Thermal design of symmetrically and asymmetrically heated channel–chimney systems in natural conv

Thermaldesignofsymmetricallyandasymmetrically

heatedchannel–chimneysystemsinnaturalconvection

AntonioAuletta,OronzioManca*,MarilenaMusto,SergioNardini

DipartimentodiIngegneriaAerospazialeeMeccanica,SecondaUniversit󰀁adegliStudidiNapoli,RealCasadell’Annunziata,ViaRoma29,Aversa(CE)81031,Italy

Received15May2002;accepted28November2002

Abstract

Inthispaper,designchartsfortheevaluationofthermalparametersfornaturalconvectionwithairinachannel–chimneysystemareproposed.Inthethermalanalysisofnaturalconvectioninchannel–chimneysystems,thevariablesthatplayanimportantroleare:theohmicheatflux,maximumwalltemperaturesandgeometricalparameterssuchastheheightoftheheatedchannel,thechannelspacingandtheheightandspacingofunheatedextensions.Asimplenumericalproceduretoobtainthethermaldesigncharts,athermaloptimizationofthesystemandanuncertaintyanalysisduetothethermophysicalpropertiesarepresented.Resultsarecarriedoutforsymmetricallyandasymmetricallyheatedchannelswithwallsatuniformheatfluxandasimpleestimationprocedureisproposedtoevaluatetheerrorintherelevantgeometricalandthermalparametersduetoadifferentvalueofthereferencetemperature.Theestimatederror,however,islessthantheuncertaintyoftheexperimentaldataemployed.Somesimpleexamplesaregiventoshowtheuseofthecharts.Theproposedresultsareobtainedfromexperimentaldatainthefollowingdimensionlessparameterranges:5:06Lh=b620;1:56L=Lh64;16B=b64;1026Ra6106.Ó2003ElsevierScienceLtd.Allrightsreserved.

Keywords:Freeconvection;Chimneyeffect;Channel;Thermaldesign

1.Introduction

Thethermaldesignofsystemsisveryimportantfortheindustrialuserand,forthisreason,

naturalconvectioninpartiallyopencavitiessuchasthesimplechanneliswidelyresearched.

*Correspondingauthor.Tel.:+39-08-150-10217;fax:+39-08-150-10264.E-mailaddress:manca@unina.it(O.Manca).

1359-4311/03/$-seefrontmatterÓ2003ElsevierScienceLtd.Allrightsreserved.

doi:10.1016/S1359-4311(02)00241-7AppliedThermalEngineering23(2003)605–621

www.elsevier.com/locate/apthermengThisconfigurationiswidelyusedinengineeringapplications,particularlyinthermalcontrolof

componentsofelectronicsystems,asreportedin[1–5]andreviewedmorerecentlyin[6,7].

TheNomenclature

bchannelspacing,m

Bchimneyspacing,m

gaccelerationduetogravity,m/s2

GrGrashofnumber,Eq.(2)

hthermalconvectioncoefficient,W/m2K

kthermalconductivity,W/mK

LtotalsystemlengthðLhþLextÞ,m

NuNusseltnumber,Eq.(4)

PrPrandtlnumber

qheatflux,W/m2

QTtotalheattransferrate,W

r2regressioncoefficient

RachannelRayleighnumber,Eq.(2)

Splatesurface,m2

Ttemperature,K

TÃw;maxdimensionlessmaximumwalltemperature,Eq.(1)

Udependentvariable

Urreferencedependentvariable

Xiindependentvariable

xcoordinatealongthechannellength,m

Greeksymbols

bvolumetriccoefficientofexpansion,1/K

mkinematicviscosity,m2/s

Subscripts

cconvective

extextensions

hheated

kconductive

lleft

maxmaximum

0ambientair

optoptimum

rradiative,right

Ttotal

wwall

Xohmic606A.Aulettaetal./AppliedThermalEngineering23(2003)605–621presenttrendisalsoorientedtowardtheevaluationofoptimalgeometricalconfigurationsthat

derivefromthesimplechannel[6,8,9].Inthiscontext,aparticularlyinterestinggeometryisthe

channel–chimneysystem.Recently,thissystemhasreceivedmuchattentionasshownin[10–24].

In[10],thechimneyeffectduetoaparallel-walledadiabaticchannelwithheatsourcesat

thechannelinletwasanalyzed.Asimilarconfigurationisthechannelwithstraightadiabatic

downstreamextensionsthatwasinvestigatedin[11,14,18].In[11],anumericalstudyonavertical

channelwithisothermalparallelwallswascarriedoutandresultsforairwereobtained.In[14],an

investigationonaverticalisothermalorisofluxchannelwithstraightunheatedextensionslocated

upstreamordownstreamofthechannelwascarriedoutnumerically.Inthecaseofthedown-

streamextensions,anincreaseofmassflowrateandheattransferwasobtained.In[18]the

problemtreatedin[14]wasreformulatedforanisofluxchannelusingtheellipticformofthe

governingequationsinordertoobtainamorerealisticmodel.Inthesestudiesnothermaldesign

evaluationandsuggestionsweregiven.

Theeffectofexpansionratio(chimneyspacing/channelspacing)greaterthan1.0wasalsoin-

vestigatedin[12,13,16,22–24].In[12],theincreaseofheattransferrateinaverticalisothermal

tubeduetoanunheatedchimneyattacheddownstreamwasstudiednumerically.Anisothermal

channel–chimneysystemwasstudiednumericallyandexperimentallyin[13].Theeffectsofthe

geometry,i.e.thestraightextensionsandtheabruptordiffuseexpansions,ontheheattransfer

characteristicsinthechannelwerestudied.Asystemwiththesymmetricallyheatedchannelat

uniformwallheatfluxwasstudiedexperimentallyin[16,22–24].In[16],resultswerederivedin

termsofgeometricparametersandRayleighnumbers.In[22],theexperimentalinvestigation

extendedtheresultsgivenin[16].Optimalconfigurationswereidentifiedthroughthemeasured

walltemperatureprofiles,withreferencetotheextensionandexpansionratiosoftheinsulated

extensions.Morerecently,localtemperaturemeasurementsoftheairflowinthechannelandthe

chimneywerecarriedoutin[23,24].In[23],theeffectoftheheatingmode,symmetricaland

asymmetrical,waspointedout.In[24],symmetricalheatingwasinvestigatedmoredeeply.Dif-

ferentfluidmotionregionswereobservedinsidethechimneyandsomeofthemconfirmedthe

resultsof[23].Nothermaldesignprocedurewaselaboratedorproposedin[16,22–24].Aperiodic

isothermalverticalchannelexpandedchimneywasexaminedin[19].Eachsubsystemchannel–

chimneywasthesameastheanalyzedconfigurationin[13].Resultsshowedthattheinteraction

betweenmultiplechannel–chimneysystemspresentedanassociatedchimneyeffectstrongerthan

inasinglechannelwithadiabaticextensions.

Heatsinkchimneysystemswerestudiedanalyticallyin[15,17]andexperimentallyin[20,21].

Theanalyticalsolutionforaverticalparallel-platefinnedheatsinkwithachimneywasdeveloped

in[15].Thesolutionpermittedeasyparameterevaluationaimingtorecognizeconditionsof

maximumheattransfer.In[17],theanalysiswasextendedtopin-finheatsinks.Optimalvaluesof

thepin-findiameterandheatsinkporositywereobtainedforassignedthermaldissipationand

systemsize.Thesetwostudiesprovidedusefulguidanceforthethermaldesignoftheheatsink.

Theexperimentalinvestigationscarriedoutin[20,21]allowedacomparisonwiththeresults

obtainedin[15,17].In[20],averticalparallel-platefinnedheatsinkwithachimneywasinves-

tigated.Resultsconfirmedtheoreticalpredictionsforoverallheattransferandlocationofoptima

givenin[15].In[21],theperformanceofpin-finheatsinkwithachimneywasobtained.Exper-

imentswerecomparedwiththeoreticalpredictionsgivenin[17]andareasonableagreementwas

observedforoverallheattransfer.A.Aulettaetal./AppliedThermalEngineering23(2003)605–621607