Princ of Heat Transfer
Princ of Heat Transfer MAE 4171
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This 17 page Class Notes was uploaded by Marie Nicolas on Monday October 12, 2015. The Class Notes belongs to MAE 4171 at Florida Institute of Technology taught by Kunal Mitra in Fall. Since its upload, it has received 25 views. For similar materials see /class/221695/mae-4171-florida-institute-of-technology in Mechanical and Aerospace Engineering at Florida Institute of Technology.
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Date Created: 10/12/15
Heat Transfer Physical Origins and Rate Equations Chapter One Heat Transfer and Thermal Energy What is heat transfer Heat transfer is thermal energy in transit due to a temperature difference What is thermal energy Thermal energy is associated with the translation rotation Vibration and electronic states of the atoms and molecules that comprise matter It represents the cumulative effect of microscopic activities and is directly linked to the temperature of matter Heat Transfer and Thermal Energy cont DO NOT confuse or interchange the meanings of Thermal Energy Temperature and Heat Transfer Quantity 39l39hcnnal l39ncrg 39 lcmpcrul ch llcul lrzlnsl cr llcul Heal Rule llcal Hm Meaning Energy associated with microscopic behavior of matter Ameans of indirectly assessing the amount of thermal energy stored in matter Thermal energy transport due to temperature gradients Amount of thermal energy transferred over a time interval A t gt 0 Thermal energy transfer per unit time Thermal energy transfer per unit time and surface area Symbol Uoru T Units J or Jkg Kor OC Wm2 U gt Thermal energy of system u gt Thermal energy per unit mass of system Modes of Heat Transfer Modes of Heat Transfer Net radiation heat exchange between two surfaces Conduction through a solid Convection f or a stationaiy fluid to a moving flu Conduction Heat transfer in a solid or a stationary uid gas or liquid due to the land ll motion of its constituent atoms molecules and or electrons Convection Heat transfer due to the combined in uence of bulk and random niulion for uid ow over a surface Energy that is cimllcd in millle due to changes in the electron configurations of its atoms or molecules and is transported as electromagnetic waves or photons Radiation 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 Heat Transfer Rates Conduction Heat Transfer Rates Conduction General vector form of Fourier s Law quot kVT 1 v llcul ux Hmmal Conductn39m 39l cmpcxutm c gtmhcnt Wm2 Wm K Cm or Km Application to onedimensional steady conduction across a plane wall of constant thermal conductix ity 12 Heat rate W qx q 39A Heat Transfer Rates Convection Heat Transfer Rates Convection Relation of convection to ow over a surface and development of velocity and thermal boundary layers Velocity distribution distribution My T0quot gt My Heated 39 surface Newton s law ol cooling qquot hTs Tw 13a h Convection heat transfer coef cient Wm2 39K Heat Transfer Rates Radiation Heat Transfer Rates Radiation Heat transfer at a gas surface interface involves radiation emission from the surface and may also involve the absorption of radiation incident from the surroundings irradiation G as well as convectionif TS 2 TOO Energy out ow due to emission E 5E5 80114 15 E imisswc power Wmz 8 Surface emissivin O S 5 1 Surface of emissivity E b Emissive power of a blackbody the perfect emitter and a StefanBoltzmann constant 567X10398Wm2 K a Energy absorption due to in adiation Gm 05G Gm b501 bcd incident radiationWm2 a Surface absorptivin O S a S l G Irradiation Wmz Heat Transfer Rates Radiation Cont Heat Transfer Rates Irradiation Special case of surface exposed to large surroundings of uniform temperature TSW 4 G Gm O39TW Gas T It Surroundings at T sur n u 39r u qrad i Iconv z Surface of emissivity s at area A and temperature T3 7 If at 8 the not radiation heat ux from the surface due to exchange with the surroundings is grid 8EbTs aG80TS4 Tsir 17 Heat Transfer Rates Radiation Cont Heat Transfer Rates Alternatively 612m 2 hr Tsur 18 hr Radiation heat transfer coef cient Wm2 hr80TsT TSZT2 19 110 For comblned convectlon and radlatlon q 170m qd W Twhr Ts 4W Alternative Formulations CONSERVATION OF ENERGY FIRST LAW OF THERMODYNAMICS An important tool in heat transfer analysis often providing the basis for determining the temperature of a system Alternative Formulations Time Basis At an instant or Over a time interval Type of System Control volume Control surface CV at an Instant and over a Time Interval APPLICATION TO A CONTROL VOLUME At an Instant olhl imc Note representation of system by a control surface dashed line at the boundaries Surf lce D hcnomena EmEom rate of thermal andor mechanical may transfer ileum lhe control surface due to heat transfer uid ow andor work interactions Volu mctric Phenomena E g rate of thermal energy generation due to conversion from another enegy form eg electrical nuclear or chemical energy conversion process occurs within the system D Est rate ofchange of energy storage m the s stern Counsen alDion oI DEncrgV D Es 111c Ein Eoul Eg dt st Each term has units of Js or W 0 Over a Time Inlcn al Em Em Eg AESI 111b Each term has units of J Closed System Special Cases Linkages to Thermodynamics i 39I ransicnl Process for a Closed Syslcm of Mass AI Assuming Heat Transfer to the System In ow and Work Done by the System Out ow Over a lime Intcn al Q rrAE 111a For negligible changes in potential or kinetic energy Q WzAu Internal thermal energy At an instant Example 13 Example 13 Application to thermal response of a conductor with Ohmic heating generation Diameter D Involves change in lhcmml cncrg and for an incompressible substance dU 617 t 2 MC dt dt Heat transfer is from the conductor negative q I Generation may be viewed as cluclmal u L done on the system negative W Example 14 Example 14 Application to isothermal solidliquid phase change in a container Latent Heat of Fusion Mhsf Icewater mixture Tf Open System in Stead State for Flow through an Open S stem Without Phase Change or Generation up pu Vlm gt Reference height At an Inslanl oI Timc 2 2 mutpvV4ng 61 mutPVVzgZ W0 1111 in pv gt Ho ork 0 Mt 1711 2139 gt cnllialp out 0 For an ldC l gas with constant speci c heal iin iout cp Tout 0 For an uncompressiblc liquid um your 2 Tout pvm pvout z 0 For systems with significant heat transfer W V m out gZLn gem e 0 THE SURFACE ENERGY BALANCE A special case for which no volume or mass is encompassed by the control surface Conscn39alion Encrg Instant in Time D D Em Em 0 112 0 Applies for steadystate and transient conditions 0 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 Consider surface of wall with heat transfer by conduction convection and radiation Surroundings sur Fluid II n n qcond qconv qrad 0 H le LTZ MTZ TOO 82039T24 4 20 METHODOLOGY OF FIRST LAW ANALYSIS 0 On a schematic of the system represent the control surface by dashed 1ines Choose the appropriate time basis Identify relevant energy transport generation andor storage terms by labeled arrows on the schematic 0 Write the governing form of the Conservation of Energy requirement Substitute appropriate expressions for terms of the energy equation Solve for the unknown quantity