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Transferncia de Calor e MassaProf. Lucas Freitas BertiEngenharia de Materiais - UTFPR1EngMatLucas F. BertiDISCIPLINA/UNIDADE CURRICULARCDIGOPERODOCARGA HORRIATRANSFERNCIA DE CALOR E MASSAEM96D6AT(aulas)AP(aulas)APS(aulas)AD(aulas)Total(aulas)Total(horas)3417035445AT: Atividades Tericas, AP: Atividades Prticas, APS: Atividades Prticas Supervisionadas, AD: Atividades a Distncia,2EmentaPR-REQUISITOFsica 2; Equaes Diferenciais OrdinriasEQUIVALNCIAOBJETIVOSAo final da disciplina o aluno ser capaz de: apontar os principais fenmenos de transferncia de calor e massa; distinguir os principais processos de transferncia de calor e massa; identificar os regimes de transferncia de calor e massa.EMENTAIntroduo aos fenmenos e transferncia de calor; conduo em regime permanente; conduo em regime transitrio; radiao trmica; transferncia de calor por conveco; transferncia de massa; mecanismos de difuso de massa.EngMatLucas F. BertiPROCEDIMENTOS DE ENSINOAulas TericasAulas expositivas dialogadas, permeadas com atividades de resoluo de exerccios e questes propostas. Como meios de ensino sero utilizados lousa e equipamento multimdia. Durante as aulas tericas, os alunos sero freqentemente incentivados a participar a fim de esclarecer dvidas e contribuir com exemplos e sugestes, alm de tornar a aula mais dinmica e produtiva. Aulas PRTICAS Atividades prticas realizadas nos laboratrios do curso de Engenharia de Materiais da UTFPR-LD. Pesquisas em bibliotecas e internet, apresentao de trabalhos na forma de seminrios relacionados disciplina aplicada a engenharia de materiais. Os contedos dos relatrios das aulas prticas sero cobrados na prova escrita.Atividades Prticas SupervisionadasAlguns exerccios sero indicados para resoluo, antes da prova. No dia da resoluo dos exerccios ser realizado um sorteio com os alunos para a resoluo dos exerccios em sala de aula, onde o aluno sorteado poder ser questionado sobre os conceitos envolvidos na sua resoluo. O aluno sorteado fica excludo do sorteio posterior, s retornando aps este. Todos os alunos devem participar ao menos 2 (duas) vezes, de modo que, nos ltimos captulos os alunos que ainda no tiverem sido sorteados participaro de um sorteio especial com apenas os alunos nesta situao. A avaliao ser feita segundo: resoluo correta, clareza, organizao e desenvoltura aos questionamentos. Em outra atividade ser necessrio fazer resumo de aula, escolhida aleatoriamente, de forma a motivar o aluno a prestar ateno nas aulas (o nmero de resumos ser entre 1 e 3, de acordo com a combinao entre professor e alunos). A nota da atividade prtica supervisionada dos alunos ser 10% da mdia final.Atividades A DISTNCIANo possui. Disciplina exclusivamente presencial.Atividades Prticas como Componente Curricular3EmentaEngMatLucas F. BertiPROCEDIMENTOS DE AVALIAOA Mdia Parcial (MP) ser o resultado da mdia aritmtica das quatro notas parciais, MP = [(2*NP1 + 3*NP2 + 1*NP3+ 1*NP4)/7]As notas NP1, NP2 e NP3 so as notas das trs avaliaes tericas e escritas. A nota NP4 referente apresentao de seminrios relacionados aos temas da rea de materiais metlicos.A mdia final (MF) ser: MF = MPx0,9 + APSx0,1.Caso o aluno falte a alguma das avaliaes escritas, dever verificar o Artigo 36 da Resoluo n 112/10-COEPP. No haver segunda chamada dos seminrios.A avaliao substitutiva, realizada para possibilitar a recuperao do aproveitamento acadmico, substituir a menor nota das avaliaes parciais, ser escrita e realizada com todo o contedo da matria. Apenas os alunos com mdia final inferior a 6,0 podero fazer a prova substitutiva. A data de realizao da avaliao substitutiva est na programao e no haver segunda chamada desta avaliao. A avaliao substitutiva ter peso igual prova substituda.4EmentaINFORMAES COMPLEMENTARESPresena: A presena em sala de aula ser verificada atravs de chamada. O aluno ter que ter um mnimo de 75% de presena, do contrrio no sero computadas as notas do aluno.Celulares: Celulares em sala de aula somente em modo silencioso.Grupos de discusso: Estudo e discusso de exerccios em grupos so permitidos, porm cada aluno deve apresentar suas solues individuais para qualquer material a receber nota.Trabalhos prticos: Os trabalhos prticos sero em grupo e na apresentao algum dos alunos ser sorteado para apresentao.Poltica para desconto por atraso: A frmula para o valor, em pontos, por atraso na entrega do trabalho prtico : 1 + (2d-1) onde d o atraso em dias teis, para d 1. Note que aps o quinto dia, o trabalho no ter mais validade. Obs. Sero tolerados 15 minutos de atraso para entrada na sala de aula, em caso de urgncia/emergncia, quando avisado, ser liberada a entrada na sala de aula.EngMatLucas F. Berti5EmentaPROGRAMAO E CONTEDOS DAS AULAS (PREviso)Dia/Ms ou SemanaContedo das AulasNmero de Aulas09/10Apresentao da disciplina e das Atividades Prticas Supervisionadas316/10conduo em regime permanente 323/10conduo em regime permanente330/10conduo em regime transitrio306/11conduo em regime transitrio313/111 Avaliao327/11transferncia de calor por conveco304/12transferncia de calor por conveco311/12transferncia de massa318/12mecanismos de difuso de massa.322/01mecanismos de difuso de massa.329/012 avaliao305/02radiao trmica312/023 avaliao319/02Avaliao substitutiva326/02Vista de prova substitutiva e Encerramento da disciplina3EngMatLucas F. Berti6EmentaREFERNCIASReferencias Bsicas:INCROPERA, Frank P. DEWITT, David P., BERGMAN, Theodore L., LAVINE, Adrienne. Fundamentos de transferncia de calor e de massa. 6. ed. Rio de Janeiro, RJ: LTC, 2008. xix, 643 p. + CD-ROM ISBN 8521613784.ENGEL, Yunus A.; GHAJAR, Afshin J. Transferncia de calor e massa: uma abordagem prtica. 4. ed. So Paulo: McGraw-Hill, Bookman, AMGH, 2012. 902 p. + CD-ROM ISBN 9788580551273.CREMASCO, Marco Aurlio. Fundamentos de transferncia de massa. 2. ed. Campinas, SP: Editora da UNICAMP, 2002. 725 p. ISBN 8526805959.Referncias Complementares:LIENHARD V, John H., LIENHARD IV, John H., A Heat Transfer Textbook: Fourth Edition, 6. ed. Ed. Dover Publications, 2011, 768 p. ISBN: 978-0486479316; Tambm disponvel em formato virtual em: http://web.mit.edu/lienhard/www/ahtt.html BEJAN, A. & KRAUS, A.D.. Heat Transfer Handbook. Hoboken, NJ, USA: John Wiley & Sons, 2003. 1480pKREITH, F., BOHN, M.S., 2003. Princpios de Transferncia de Calor. So Paulo, SP: Thomson, 623p. ISBN 8522102848BIRD, R. Byron; STEWART, Warren E; LIGHTFOOT, Edwin N. Transport phenomena. 2nd ed. rev. New York: J. Wiley, 2007. xii, 905 p. : ISBN 9780470115398EngMatLucas F. Berti

Transferncia de Calor e MassaProf. Lucas Freitas BertiEngenharia de Materiais - UTFPR7EngMatLucas F. Berti8EmentaEMENTATranscal:Introduo aos fenmenos e transferncia de calor; Conduo:conduo em regime permanente; conduo em regime transiente; Conveco:transferncia de calor por conveco;Radiao:radiao trmica; Transmassa:mecanismos de difuso de massa.Difuso;Conveco.EngMatLucas F. BertiHeat Transfer: Physical Origins andRate EquationsChapter OneSections 1.1 and 1.2EngMatLucas F. BertiHeat Transfer and Thermal EnergyWhat is heat transfer?

Heat transfer is thermal energy in transit due to a temperaturedifference.What is thermal energy?

Thermal energy is associated with the translation, rotation,vibration and electronic states of the atoms and moleculesthat comprise matter. It represents the cumulative effect ofmicroscopic activities and is directly linked to the temperatureof matter.EngMatLucas F. BertiHeat Transfer and Thermal Energy (cont.)QuantityMeaningSymbolUnitsThermal Energy+Energy associated with microscopic behavior of matter

TemperatureA means of indirectly assessing the amount of thermal energy stored in matterHeat TransferThermal energy transport due to temperature gradientsHeatAmount of thermal energy transferred over a time interval t 0Heat RateThermal energy transfer per unit timeHeat FluxThermal energy transfer per unit time and surface area

DO NOT confuse or interchange the meanings of Thermal Energy, Temperature and Heat TransferEngMatLucas F. BertiModes of Heat TransferConduction:Heat transfer in a solid or a stationary fluid (gas or liquid) due to the random motion of its constituent atoms, molecules and /or electrons.Convection: Heat transfer due to the combined influence of bulk and random motion for fluid flow over a surface.Radiation: Energy that is emitted by matter due to changes in the electron configurations of its atoms or molecules and is transported aselectromagnetic waves (or photons). Conduction and convection require the presence of temperature variations in a material medium.

Although radiation originates from matter, its transport does not require a material medium and occurs most efficiently in a vacuum.EngMatLucas F. BertiHeat Transfer Rates: Conduction

(1.2)Heat rate (W):

Application to one-dimensional, steady conduction across aplane wall of constant thermal conductivity:Conduction:General (vector) form of Fouriers Law:Heat flux

Thermal conductivityTemperature gradient

EngMatLucas F. BertiHeat Transfer Rates: ConvectionConvectionRelation of convection to flow over a surface and developmentof velocity and thermal boundary layers:Newtons law of cooling:

(1.3a)

EngMatLucas F. BertiHeat Transfer Rates: RadiationRadiationHeat transfer at a gas/surface interface involves radiation emission from the surface and may also involve theabsorption of radiation incident from the surroundings(irradiation, ), as well as convection

Energy outflow due to emission:

(1.5)

Energy absorption due to irradiation:

EngMatLucas F. BertiHeat Transfer Rates Radiation (Cont.)Irradiation: Special case of surface exposed to large surroundings of uniform temperature,

(1.7)

EngMatLucas F. BertiHeat Transfer Rates: Radiation (Cont.)Alternatively,

(1.8)(1.9)For combined convection and radiation,

(1.10)EngMatLucas F. BertiSchematic:Problem 1.73(a): Process identification for single-and double-pane windows

Process IdentificationConvection from room air to inner surface of first pane

Net radiation exchange between room walls and inner surface of first pane

Conduction through first pane

Convection across airspace between panes

Net radiation exchange between outer surface of first pane and inner surface of second pane (across airspace)

Conduction through a second pane

Convection from outer surface of single (or second) pane to ambient air

Net radiation exchange between outer surface of single (or second) pane and surroundings such as the ground

Incident solar radiation during day; fraction transmitted to room is smaller for double pane

EngMatLucas F. BertiProblem 1.31: Power dissipation from chips operating at a surface temperature of 85C and in an enclosure whose walls and air are at 25C for(a) free convection and (b) forced convection.

Schematic:Assumptions: (1) Steady-state conditions, (2) Radiation exchange between a small surface and a large enclosure, (3) Negligible heat transfer from sides of chip or from back of chip by conduction through the substrate.Analysis:

(a) If heat transfer is by natural convection,

(b) If heat transfer is by forced convection,

Problem: Electronic CoolingEngMatLucas F. BertiConservation of EnergyChapter One Section 1.3EngMatLucas F. Berti20Alternative Formulations Alternative FormulationsTime Basis:At an instantorOver a time intervalType of System:Control volumeControl surface An important tool in heat transfer analysis, often providing the basis for determining the temperature of a system. CONSERVATION OF ENERGY (FIRST LAW OF THERMODYNAMICS)EngMatLucas F. Berti21At an Instant of Time:

CV at an Instant and over a Time Interval

Note representation of system by a control surface (dashed line) at the boundaries.Surface Phenomena

Volumetric Phenomena

Conservation of Energy

(1.11c)Each term has units of J/s or W.APPLICATION TO A CONTROL VOLUME Over a Time IntervalEach term has units of J.

(1.11b)EngMatLucas F. Berti22At an instant

Special Cases (Linkages to Thermodynamics)Transient Process for a Closed System of Mass (M) Assuming Heat Transfer to the System (Inflow) and Work Done by the System (Outflow).Over a time interval

(1.11a)Closed System

For negligible changes in potential or kinetic energy

Internal thermal energyEngMatLucas F. Berti23

Example 1.3: Application to thermal response of a conductor with Ohmic heating (generation): Involves change in thermal energy and for an incompressible substance.

Heat transfer is from the conductor (negative )

Generation may be viewed as electrical work done on the system (negative )

Example 1.3EngMatLucas F. Berti24Example 1.4: Application to isothermal solid-liquid phase change in a container:Latent Heat of Fusion

Example 1.4EngMatLucas F. Berti25Steady State for Flow through an Open System without Phase Change or Generation:

At an Instant of Time:

(1.11d)Open System

EngMatLucas F. Berti26Surface Energy BalanceA special case for which no volume or mass is encompassed by the control surface.Conservation Energy (Instant in Time):

(1.12) Applies for steady-state and transient conditions.Consider surface of wall with heat transfer by conduction, convection and radiation.

With no mass and volume, energy storage and generation are not pertinent to the energy balance, even if they occur in the medium bounded by the surface.THE SURFACE ENERGY BALANCEEngMatLucas F. Berti27Methodology On a schematic of the system, represent the control surface by dashed line(s). Choose the appropriate time basis. Identify relevant energy transport, generation and/or storage terms by labeled arrows on the schematic. Write the governing form of the Conservation of Energy requirement. Substitute appropriate expressions for terms of the energy equation. Solve for the unknown quantity.METHODOLOGY OF FIRST LAW ANALYSISEngMatLucas F. Berti28

Problem 1.43: Thermal processing of silicon wafers in a two-zone furnace. Determine (a) the initial rate of change of the wafer temperature and (b) the steady-state temperature.

Problem: Silicon Wafer

SCHEMATIC:

EngMatLucas F. Berti29Problem: Silicon Wafer (cont.)

or, per unit surface area

EngMatLucas F. Berti30Problem: Silicon Wafer (cont.)

EngMatLucas F. Berti31Problem Cooling of Spherical CanisterProblem 1.48: Cooling of spherical canister used to store reacting chemicals.Determine (a) the initial rate of change of the canister temperature,(b) the steady-state temperature, and (c) the effect of convectionon the steady-state temperature.

535 J/kgKEngMatLucas F. BertiProblem Cooling of Spherical Canister

SCHEMATIC:EngMatLucas F. BertiProblem Cooling of Spherical Canister

EngMatLucas F. BertiProblem Cooling of Spherical Canister

EngMatLucas F. BertiFIND: (a) Initial rate of change of the wafer temperature from a value of and (b) steady-state temperature. Is convection significant? Sketch the variation of wafer temperature with vertical distance.

_1111561843.unknown

_1430055995.unknown

KNOWN: Silicon wafer positioned in furnace with top and bottom surfaces exposed to hot and cool zones, respectively. ASSUMPTIONS: (1) Wafer temperature is uniform, (2) Hot and cool zones have uniform temperatures, (3) Radiation exchange is between small surface (wafer) and large enclosure (chamber, hot or cold zone), and (4) Negligible heat losses from wafer to pin holder.ANALYSIS: The energy balance on the wafer includes convection from the upper (u) and lower (l) surfaces with the ambient gas, radiation exchange with the hot- and cool-zone and an energy storage term for the transient condition. Hence, from Eq. (1.11c),(a) For the initial condition, the time rate of change of the wafer temperature is determined using the foregoing energy balance with

_1111566081.unknown

_1430056108.unknown

(b) For the steady-state condition, the energy storage term is zero, and the energy balance can be solved for the steady-state wafer temperature,

_1111562901.unknown

_1430056242.unknown

To assess the relative importance of convection, solve the energy balances assuming no convection. With , we conclude that the radiation exchange processes control the initial rate of change and the steady-state temperature._1111563179.unknown

_1430056240.unknown

If the wafer were elevated above the present operating position, its temperature would increase, since the lower surface would begin to experience radiant exchange with progressively more of the hot zone. Conversely, by lowering the wafer, the upper surface would experience less radiant exchange with the hot zone, and its temperature would decrease. The temperature-distance relation might appear as shown in the sketch.

KNOWN: Inner surface heating and new environmental conditions associated with a spherical shell of prescribed dimensions and material.

FIND: (a) Governing equation for variation of wall temperature with time and the initial rate of change, (b) Steady-state wall temperature and, (c) Effect of convection coefficient on canister temperature.

ASSUMPTIONS: (1) Negligible temperature gradients in wall, (2) Constant properties, (3) Uniform, time-independent heat flux at inner surface.

PROPERTIES: Table A.1, Stainless Steel, AISI 302: ( = 8055 kg/m3, = 535 J/kg(K.

ANALYSIS: (a) Performing an energy balance on the shell at an instant of time, . Identifying relevant processes and solving for dT/dt,

.

(b) Under steady-state conditions with = 0, it follows that

(c) Parametric calculations show a sharp increase in temperature with decreasing values of h < 1000 W/m2(K. For T > 380 K, boiling will occur at the canister surface, and for T > 410 K a condition known as film boiling (Chapter 10) will occur. The condition corresponds to a precipitous reduction in h and increase in T.Substituting numerical values for the initial condition, find

Although the canister remains well below the melting point of stainless steel for h = 100 W/m2(K, boiling should be avoided, in which case the convection coefficient should be maintained at h > 1000 W/m2(K.

COMMENTS: The governing equation of part (a) is a first order, nonhomogenous differential equation with constant coefficients. Its solution is , where , , . Note results for t ( ( and for S = 0.