K1)Wave vector (=2=\); Boltzmannconstant (=1.381023J K1)| Distance (m)m Mass (kg) Air-mass-ration Number Number of nozzles, of hours ofbright sunshine, of wind-turbineblades; electron concentration(m3)p Pressure (Nm2=Pa) Hole concentration (m3)o Power per unit area (Wm2)r Thermal resistivity of unitarea (R-value = RA)(m2KW1)Radius (m); distance (m)s Angle of slope (degrees)t Time (s) Thickness (m)u Velocity along stream (ms1) Group velocity (ms1)v Velocity (not along stream)(ms1)w Distance (m) Moisture content (dry basis, %);moisture content (wet basis, %)(w/)x Co-ordinate (along stream)(m), Co-ordinate (across stream)(m)z Co-ordinate (vertical) (m)Greek capitals!(gamma) Torque (Nm) Gamma functionA (delta) Increment of. . . (othersymbol)A (lambda) Latent heat ( J kg1)l (sigma) Summation sign4 (phi) Radiant flux (W) Probability function4uProbability distribution ofwind speed ((ms1)1)H (omega) Solid angle (steradian) Phonon frequency (s1); angularvelocity of blade (rads1)Greek lower caseo (alpha) Absorptance Angle of attack (deg)o\Monochromatic absorptance8 (beta) Angle (deg) Volumetric Expansion coefficient(K1) (gamma) Angle (deg) Blade setting angle (deg)o (delta) Boundary layer thickness (m) Angle of declination (deg): epsilon Emittance Wave spectral width; permittivity;dielectric constant:\Monochromatic emittance (eta) Efficiency(Continued)Symbol Main use Other use or comment0 (theta) Angle of incidence (deg) Temperature difference (oC) (kappa) Thermal diffusivity (m2s1)\ (lambda) Wavelength (m) Tip speed ratio of wind-turbine (mu) Dynamic viscosity (Nm2s) (nu) Kinematic viscosity (m2s1) (xi) Electrode potential (V) Roughness height (m)=(pi) 3.1416 (rho) Density (kg m3) Reflectance; electrical resistivity(H m)\Monochromatic reflectanceu(sigma) StefanBoltzmann constantt(tau) Transmittance Relaxation time (s); duration (s);shear stress (Nm2)t\Monochromatic transmittancem (phi) Radiant flux density (RFD)(Wm2)Wind-blade angle (deg); potentialdifference (\); latitude (deg)m\Spectral distribution of RFD(Wm3)+(chi) Absolute humidity (kg m3) (psi) Longitude (deg) Angle (deg)w (omega) Angular frequency (=2=[ )(rads1)Hour angle (deg); solid angle(steradian)SubscriptsB Black body BandD Drag DarkE EarthF ForceG GeneratorL LiftM MoonP PowerR RatedS SunT Tangential Turbinea Ambient Aperture; available (head); aquiferabs Absorbedb Beam Blade; bottom; base; biogasc Collector Coldci Cut-inco Cut-outcov Coverd Diffuse Dopant; digestere Electrical Equilibrium; energyf Fluid Forced; friction; flowg Glass Generation current; band gaph Horizontal HotSymbol Main use Other use or commenti Integer Intrinsicin Incident (incoming)int Internalj Integerm mass transfer Mean (average); methanemax Maximumn conductionnet Heat flow across surfaceo (read as numeral zero)oc Open circuitp Plate Peak; positive charge carriers(holes)r radiation Relative; recombination;room; resonant; rockrad Radiatedrefl Reflectedrms Root mean squares Surface Significant; saturated; Sunsc Short circuitt Tip Totalth Thermaltrans Transmittedu Usefulv convection Vapourw Wind Waterz Zenith\ Monochromatic, e.g.o\0 Distant approach Ambient; extra-terrestrial;dry matter; saturated;ground-level1 Entry to device First2 Exit from device Second3 Output ThirdSuperscriptm or max MaximumMeasured perpendicular to directionof propagation (e.g.Cb).(dot) Rate of, e.g. mOther symbolsBold face Vector, e.g. F= Mathematical equality Approximate equality (within afew %) Equality in order of magnitude(within a factor of 210) Mathematical identity (or definition),equivalentChapter 1Principles of renewable energy1.1 IntroductionThe aim ofthis textis toanalyse the fullrange ofrenewable energy sup-pliesavailableformoderneconomies. Suchrenewablesarerecognisedasvital inputsforsustainabilityandsoencouragingtheirgrowthissignifi-cant. Subjects will include power from wind, water, biomass, sunshine andother such continuing sources, including wastes. Although the scale of localapplication ranges from tens to many millions of watts, and the totality isa global resource, four questions are asked for practical application:1 How much energy is available in the immediate environment what isthe resource?2 For what purposes can this energy be used what is the end-use?3 What is the environmental impact of the technology is it sustainable?4 What is the cost of the energy is it cost-effective?The first two are technical questions considered in the central chapters bythe type of renewables technology. The third question relates to broad issuesof planning, social responsibilityandsustainabledevelopment; theseareconsidered in this chapter and in Chapter 17. The environmental impactsof specific renewable energy technologies are summarised in the last sectionof eachtechnologychapter. Thefourthquestion, consideredwithotherinstitutionalfactorsinthelastchapter,maydominateforconsumersandusually becomes the major criterion for commercial installations. However,cost-effectiveness depends significantly on:a Appreciatingthedistinctivescientificprinciplesof renewableenergy(Section 1.4).b Makingeachstageoftheenergysupplyprocessefficientintermsofboth minimising losses and maximising economic, social and environ-mental benefits.c Like-for-likecomparisons,includingexternalities,withfossilfuelandnuclear power.2 Principles of renewable energyWhentheseconditionshavebeenmet,itispossibletocalculatethecostsand benefits of a particular scheme and compare these with alternatives foran economic and environmental assessment.Failuretounderstandthedistinctivescientificprinciplesforharnessingrenewable energy will almost certainly lead to poor engineering and uneco-nomicoperation.Frequentlytherewillbeamarkedcontrastbetweenthemethods developedfor renewablesupplies andthoseusedfor thenon-renewable fossil fuel and nuclear supplies.1.2 Energy and sustainable development1.2.1 Principles and major issuesSustainabledevelopmentcanbebroadlydefinedasliving,producingandconsuming in a manner that meets the needs of the present without com-promising the ability of future generations to meet their own needs. It hasbecome a key guiding principle for policy in the 21st century. Worldwide,politicians, industrialists, environmentalists, economists andtheologiansaffirm that the principle must be applied at international, national and locallevel. Actually applying it in practice and in detail is of course much harder!In the international context, the word development refers to improve-ment in quality of life, and, especially, standard of living in the less devel-oped countries of the world. The aim of sustainable development is for theimprovement to be achieved whilst maintaining the ecological processes onwhich life depends. At a local level, progressive businesses aim to report apositive triple bottomline, i.e. a positive contribution to the economic, socialand environmental well-being of the community in which they operate.Theconcept of sustainabledevelopment becamewidelyacceptedfol-lowing the seminal report of the World Commission on Environment andDevelopment(1987). ThecommissionwassetupbytheUnitedNationsbecause the scale and unevenness of economic development and populationgrowth were, and still are, placing unprecedented pressures on our planetslands, waters and other natural resources. Some of these pressures are severeenough to threaten the very survival of some regional populations and, inthe longer term, to lead to global catastrophes. Changes in lifestyle, espe-cially regarding production and consumption, will eventually be forced onpopulationsbyecologicalandeconomicpressures.Nevertheless,theeco-nomic and social pain of such changes can be eased by foresight, planningand political (i.e. community) will.Energy resources exemplify these issues. Reliable energy supply is essentialin all economies for lighting, heating, communications, computers, indus-trial equipment, transport, etc. Purchases of energy account for 510% ofgrossnationalproductindevelopedeconomies.However,insomedevel-oping countries, energy imports may have cost over half the value of total1.2 Energy and sustainable development 3exports; such economies are unsustainable and an economic challenge forsustainabledevelopment. Worldenergyuseincreasedmorethantenfoldoverthe20thcentury, predominantlyfromfossil fuels(i.e. coal, oil andgas)andwiththeadditionofelectricityfromnuclearpower. Inthe21stcentury, furtherincreasesinworldenergyconsumptioncanbeexpected,much for rising industrialisation and demand in previously less developedcountries, aggravated by gross inefficiencies in all countries. Whatever theenergy source, there is an overriding need for efficient generation and useof energy.Fossil fuels are not being newly formed at any significant rate, and thuspresentstocksareultimatelyfinite.Thelocationandtheamountofsuchstocks depend on the latest surveys. Clearly the dominant fossil fuel type bymass is coal, with oil and gas much less. The reserve lifetime of a resourcemaybedefinedastheknownaccessibleamount dividedbytherateofpresent use. By this definition, the lifetime of oil and gas resources is usuallyonly a few decades; whereas lifetime for coal is a few centuries. Economicspredictsthat asthelifetimeof afuel reserveshortens, sothefuel priceincreases; consequently demand for that fuel reduces and previously moreexpensive sources and alternatives enter the market. This process tends tomaketheoriginal sourcelastlongerthananimmediatecalculationindi-cates. In practice, many other factors are involved, especially governmentalpolicyandinternational relations. Nevertheless, thebasicgeological factremains: fossil fuel reserves are limited and so the present patterns of energyconsumption and growth are not sustainable in the longer term.Moreover, it istheemissionsfromfossil fuel use(andindeednuclearpower) that increasingly determine the fundamental limitations. Increasingconcentration of CO2 in the Atmosphere is such an example. Indeed, froman ecological understanding of our Earths long-term history over billions ofyears, carbon was in excess in the Atmosphere originally and needed to besequestered below ground to provide our present oxygen-rich atmosphere.Therefore from arguments of: (i) the finite nature of fossil and nuclear fuelmaterials, (ii) theharmof emissionsand(iii) ecological sustainability, itisessential toexpandrenewableenergysuppliesandtouseenergymoreefficiently. Such conclusions are supported in economics if the full externalcosts of both obtaining the fuels and paying for the damage from emissionsare internalised in the price. Such fundamental analyses may conclude thatrenewableenergyandtheefficient useof energyarecheaperforsocietythan the traditional use of fossil and nuclear fuels.The detrimental environmental effects of burning the fossil fuels likewiseimply that current patterns of use are unsustainable in the longer term. Inparticular, CO2emissions from the combustion of fossil fuels have signifi-cantly raised the concentration of CO2in the Atmosphere. The balance ofscientificopinionisthatifthiscontinues, itwill enhancethegreenhouse4 Principles of renewable energyeffect1and lead to significant climate change within a century or less, whichcouldhavemajoradverseimpactonfoodproduction, watersupplyandhuman,e.g.throughfloodsandcyclones(IPCC).Recognisingthatthisisa global problem, which no single country can avert on its own, over 150nationalgovernmentssignedtheUNFrameworkConventiononClimateChange, which set up a framework for concerted action on the issue. Sadly,concrete action is slow, not least because of the reluctance of governmentsin industrialised countries to disturb the lifestyle of their voters. However,potential climate change, and related sustainability issues, is nowestablishedas one of the major drivers of energy policy.In short, renewable energy supplies are much more compatible with sus-tainabledevelopmentthanarefossil andnuclearfuels, inregardtobothresource limitations and environmental impacts (see Table 1.1).Consequently almost all national energy plans include four vital factorsfor improving or maintaining social benefit from energy:1 increased harnessing of renewable supplies2 increased efficiency of supply and end-use3 reduction in pollution4 consideration of lifestyle.1.2.2 A simple numerical modelConsiderthefollowingsimplemodel describingtheneedforcommercialand non-commercial energy resources:B =IN (1.1)Here B is the total yearly energy requirement for a population of Npeople.Iisthepercapitaenergy-useaveragedoveroneyear, relatedcloselytoprovisionoffoodandmanufacturedgoods. Theunitof Iisenergyperunit time, i.e. power. On a world scale, the dominant supply of energy isfrom commercial sources, especially fossil fuels; however, significant use ofnon-commercial energy may occur (e.g. fuel wood, passive solar heating),which is often absent from most official and company statistics. In terms oftotal commercial energy use, the average per capita value ofIworldwideis about 2 kW; however, regional average values range widely, with NorthAmerica9 kW, Europeasawhole4 kW, andseveral regionsof CentralAfrica as small as 0.1 kW. The inclusion of non-commercial energy increases1As described in Chapter 4, the presence of CO2 (and certain other gases) in the atmospherekeepstheEarthsome30degreeswarmerthanit wouldotherwisebe. Byanalogywithhorticultural greenhouses, this is called the greenhouse effect.Table1.1ComparisonofrenewableandconventionalenergysystemsRenewableenergysupplies(green)Conventionalenergysupplies(brown)ExamplesWind,solar,biomass,tidalCoal,oil,gas,radioactiveoreSourceNaturallocalenvironmentConcentratedstockNormalstateAcurrentorflowofenergy.AnincomeStaticstoreofenergy.CapitalInitialaverageintensityLowintensity,dispersed:300Wm2Releasedat100kWm2LifetimeofsupplyInfiniteFiniteCostatsourceFreeIncreasinglyexpensive.EquipmentcapitalcostperkWcapacityExpensive,commonlyUS$1000kW1Moderate,perhaps$500kW1withoutemissionscontrol;yetexpensive>US$1000kW1withemissionsreductionVariationandcontrolFluctuating;bestcontrolledbychangeofloadusingpositivefeedforwardcontrolSteady,bestcontrolledbyadjustingsourcewithnegativefeedbackcontrolLocationforuseSite-andsociety-specificGeneralandinvariantuseScaleSmallandmoderatescaleofteneconomic,largescalemaypresentdifficultiesIncreasedscaleoftenimprovessupplycosts,largescalefrequentlyfavouredSkillsInterdisciplinaryandvaried.Widerangeofskills.ImportanceofbioscienceandagricultureStronglinkswithelectricalandmechanicalengineering.NarrowrangeofpersonalskillsContextBiastorural,decentralisedindustryBiastourban,centralisedindustryDependenceSelf-sufficientandislandedsystemssupportedSystemsdependentonoutsideinputsSafetyLocalhazardspossibleinoperation:usuallysafewhenoutofactionMaybeshieldedandenclosedtolessengreatpotentialdangers;mostdangerouswhenfaultyPollutionandenvironmentaldamageUsuallylittleenvironmentalharm,especiallyatmoderatescaleEnvironmentalpollutionintrinsicandcommon,especiallyofairandwaterHazardsfromexcessbiomassburningSoilerosionfromexcessivebiofueluseLargehydroreservoirsdisruptiveCompatiblewithnaturalecologyPermanentdamagecommonfromminingandradioactiveelementsenteringwatertable.DeforestationandecologicalsterilisationfromexcessiveairpollutionClimatechangeemissionsAesthetics,visualimpactLocalperturbationsmaybeunpopular,butusuallyacceptableiflocalneedperceivedUsuallyutilitarian,withcentralisationandeconomyoflargescale6 Principles of renewable energyall these figures and has the major proportional benefit in countries wherethe value of I is small.Standard of living relates in a complex and an ill-defined way to I. Thusper capita gross national product S (a crude measure of standard of living)may be related to I by:S =f I (1.2)Heref isacomplexandnon-linearcoefficientthatisitselfafunctionofmanyfactors.Itmaybeconsideredanefficiencyfortransformingenergyintowealthand, bytraditional economics, isexpectedtobeaslargeaspossible. However, SdoesnotincreaseuniformlyasIincreases. IndeedSmayevendecreasefor largeE(e.g. becauseof pollutionor technicalinefficiency). Obviously unnecessary waste of energy leads to a lower valueof f thanwouldotherwisebepossible. Substitutingfor Iin(1.1), thenational requirement for energy becomes:B =(SNif(1.3)soABB=ASSANNAff(1.4)Nowconsidersubstitutingglobalvaluesfortheparametersin(1.4).In50 years the world populationNincreased from 2500 million in 1950 toover 6000 million in 2000. It is now increasing at approximately 23% peryear so as to double every 2030 years. Tragically, high infant mortality andlow life expectancy tend to hide the intrinsic pressures of population growthin many countries. Conventional economists seek exponential growth ofSat25%peryear. Thusin(1.4), atconstantefficiencyf , thegrowthoftotal world energy supply is effectively the sum of population and economicgrowth, i.e. 48%per year. Without newsupplies suchgrowthcannotbemaintained. Yet at thesametimeas moreenergyis required, fossiland nuclear fuels are being depleted and debilitating pollution and climatechange increase; so an obvious conclusion to overcome such constraints isto increase renewable energy supplies. Moreover, from (1.3) and (1.4), it ismost beneficial to increase the parameterf , i.e. to have a positive value off .Consequentlythereisagrowthrateinenergyefficiency,sothatScanincrease, while B decreases.1.2.3 Global resourcesConsidering these aims, and with the most energy-efficient modern equip-ment, buildings and transportation, a justifiable target for energy use in a1.3 Fundamentals 7modern society with an appropriate lifestyle isI =2kW per person. Sucha target is consistent with an energy policy of contract and converge forglobal equity, sinceworldwideenergysupplywouldtotal approximatelythe present global average usage, but would be consumed for a far higherstandard of living. Is this possible, even in principle, from renewable energy?Each square metre of the earths habitable surface is crossed by, or accessibleto, an average energy flux from all renewable sources of about 500 W (seeProblem1.1).Thisincludessolar,windorotherrenewableenergyformsin an overall estimate. If this flux is harnessed at just 4% efficiency, 2 kWofpowercanbedrawnfromanareaof10m10m, assumingsuitablemethods. Suburbanareas of residential towns havepopulationdensitiesofabout500peoplepersquarekilometre.At2 kWperperson,thetotalenergydemandof1000kWkm2couldbeobtainedinprinciplebyusingjust 5% of the local land area for energy production. Thus renewable energysupplies can provide a satisfactory standard of living, but only if the tech-nical methods and institutional frameworks exist to extract, use and storetheenergyinanappropriateformatrealisticcosts. Thisbookconsidersboth the technical background of a great variety of possible methods andasummaryof theinstitutional factorsinvolved. Implementationistheneveryones responsibility.1.3 Fundamentals1.3.1 DefinitionsFor all practical purposes energy supplies can be divided into two classes:1 Renewable energy. Energy obtained from natural and persistent flowsof energy occurring in the immediate environment. An obvious exampleis solar (sunshine) energy, where repetitive refers to the 24-hour majorperiod. Note that the energy is already passing through the environmentasacurrentorflow, irrespectiveoftherebeingadevicetointerceptand harness this power. Such energy may also be called Green Energyor Sustainable Energy.2 Non-renewableenergy. Energyobtainedfromstaticstoresofenergythat remain underground unless released by human interaction. Exam-ples are nuclear fuels and fossil fuels of coal, oil and natural gas. Notethat theenergyisinitiallyanisolatedenergypotential, andexternalactionisrequiredtoinitiatethesupplyof energyforpractical pur-poses. To avoid using the ungainly word non-renewable, such energysupplies are called finite supplies or Brown Energy.These two definitions are portrayed in Figure 1.1. Table 1.1 provides acomparison of renewable and conventional energy systems.8 Principles of renewable energyNatural Environment:greenMined resource: brownCurrent source of continuousenergy flowACDEFBDeviceUseDEFDeviceUseEnvironment Sink Environment SinkFinite source ofenergy potentialRenewable energy Finite energyFigure1.1Contrast between renewable (green) and finite (brown) energy supplies.Environmental energy flow ABC, harnessed energy flow DEF.1.3.2 Energy sourcesThere are five ultimate primary sources of useful energy:1 The Sun.2 The motion and gravitational potential of the Sun, Moon and Earth.3 Geothermal energyfromcooling, chemical reactionsandradioactivedecay in the Earth.4 Human-induced nuclear reactions.5 Chemical reactions from mineral sources.Renewable energy derives continuously fromsources 1, 2 and 3 (aquifers).Finiteenergyderivesfromsources1(fossilfuels),3(hotrocks),4and5.The sources of most significance for global energy supplies are 1 and 4. Thefifth category is relatively minor, but useful for primary batteries, e.g. drycells.1.3.3 Environmental energyThe flows of energy passing continuously as renewable energy through theEarthareshowninFigure1.2.Forinstance,totalsolarfluxabsorbedatsealevel isabout1.2 1017W. ThusthesolarfluxreachingtheEarthssurfaceis 20MWper person; 20 MWis thepower of tenverylarge1.3 Fundamentals 9Reflectedto space50 000SolarradiationFromSunFromEarthFromplanetarymotion120 000Absorbed onEarth40 00080 000SensibleheatingLatent heatand potentialenergy300Kinetic energyPhotonprocessesGeothermal30100HeatGravitation,orbital motionTidal motion3InfraredradiationSolar water heatersSolar buildingsSolar dryersOcean thermal energyHydropowerWind and wave turbinesBiomass and biofuelsPhotovoltaicsGeothermal heatGeothermal powerTidal range powerTidal current powerFigure1.2Natural energycurrentsonearth, showingrenewableenergysystem. Notethegreatrangeofenergyflux(1: 105)andthedominanceofsolarradiationand heat. Units terawatts(1012W).diesel electric generators, enough to supply all the energy needs of a townof about 50 000people. The maximumsolar fluxdensity (irradiance)perpendicular tothe solar beamis about 1kWm2; averyuseful andeasynumber toremember. Ingeneral terms, ahumanbeingis abletointercept suchanenergyfluxwithout harm, but anyincreasebeginstocause stress and difficulty. Interestingly, power flux densities of 1kWm2begintocausephysical difficultytoanadultinwind, watercurrentsorwaves.However, theglobal dataofFigure1.2areoflittlevalueforpracticalengineering applications, since particular sites can have remarkably differentenvironments and possibilities for harnessing renewable energy. Obviouslyflat regions, such as Denmark, have little opportunity for hydro-power butmay have wind power. Yet neighbouring regions, for example Norway, mayhave vast hydro potential. Tropical rain forests may have biomass energysources, but deserts at the same latitude have none (moreover, forests mustnot be destroyed so making more deserts). Thus practical renewable energysystems have to be matched to particular local environmental energy flowsoccurring in a particular region.10 Principles of renewable energy1.3.4 Primary supply to end-useAll energy systems can be visualised as a series of pipes or circuits throughwhich the energy currents are channelled and transformed to become use-ful indomestic, industrial andagricultural circumstances. Figure 1.3(a)is a Sankey diagramof energy supply, whichshows the energy flowsthroughanationalenergysystem(sometimescalledaspaghettidiagrambecauseofitsappearance).Sectionsacrosssuchadiagramcanbedrawnas pie charts showing primary energy supply and energy supply to end-useThermalelectricitygenerationRefiningCrude oilPRIMARYENERGYSUPPLIESCoalFossil gasBiomassHydroOil productsNon-energy useENERGYEND-USETransportIndustryResidentialand otherDistrictheatingWaste heatElectricity(a)300 PJFigure1.3EnergyflowdiagramsforAustriain2000, withapopulationof 8.1million.(a) Sankey (spaghetti) diagram, with flows involving thermal electricity showndashed. (b)(c)Piediagrams. Thecontributionof hydropowerandbiomass(woodandwaste)isgreaterthaninmostindustrialisedcountries, asistheuse of heat produced from thermal generation of electricity (combined heatandpower). Energyusefortransportissubstantial andverydependenton(imported) oil and oil products, therefore the Austrian government encouragesincreased use of biofuels. Austrias energy use has grown by over 50% since1970, although the population has grown by less than 10%, indicating the needfor greater efficiency of energy use. [Data source: simplified from InternationalEnergy Agency, Energy Balances of OECD countries 20002001.]1.3 Fundamentals 11(b)Energy End-Use(total: 970 PJ)Industry30%Transport30%Residential28%Other12%(c)Figure1.3(Continued).(Figure1.3(b)). Notehowthetotal energyend-useis less thanthepri-mary supply because of losses in the transformation processes, notably thegeneration of electricity from fossil fuels.1.3.5 Energy planning1 Complete energy systems must be analysed, and supply should not beconsideredseparatelyfromend-use. Unfortunatelypreciseneeds forenergy are too frequently forgotten, and supplies are not well matchedtoend-use. Energy losses anduneconomic operationtherefore fre-quentlyresult. Forinstance, if adominant domesticenergyrequire-ment is heat for warmth and hot water, it is irresponsible to generategridqualityelectricityfromafuel, wastethemajorityoftheenergyasthermal emissionfromtheboilerandturbine, distributetheelec-tricityinlossycablesandthendissipatethiselectricityasheat.Sadly12 Principles of renewable energysuchinefficiencyanddisregardfor resources oftenoccurs. Heatingwould be more efficient and cost-effective from direct heat productionwithlocal distribution. Evenbetteristocombineelectricitygenera-tion with the heat production using CHP combined heat and power(electricity).2 System efficiency calculations can be most revealing and can pinpointunnecessary losses. Here we define efficiency as the ratio of the usefulenergyoutput fromaprocesstothetotal energyinput tothat pro-cess. Consider electric lighting produced from conventional thermallygenerated electricity and lamps. Successive energy efficiencies are: elec-tricity generation 30%, distribution 90% and incandescent lighting(energy in visible radiation, usually with a light-shade) 45%. The totalefficiencyis11.5%. Contrast thiswithcogenerationof useful heatand electricity (efficiency 85%), distribution(90%i and lighting inmodernlowconsumptioncompactfluorescentlamps(CFL) (22%i.The total efficiency is now 1418%; a more than tenfold improvement!The total life cycle cost of the more efficient system will be much lessthan for the conventional, despite higher per unit capital costs, because(i) less generating capacity and fuel are needed, (ii) less per unit emissioncostsarecharged, and(iii)equipment(especiallylamps)lastslonger(see Problems 1.2 and 1.3).3 Energy management is always important to improve overall efficiencyandreduceeconomiclosses.Noenergysupplyisfree,andrenewablesupplies are usually more expensive in practice than might be assumed.Thus there is no excuse for wasting energy of any form unnecessarily.Efficiency with finite fuels reduces pollution; efficiency with renewablesreduces capital costs.1.4 Scientific principles of renewable energyThedefinitions of renewable(green) andfinite(brown) energysupplies(Section 1.3.1) indicate the fundamental differences between the two formsof supply. As a consequence the efficient use of renewable energy requiresthe correct application of certain principles.1.4.1 Energy currentsItisessentialthatasufficientrenewablecurrentisalreadypresentinthelocal environment. It is not good practice to try to create this energy currentespeciallyforaparticularsystem. Renewableenergywasonceridiculedby calculating the number of pigs required to produce dung for sufficientmethanegenerationtopowerawholecity. It isobvious, however, thatbiogas (methane) production should only be contemplated as a by-productof ananimal industryalreadyestablished, andnot viceversa. Likewise1.4 Scientific principles of renewable energy 13forabiomassenergystation, thebiomassresourcemust exist locallytoavoid large inefficiencies in transportation. The practical implication of thisprincipleisthatthelocalenvironmenthastobemonitoredandanalysedover a long period to establish precisely what energy flows are present. InFigure1.1theenergycurrent ABCmust beassessedbeforethedivertedflow through DEF is established.1.4.2 Dynamic characteristicsEnd-userequirementsforenergyvarywithtime. Forexample, electricitydemandonapower networkoftenpeaks inthemorningandevening,andreachesaminimumthroughthenight. Ifpowerisprovidedfromafinite source, such as oil, the input can be adjusted in response to demand.Unused energy is not wasted, but remains with the source fuel. However,with renewable energy systems, not only does end-use vary uncontrollablywithtimebutsotoodoesthenaturalsupplyintheenvironment.ThusarenewableenergydevicemustbematcheddynamicallyatbothDandEofFigure1.1; thecharacteristicswill probablybequitedifferentatbothinterfaces. Examplesofthesedynamiceffectswill appearinmostofthefollowing chapters.The major periodic variations of renewable sources are listed in Table 1.2,but precise dynamic behaviour may well be greatly affected by irregularities.Systemsrangefromtheveryvariable(e.g.windpower)totheaccuratelypredictable (e.g. tidal power). Solar energy may be very predicable in someregions (e.g. Khartoum) but somewhat random in others (e.g. Glasgow).1.4.3 Quality of supplyThequalityof anenergysupplyorstoreisoftendiscussed, but usuallyremains undefined. We define quality as the proportion of an energy sourcethat can be converted to mechanical work. Thus electricity has high qualitybecausewhenconsumedinanelectricmotor>95%oftheinputenergymay be converted to mechanical work, say to lift a weight; the heat lossesare correspondingly small,-5%. The quality of nuclear, fossil or biomassfuel inasinglestagethermal power stationis moderatelylow, becauseonlyabout33%ofthecalorificvalueofthefuelcanbemadetoappearasmechanical workandabout 67%islost asheat totheenvironment.If thefuel isusedinacombinedcyclepowerstation(e.g. methanegasturbinestagefollowedbysteamturbine),thenthequalityisincreasedto50%. It ispossibletoanalysesuchfactorsintermsof thethermody-namic variable energy, defined here as the theoretical maximum amount ofwork obtainable, at a particular environmental temperature, from an energysource.Table1.2IntensityandperiodicalpropertiesofrenewablesourcesSystemMajorperiodsMajorvariablesPowerrelationshipCommentTextreference(equation)Directsunshine24h,1ySolarbeamirradianceC b(Wm2);PC bcos0zDaytimeonly(4.2)Angleofbeamfromvertical0zPmax=1kWm2Diffusesunshine24h,1yCloudcover,perhapsairpollutionP 71).Infreeconvection(sometimes callednaturalconvection)the movementiscausedbytheheat flowitself. Considerthefluidincontact withthehotsurfacesofFigure3.3;forexample,wateragainsttheinsidesurfacesofaboilerorasolarcollector.Initiallythefluidabsorbsenergybycon-ductionfromthehot surface, andsothefluiddensitydecreasesbyvol-ume expansion. The heated portion then rises through the unheated fluid,therebytransportingheatphysicallyupwards, butdownthetemperaturegradient.Inforcedconvection the fluid is moved across a surface by an externalagencysuchasapump(e.g. waterinasolarcollectortoastoragetankbelow) or wind (e.g. heat loss from the outside surfaces of a solar collector).The movement occurs independently of the heat transfer (i.e. is not a func-tionofthelocal temperaturegradients). Obviouslyconvectionisusuallypartly forced and partly free, yet usually one process dominates.3.4.2 Nusselt numberThe analysis of convectionproceeds fromagross simplificationof theprocesses. We imagine the fluid near the surface to be stationary. We thenconsider the heat flowing across an idealised boundary layer of stationaryfluid of thickness o and cross-sectional area A(Figure 3.4). The temperaturesFigure3.4Idealisedthermal boundary layer infree convection. (a) Hot surfacehorizontal. (b) Hot surface vertical.3.4 Convection 53across the fictitious boundary areTf, the fluid temperature away from thesurface, and Ts, the surface temperature. This being so, the heat transfer byconduction across unit area of the stationary fluid iso =IA =l(TsTfio(3.16)where l is the thermal conductivity of the fluid.As described here, o is fictitious and cannot be measured. We can, how-ever, measure X, a characteristic dimension specified rather arbitrarily foreach particular surface (see Figure 3.4 and Appendix C).From (3.13),o =IA =l(TsTfio=Xol(TsTfiX=l(TsTfiX(3.17)is the Nusselt number for the particular circumstance. It is a dimension-lessscalingfactor, useful forall bodiesof thesameshapeinequivalentconditions of fluidflow. Tables of values ofare available for spec-ifiedconditions, withtheappropriatecharacteristicdimensionidentified(Appendix C).From Section 3.2 it follows that:thermal resistance of convection Bv=XlA(3.18)convective thermal resistivity of unit area rv=BvA =Xl(3.19)convective heat transfer coefficient lv=1rv=lX(3.20)The amount of heat transferred by convection will depend on three factors:1 The properties of the fluid2 The speed of the fluid flow and its characteristics, i.e. laminar or tur-bulent3 The shape and size of the surface.TheNusselt number isadimensionlessmeasureof theheat transfer.Therefore it can depend only on dimensionless measures of the three factorslisted. In choosing these measures, it is convenient to separate the cases offorced and free convection.54 Heat transfer3.4.3 Forced convectionForagivenshapeofsurface,anon-dimensionalmeasureofthespeedofthe flow is the Reynolds number:=uX:(3.21)WesawinSection2.5that determines thepatternof theflow, andinparticularwhetheritislaminarorturbulent. Inflowoveraflatplate(Figure 3.5), turbulence occurs when 3105, with subsequent increasein the heat transfer because of the perpendicular motions involved.The flowof heat into or froma fluid depends on (a) the thermal diffusivityof thefluid, and(b) thekinematicviscosity:, (2.10), whichmaybeconsideredthe diffusivityof momentum, since it affects the Reynoldsnumber and thus the character of the flow. These are the only two propertiesofthe fluidthatinfluence the Nusseltnumber inforcedconvection,sincethe separate effects of l, j, and c are combined in (see (3.15)).A non-dimensional measure of the properties of the fluid is the Prandtlnumber: =: (3.22)If is large, changes in momentum diffuse more quickly through the fluidthandochangesintemperature. Manycommonfluidshave 1, e.g.7.0 for water at 20oC. For air at environmental temperatures=0.7 (seeAppendix B).Thus,foreachshapeofsurface,theheattransferbyforcedconvectioncan be expressed in the form =(, i (3.23)Thatis, foreachshape, theNusseltnumberisafunctiononlyoftheReynolds number andthe Prandtl number. These relationships maybeFigure3.5Fluid flow over a hot plate.Generalview of pathlines,showing regions:(A) wellaway from the surface; (B) laminar flow near the leading edge;(C) turbulent flow in the downstream region.3.4 Convection 55expressed with other closely related dimensionless parameters, e.g. the Stan-ton number(i and the Pclet number, but neither are used inthis book.Numerical values ofare determined fromexperiment, with theirmethod of use explained in Appendix C. An example is given inSection 3.4.5. It is important to realise that these formulas are mostly onlyaccurateto 10%,partlybecausetheyareapproximationstotheexper-imental conditions, andpartlybecausetheexperimental datathemselvesusually contain both random and systematic errors.3.4.4 Free convectionIn free convection, often called natural convection, the fluid speed dependson the heat transfer (whereas in forced convection, heat transfer depends onthe fluid speed). Analysis still depends on determining the Nusselt number,but as a function of other dimensionless numbers. We replace (3.23) by =(, i (3.24)where the Rayleigh number =g8X3AT:(3.25)These formulae are sometimes expressed in terms of the Grashof number =

=g8X3AT2(3.26)Both the Grashof and Rayleigh numbers are dimensionless measures of thedriving temperature difference AT; g is the acceleration due to gravity; 8 isthe coefficient of thermal expansion and the other symbols are as before.InthisbookweprefertousetheRayleighnumberbecauseitmoredirectly relates to the physical processes indicated in Figure 3.6. Heated fluidis forced upwards by a buoyancy force proportional to g8AT, and retardedby a viscous force proportional to :. However, the excess temperature (andtherefore the buoyancy) is lost at a rate proportional to thermal diffusivity .Therefore the vigour of convection increases withg8AT(:i, i.e. with.The factor X3is inserted to make this ratio dimensionless. It is found exper-imentally that free convection is non-existent if Rayleigh number-103and is turbulent if105.This argument shows that the Nusselt number in free convection dependsmainly on the Rayleigh number. The dimensional argument used inSection 3.4.3 suggests thatmay also depend on the Prandtl number, asindicated in (3.24). Formulas to calculate these Nusselt numbers are given56 Heat transferFigure3.6Schematic diagram of a blob of fluid moving upward in free convection.It is subject to an upward buoyancy force, a retarding viscous force, anda sideways temperature loss.inAppendixCforvariousgeometries. Thesecannotbeexpectedtogivebetterthan10%accuracy. Notethat theNusselt number(andthusthethermal resistance) in free convection depends onAT, through the depen-dence on . This is because a larger temperature difference drives a strongerflow, which transfers heat more efficiently. By contrast, in forced convec-tion, the Nusselt number and thermal resistance are virtually independentof AT.3.4.5 Calculation of convective heat transferBecause of the complexity of fluid flow, there is no fundamental theory forcalculating convective heat transfer. Instead we use experiments on geomet-ricallysimilarobjects.Byexpressingtheresultsinnon-dimensionalform,they can be applied to different sizes of the objects and for different fluids.For this, working formulas are given in the tables of Appendix C for shapescommoninrenewableenergyapplications;moreextensivecollectionsaregiven in textbooks of heat transfer.All thisseemsveryconfusing. However, whenusedinearnestforcal-culatingconvection, confusionlessensbyusingthefollowingsystematicprocedure:1 Open the tables of heat transfer processes and equations (e.g.Appendix C)2 Draw a diagram of the heated object.3 Section the diagram into standard geometries (i.e. parts correspondingto the illustrations in the tables)3.4 Convection 574 For each such section:a Identify the characteristic dimension (X)b As required in the tables, calculateand/orfor each section ofthe object.c Choose the formula for from tables appropriate to that range of or. (The different formulas usually correspond to laminar orturbulent flow.)d Calculate the Nusselt number and hence the heat flow across thesection I =oA.5 Add the heat flows from each section to obtain the total heat flow fromthe object.Example 3.2 Free convection between parallel platesTwo flat plates each 1.0m1.0m are separated by 3.0 cm of air. Thelower is at 70oC and the upper at 45oC. The edges are sealed togetherby thermal insulating material acting also as walls to prevent air move-ment beyond the plates. Calculate the convective thermal resistivity ofunit area, r, and the heat flux, I, between the top and the bottom plate.SolutionFigure3.7correspondstothestandardgeometrygivenfor(C.7)inAppendixC. Since the edges are sealed, nooutside air canenterbetween the plates and only free convection occurs. Using (3.25) andTable B.1 in Appendix B, for mean temperature 57oC(=330Ki=g8X3AT:=

g8:

X3AT

=(9.8ms1i(1330Ki(2.6105m2s1i(1.8105m2s1i(0.03mi3(25Ki=4.1104Using (C.7) a reasonable value forcan be obtained, although isslightly less than 105: =0.0620.33=2.06(From (3.17), this implies the boundary layer is about half way acrossthe gap.)From (3.19)rv=Xl =0.03m(2.06i(0.028Wm1K1i =0.52KW1m258 Heat transferFigure 3.7Diagrams for worked examples on convection. (a) Parallel plates,as in Example 3.2 (b) Cooking pot with lid, as in Example 3.3.From (3.17),I =AATr=(1m2i(25Ki0.52KW1m2 =48WNote the following:1 The factor (g8:i =(X3ATi is tabulated in Appendix B for airand water.2 The fluid properties are evaluated at the mean temperature (57oCin this case).3 It is essential to use consistent units (e.g. SI) in evaluating dimen-sionless parameters like .Example 3.3 Convective cooling of a cooking potA metal cooking pot with a shiny outside surface, of the dimensionsshown in Figure 3.7(b), is filled with food and water and placed on acooking stove. What is the minimum energy required to maintain it at3.4 Convection 59boiling temperature for one hour, (1) if it is sheltered from the wind(2) if it is exposed to a breeze of 3.0ms1?SolutionWe assume that the lid is tight, so that there is no heat loss by evapora-tion. We also neglect heat loss by radiation, as justified in Problem 3.4.Since the conductive resistance of the pot wall is negligible, the prob-lemisthenreducedtocalculatingtheconvectiveheatlossfromthetop and sides of a cylinder with a surface temperature of 100oC. Weshall consider the ambient (air and surrounding walls) temperature tobe 20oC. Therefore heat transfer properties of the air are evaluated atthe mean temperature T =60oC.1 Free convection alone For the top (using Table B.1 and (3.25)), =(5.8107m3K1i(0.22mi3(80Ki =4.9107and (from (C.2)) =0.140.33=48.4andItop=AlATX=(r4i(0.22mi2(0.027Wm1K1i(48.4i (80Ki0.22m =18WFor the sides, X =0.11m:

side=top(0.11m0.22mi3=6.1106and (from (C.5)) =560.25=27.8soIside=r(0.22mi(0.11mi(0.027Wm1K1i(27.8i (80Ki0.11m =41WHenceIfree=ItopIside=59W=(0.059kWi(3600s h1i 0.2MJ h1.60 Heat transfer2 ForcedplusfreeconvectionHerewecalculatetheforcedcon-vectivepowerlossesseparately, andaddthemtothosealreadycalculatedforfreeconvection,inordertoobtainanestimateofthe total convective heat loss Itotal.For the top,=(3ms1i(0.22mi1.9105m2s1 =3.5104which suggests the use of (C.8): =0.664 0.5

0.33=110SoItop=Al(ATXi =42WFor the sides, as for the top,=3.5104which suggests the use of (C.11): =0.26 0.6

0.3=124andIside=r(0.22mi(0.11mi(0.027Wm1K1i(124i (80Ki0.22m=93WHenceIforced=9342 =135WThe total estimate isItotal=IforcedIfree=194W=(194Wi(3600s h1i 0.7MJ h1i.e. about 3 times the energy per unit time of the shelteredcooking.3.5 Radiative heat transfer 61The overall accuracy of calculations like those in Example 3.3 may be nobetterthan 50%,althoughtheindividualformulasarebetterthanthis.Thisisbecauseforcedandfreeconvectionmaybothbesignificant, buttheir separate contributions do not simply add because the flow induced byfree convection may oppose or reinforce the pre-existing flow. Similarly theflows around the separate sections of the object interact with each other.In Example 3.3 there is an additional confusion about whether the flow islaminar or turbulent. For example, on the top of the pot> 105, suggestingturbulence, but usingtheexternal flowspeedtocalculate(asearlier)gives -105, suggestinglaminarflow. Inpracticesuchaflowacrossthetopwouldbeturbulent,sinceitisdifficulttosmoothoutstreamlineswhich have become tangled by turbulence. The only safe way to accuratelyevaluateaconvectiveheattransfer, allowingforall theseinteractions, isbyexperiment!Someformulas,suchas(C.15),basedonsuchspecialisedexperiments areavailable, but haveacorrespondinglynarrowrangeofapplicability. Nevertheless, calculationof convectionis essential togiveorder-of-magnitude understanding of the processes involved.3.5 Radiative heat transfer3.5.1 IntroductionSurfaces emit energy by electromagnetic radiation according to fundamentallaws of physics. Absorption of radiation is a closely related process. Sadly,the literature and terminology concerning radiative heat transfer are confus-ing; symbols and names for the same quantities vary, and the same symboland name may be given for totally different quantities. Here, we have triedtofollowtherecommendationsoftheInternational SolarEnergySociety(ISES), whilst maintaining unique symbols throughout the whole book, asontheopeninglist.Inthischapterweconsiderradiativeheattransferingeneral. In Chapter 4 we shall consider solar radiation in particular, and inChapters 5 and 6 heating devices using solar energy.3.5.2 Radiant flux density (RFD)Radiationisenergytransportedbyelectromagneticpropagationthroughspaceortransparentmedia.Itspropertiesrelatetoitswavelength\.Thenamed regions of the spectrum are shown in Figure 3.8. The flux of energyperunitareaistheradiantfluxdensity(abbreviationRFD, unitWm2,symbol m). The variationof RFDwithwavelengthis describedbythespectral RFD (symbol m\, unit (Wm2i m1or more usually Wm2m1),which is simply the derivative dmd\. Thus m\A\ gives the power per unitarea in a (narrow) wavelength range A\, and integration of m\ with respect62 Heat transferFigure3.8Some of the named portions of the electromagnetic spectrum. (The spectrumextends both longwards and shortwards from that shown.)Figure3.9Measurements of various radiation parameters using a small totally absorbingplane. (a) Absorbs all directions. (b) Absorbs from hemisphere above one sideonly. (c) Absorbs from one direction only. (d) Absorbs from one solid angleonly.to wavelength gives the total RFD, i.e. m=

m\d\. Radiation coming ontoa surface is usually called irradiance.It is obvious that radiation has directional properties, and that these needto be specified. Understanding of this is always helped by:1 Drawing pictures of the radiant fluxes and the methods of measurement2 Clarifying the units of the parameters.Consider a small test instrument for measuring radiation parameters in anideal manner. This could consist of a small, totally absorbing, black plane(Figure 3.9) that can be adapted to (a) absorb on both sides, (b) absorb onone side only, (c) absorb from one direction only and (d) absorb from onethree-dimensional solid angle only.3.5 Radiative heat transfer 63The energy AI absorbed in time Ai could be measured from the tempera-ture rise of the plane of area of one side, AA, knowing its thermal capacity.FromFigure3.9(a)theradiantfluxdensityfromall directionswouldbem=(AIAii(2AAi. In Figure 3.9(b) the radiation is incident from the hemi-sphere above one side of the test plane (which may be labelled or ), som =AI(AAAii(3.27)InFigure3.9(c)avectorquantityisnowmeasured,withthedirectionofthe radiation flux perpendicular to the receiving plane. In Figure 3.9(d) theradiation flux is measured within a solid angleAw, centred perpendicularto the plane of measurement and with the unit of W(m2sri1.The wavelength(s) of the received radiation need not be specified, sincethe absorbing surface is assumed to be totally black. However, if a dispersingdevice is placed in front of the instrument which passes only a small rangeof wavelength from \(A\2i to \(A\2i, then the spectral radiant fluxdensity may be measured asm\=AIAAAiA\|unit Wm2m1] (3.28)This quantity can also be given directional properties per steradian (sr) aswith m. Difficulty may sometimes arise, especially regarding certain measur-ing instruments. There are two systems of units relating to the measurementof radiation quantities photometric and radiometric units (see Kaye andLaby 1995). Photometric units have been established to quantify responsesas recorded by the human eye, and relate to the SI unit of the candela. Radio-metric units quantify total energy effects irrespective of visual response, andrelate to the basic energy units of the joule and watt. For our purposes, onlyradiometric units need be used. As an aside, we note that a similar pair ofunits exists for noise.3.5.3 Absorption, reflection and transmission of radiationRadiationincident onmattermaybereflected, absorbedortransmitted(Figure3.10).Theseinteractionswilldependonthetypeofmaterial,thesurface properties, the wavelength of the radiation and the angle of incidence0.Normalincidence(0 = 0imaybeinferredifnototherwisementioned,but at grazing incidence (90o >0 70oi there are significant changes in theproperties.At wavelength\, withinwavelengthinterval A\, themonochromaticabsorptanceo\is the fraction absorbed of the incident flux densitym\A\.Note that o\ is a property of the surface alone, depending, for example, onthe energy levels of the atoms in the surface . It specifies what proportion of64 Heat transferFigure3.10Reflection, absorptionandtransmissionof radiation(mistheincidentradiation flux density).radiation at a particular wavelength would be absorbed if that wavelengthwas present in the incident radiation. The subscript ono\, unlike that onm\, does not indicate differentiation.Similarly, we define the monochromatic reflectance \ and the monochro-matic transmittance t\.Conservation of energy implies thato\\t\=1 (3.29)and that 0 o\, \, t\1. All of these properties are almost independent ofthe angle of incidence 0, unless 0 is near grazing incidence. In practice, theradiationincidentonasurfacecontainsawidespectrumofwavelengths,andnot just onesmall interval. Wedefinetheabsorptanceotobetheabsorbed proportion of the total incident radiant flux density:o =mabsmin(3.30)It follows thato =

~\=0o\m\,ind\

~\=0m\,ind\(3.31)Equation(3.31) describeshowthetotal absorptanceo, unlikeo\, doesdepend on the spectral distribution of the incident radiation. For example,a surface appearing blue in white daylight is black in orange sodium-light.Thisisbecausethesurfaceabsorbsthephotonsoforangecolourofbothlights, and so the remaining reflected daylight appears blue.3.5 Radiative heat transfer 6510(a)(b)2 4 6 80.80.2 m12 4 6 8 m1200010000 / Wm2m1IIIIIIFigure3.11Data for Example 3.4. The maxima of curves I, II, III in (b) are at (0.5,2000), (3.0, 1000) and (6.0, 400) respectively.The total reflectance =mreflmin and the total transmittance t =ttranstinare similarly defined, and againot =1 (3.32)Example 3.4 Calculation of absorbed radiationAcertain surface has o\varying with wavelength as shown inFigure3.11(a)(thisisatypical variationforaselectivesurface, asusedonsolarcollectors,Section5.6).Calculatethepowerabsorbedby 1.0m2of this surface from each of the following incident spectraldistributions of RFD:1 m\ given by curve I of Figure 3.11(b) (this approximates a sourceat 6000 K).2 m\ given by curve II (approximating a source at 1000 K).3 m\ given by curve III (approximating a source at 500 K).66 Heat transferSolution1 Over the entire range of \, o\=0.8. Therefore from (3.31) o=0.8also, and the absorbed power isI =o(1m2i

m\,ind\=(0.8i(1m2i12

2000Wm2m1

(2mi=1600W(The integral is the area under curve I.)2 Herewehavetoexplicitlycalculatetheintegral o\m\,ind\of(3.31). Tabulate as follows (the interval of\ is chosen to matchthe accuracy of the data; here the spectra are obviously linearised,so an interval A\ 1m is adequate):\(m) A\(m) o\m\(Wm2m1) o\m\A\(Wm2)2.5 1 0.62 500 3103.5 1 0.33 750 2504.5 1 0.2 200 40Total 600Therefore the power absorbed is approximately 600 W.3 In a manner similar to part 1 of this solution, o\= 0.2 over therelevant wavelength interval. Thus the power absorbed isI =(0.2i(1m2i12

400Wm2m1

(5mi=200W.Note: The accuracy of calculations of radiative energy transfer is gen-erallybetterthanforconvection. Thisisbecausethetheoryof thephysical processes is exactly understood.3.5.4 Black bodies, emittance and Kirchhoffs lawsAn idealised surface absorbing all incident irradiation, visible and invisible,isnamedablackbody. Thenameisbecausesurfaceshavingthecolourblack absorb all visible radiation; note, however, that black bodies absorbat all wavelengths, i.e. bothvisibleandinvisibleradiation. Therefore, ablackbodyhaso\= 1forall \,andthereforealsohastotalabsorptanceo = 1. Nothingcanabsorbmoreradiationthanasimilarlydimensionedblack body placed in the same incident irradiation.3.5 Radiative heat transfer 67Kirchhoff provedalsothat nobodycanemit more radiationthanasimilarly dimensioned black body at the same temperature.The emittance a of a surface is the ratio of the RFD emitted by the surfaceto the RFD emitted by a black body at the same temperature:a =mfromsurface(Timfromblackbody(Ti(3.33)The monochromatic emittance,a\, of any real surface is similarly definedby comparison with the ideal black body, as the corresponding ratio of RFDin the wavelength range A\ (from \(A\2i to (\A\2i. It follows that0 a, a\1 (3.34)Note that the emittance a of a real surface may vary with temperature.Kirchhoff extended his theoretical argument to prove Kirchhoffs law: foranysurfaceataspecifiedtemperature,andforthesamewavelength,themonochromatic emittance and monochromatic absorptance are identical,o\=a\(3.35)Note that botho\anda\are characteristics of the surface itself, and notof the surroundings.Forsolarenergydevices, theincomingradiationisexpectedfromtheSuns surface at atemperature of 5800 K, emittingwithpeakintensityat \ 0.5m. However, thereceivingsurfacemaybeat about 350 K,emitting with peak intensity at about \ 10m. The dominant monochro-matic absorptance is thereforeo\=0.5mand the dominant monochromaticemittanceis a\ = 10m. Thesetwocoefficients neednot beequal, seeSection 5.6. Nevertheless, Kirchhoffs Law is important for the determina-tion of such parameters, e.g. at the same wavelength of 10m, a\=10m=o\=10m3.5.5 Radiation emitted by a bodyThe monochromatic RFD emitted by a black body of absolute temperatureT, mB\, is derived from quantum mechanics as Plancks radiation law:mB\=C1\5|exp(C2\Ti 1](3.36)whereC1=lc2, andC2=lcl (c, the speed of light in vacuum;l, Planckconstant; andl, Boltzmann constant). HenceC1= 3.741016Wm2andC2= 0.0144mKarealsofundamentalconstants.Figure3.12showshowthis spectral distribution mB\ varies with wavelength \ and temperature T.68 Heat transfer1081061041024(a)8 12 16 20Locus ofmaxima B/Wm2m1 m1T=6000K1000K400K(b)0 2000 4000 6000 8000 10 00010.80.60.40.20T/(mK)DFigure3.12(a) Spectral distribution of black body radiation. After Duffie andBeckman (1991).(b) Cumulative version of (a),in dimensionless form,as in eqn (3.40). Note thatu 1 as\7 ~.Note that the wavelength\m, at whichmB\is most intense, increases asTdecreases. Indeed, as we know also from experience, when any surfacetemperatureincreases above T 700K(430oCi significant radiationisemittedinthevisibleregionandthesurfacedoesnotappearblack, butprogresses from red heat to white heat.By differentiating (3.36) and setting d(mB\id\ =0, we find that\mT =2898mK (3.37)This is Wiens displacement law. Knowing T, it is extremely easy to deter-mine \m, and thence to sketch the form of the spectral distribution mB\.3.5 Radiative heat transfer 69From (3.36) the total RFD emitted by a black body ismB=

~0mB\d\Standard methods (e.g. see Joos and Freeman, Theoretical Physics, p. 616)give the result for this integration asmB=

~0mB\d\ =uT4(3.38)where u =5.67108Wm2K4is the StefanBoltzmann constant,another fundamental constant.It follows from (3.33) that the heat flow from a real body of emittancea(a -1i, area A and absolute (surface) temperature TisIr=auAT4(3.39)Note:a in using radiation formulae, it is essential to convert surface tempera-tures in, say, degrees Celsius to absolute temperature, Kelvin; i.e. xoC=(x273i K,b the radiant flux dependence on the 4th power of absolute temperatureis highly non-linear and causes radiant heat loss to become a dominantheat transfer mode as surface temperatures increase more than 100oC.TheStefanBoltzmannequation(3.39)givestheradiationemittedbythebody. The net radiative flux away fromthe body may be much less(e.g. (3.44)). More convenient for calculation than (3.36) is the dimension-less function D, whereD=

\0mB\d\uT4(3.40)which turns out to be a function of the single variable \T. This function isgraphed in Figure 3.12(b).3.5.6 Radiative exchange between black surfacesAll material bodies, including the sky, emit radiation. However, we do notneedtocalculatehowmuchradiationeachbodyemitsindividually, butrather what is the net gain (or loss) of radiant energy by each body.Figure 3.13 shows two surfaces 1 and 2, each exchanging radiation. Thenet rate of exchange depends on the surface properties and on the geometry.Inparticularwemustknowtheproportionoftheradiationemittedby1actually reaching 2, and vice versa.70 Heat transferFigure3.13Exchange of radiation between two (black) surfaces.Consider the simplest case with both surfaces diffuse and black, and withno absorbing medium between them. (A diffuse surface is one which emitsequally in all directions; its radiation is not concentrated into a beam. Mostopaque surfaces, other than mirrors, are diffuse.) The shape factor Itjis theproportion of radiation emitted by surfacet reaching surfacej. It dependsonly on the geometry and not on the properties of the surfaces. LetmBbethe RFD emitted by a black body surface into the hemisphere above it. Theradiant power reaching 2 from 1 isI/12=A1mB1I12(3.41)Similarly the radiant power reaching 1 from 2 isI/21=A2mB2I21(3.42)If the two surfaces are in thermal equilibrium, I/12=I/21 and T1=T2: so by(3.38)mB1=uT41 =uT42 =mB2ThereforeA1I12=A2I21(3.43)This is a geometrical relationship independent of the surface properties andtemperature.3.5 Radiative heat transfer 71Ifthesurfacesarenotatthesametemperature, thenthenetradiativeheat flow from 1 to 2, using (3.43), isI12=I/12I/21=mB1A1I12mB2A2I21=uT41A1I12uT42A2I21(3.44)=u

T41 T42

A1I12Or, if it is easier to calculate I21,I12=u

T41 T42

A2I21(3.45)Ingeneral, thecalculationof Itjrequiresacomplicatedintegration, andresultsaretabulatedinhandbooks(e.g. seeWong1977). Solarcollectorconfigurations frequentlyapproximate toFigure 3.14, where the shapefactor becomes unity.3.5.7 Radiative exchange between grey surfacesAgreybodyhasadiffuseopaquesurfacewitha = o = 1 = constant,independent of surfacetemperature, wavelengthandangleof incidence.Figure3.14Geometrieswithshapefactor l12 = 1. (a) convexorflat surface(1)completely surrounded by surface (2). (b) One long cylinder (1) insideanother (2). (c) Closely spaced large parallel plates(Lu, L/u 1).72 Heat transferThis is a reasonable approximation for most opaque surfaces in commonsolarenergyapplicationswheremaximumtemperaturesare 200oCandwavelengths are between 0.3 and 15m.The radiation exchange between any number of grey bodies may be anal-ysed allowing for absorption, re-emission and reflection. The resulting sys-temofequationscanbesolvedtoyieldtheheatflowfromeachbodyifthe temperatures are known, or vice versa. If there are only two bodies, theheat flow from body 1 to body 2 can be expressed in the formI12=uA1I/12

T41 T42

(3.46)where theexchangefactorI/12depends on the geometric shape factorI12,the area ratio(A1A2i and the surface propertiesa1,a2. Comparison with(3.44) shows that for black bodies only, I/12=I12.As in Figure 3.14(c), a common situation is parallel plates withD 3mi. Glassisagoodabsorberinthiswaveband, andhenceuseful asagreenhouseor solar collector cover to prevent loss of infrared heat. In contrast,Figure 3.15(b) shows that polythene is unusual in being transparent in boththe visible and infrared, and hence not a good greenhouse or solar collectorcover. PlasticssuchasMylar, withgreatermolecularcomplication, havetransmittance characteristics lying between those of glass and polythene.3.7 Heat transfer by mass transportFree and forced convection (Section 3.4) is heat transfer by the movement offluid mass. Analysis proceeds by considering thermal interactions between a(solid) surface and the moving fluid. However, there are frequent practicalapplications where energy is transported by a moving fluid or solid withoutconsideringheattransferacrossasurfaceforexample,whenhotwateris pumped through a pipe from a solar collector to a storage tank. These3.7 Heat transfer by mass transport 75systems of heat transfer by mass transport are analysed by considering thefluid alone.3.7.1 Single phase heat transferConsider the fluid flowthrough a heated pipe shown in Figure 3.16. Accord-ingto(2.6), thenetheatflowoutofthecontrol volume(i.e. outofthepipe) isIm= nc(T3T1i (3.54)where nisthemassflowratethroughthepipe(kg/s), cisthespecificheatcapacityofthefluid(J kg1K1i andT1, T3arethetemperaturesofthefluidonentryandexitrespectively. IfbothT1andT3aremeasuredexperimentally, Immaybecalculatedwithoutknowingthedetailsofthetransfer process at the pipe wall. The thermal resistance for this process isdefined asBm=T3T1Im=1 nc(3.55)Note here that the heat flowis determined by external factors controlling therate of mass flow n, and not by temperature differences. Thus temperaturedifferenceisnotadrivingfunctionhereforthemass-flowheattransfer,unlike for conduction, radiation and free convection.3.7.2 Phase changeAmost effective means of heat transfer is as latent heat of vaporisa-tion/condensation. For example, 2.4 MJ of heat vaporises 1.0 kg of water,which is much greater than the 0.42 MJ to heat 1.0 kg through 100oC. HeatFigure3.16Mass flow through a heated pipe. Heat is taken out by the fluid at a ratePm= mc(7371) regardless of how the heat enters the fluid at (2).76 Heat transferFigure3.17Heat transfer by phase change. Liquid absorbs heat, changes to vapour,then condenses, so releasing heat.takenfromtheheatsource(asinFigure3.17)iscarriedtowhereverthevapour condenses (the heat sink). The associated heat flow isIm= nA (3.56)where n is the rate at which fluid is being evaporated (or condensed) andA is the latent heat of vaporisation. This expression is most useful when nis known (e.g. from experiment).Theoretical predictionofevaporationratesisverydifficult, becauseofthe multitude of factors involved, such as (i) the density, viscosity, specificheatandthermalconductivityofboththeliquidandthevapour;(ii)thelatent heat, the pressure and the temperature difference; and (iii) the size,shape and nucleation properties of the surface. Some guidance and specificempirical formulas are given in the specialised textbooks cited at the end ofthe chapter.Since evaporation and condensation are both nearly isothermal processes,the heat flowbythis mass transport is not determineddirectlybythesource temperature T1 and the sink temperature T2. The associated thermalresistance can, however, be defined asBm=T1T2 nA(3.57)A heat pipe is a device for conducting heat efficiently and relatively cheaplyfor short distances, -1m, between a separated heat source and heat sink(Figure3.18).Theclosedpipecontainsafluidthatevaporatesincontactwith the heat source (at A in the diagram). The vapour rises in the tube (B)andcondensesontheupperheatsink(atC). Thecondensedliquidthendiffusesdownaclothwickinsidethepipe(atD),toreturntothelowerend(at E) whenceit cancontinuethecycle. Theheat istransferredbymass transfer in the vapour state with very small thermal resistance (highthermal conductance). Manytypesofevacuated-tubesolarwaterheaters3.8 Multimode transfer and circuit analysis 77ABDECColderHotterHeatinHeatoutFigure3.18Schematicdiagramofaheatpipe(cut-awayview). Heattransferbyevapo-rationandcondensationwithintheclosedpipegivesitaverylowthermalresistance. See text for further description.use the heat pipe principle for heat transfer from the collector elements toseparately circulating heat transfer fluid.3.8 Multimode transfer and circuit analysis3.8.1 Resistances onlySection3.2showedingeneral terms howthermal resistances couldbecombinedinseriesorparallel(orindeedinmorecomplicatednetworks).The resistances that are combined do not have to refer to the same mode:conduction,convection,radiationandmasstransfercanbeintegratedbythis method. Manyexamples will befoundinlater chapters, especiallyChapter 5.3.8.2 Thermal capacitanceThe circuit analogy can be developed further. Thermal energy can be storedin bulk materials (bodies) similar to electrical energy stored in capacitors.78 Heat transferFigure3.19Ahot object loses heat toits surroundings. (a) Physical situation.(b) Thermal circuit analogue. (c) Electrical circuit analogue.For example, consider a tank of hot water standing in a constant tempera-ture environment atT0(Figure 3.19a). The water (of massn and specificheat capacityci is at some temperatureT1above the ambient temperatureT0. Heat flows from the water to the env