across the upper surface only, (3) Chip surface is isothermal, (4) The average heat transfer coefficient for the chip surface is equivalent to the local value at x= L, (5) Negligible radiation.
Problem: Chip Cooling (cont.)From Eq. (2), the surface temperature of the chip is 2-3225C3010W/107 W/mK0.004m42.5 C.sTCOMMENTS:(1) The estimated value of Tavgused to evaluate the air properties is reasonable. (2) How else could chiphhave been evaluated? Is the assumption of Lhhreasonable?0.851/32-620.0269 W/mK10 m/s0.120 m0.040.703107 W/mK.0.120 m16.6910m/ sLh<
Concentration Boundary LayerThe Concentration Boundary Layer•Features–A consequence of evaporation orsublimation of species A from a liquid or solid surface across which a second fluid species Bis flowing.–A region of the flow characterizedby species fluxes and concentrationgradients.–A region between the surface andfree stream whose thickness increases in the flow direction.c–Why does increase in the flowdirection?c–Manifested by a surface speciesfluxand a convection masstransfer coefficient .,A sNmh–What is the heat transfer analog to Fick’s law?A,AA,A,0.99scsCCyCCAAAB' Fick s lawCNDy AA,AB0syCNDy A,A,A,smsNhCCABA0A,A,/ymsDCyhCCMass Transfer
Concentration Boundary Layer (cont.)•DefinitionsTermVariableUnitsSpecies molar fluxkmol/s·m2A,sNSpecies molar ratekmol/sA,sNSpecies mass fluxkg/s·m2 A,snSpecies mass ratekg/sAnSpecies molar concentrationkmol/m3Species mass concentration (density)kg/m3ACASpecies molecular weightkg/kmolAMConvection mass transfer coefficientm/smhBinary diffusion coefficient1m2/sABD1Table A.8Mass Transfer
Concentration Boundary Layer (cont.)•Convection CalculationsSpecies Molar Flux:A,A,A,smsNhCCSpecies Mass Flux:AAAAAA,nNCMMA,A,A,ssmnhTotal Transfer Rates:A,A,A,smssNh ACCA,A,A,smssnh AAverage Mass Transfer Coefficient:1smmssAhdAAhMass Transfer
Vapor ConcentrationSpecies Vapor Concentration or Density•At a Vapor/Liquidor Vapor/SolidInterfaceThe vapor concentration/density corresponds to saturated conditions at the interface temperature Ts .A,A,satssCCTA,A,satAA,satsssTCTMAssumingperfect gas behavior, the concentration/density may be estimated fromknowledge of the saturation pressure.A,satA,A,AsssspTCTRMThe concentration may also be directly determined from saturation tables.For example, from Table A.6for saturated water,1A,AA,sgssTCMMass Transfer
Vapor Concentration (cont.)•Free Stream Conditions–The free stream concentration/density may be determined from knowledgeof the vapor pressure,assuming perfect gas behavior.