Table Of ContentSPRINGER BRIEFS IN APPLIED SCIENCES AND TECHNOLOGY
THERMAL ENGINEERING AND APPLIED SCIENCE
William F. Mohs
Francis A. Kulacki
Heat and Mass
Transfer in the
Melting of Frost
123
SpringerBriefs in Applied Sciences
and Technology
Thermal Engineering and Applied Science
SeriesEditor
FrancisA.Kulacki,Minnesota,USA
Moreinformationabout thisseries athttp://www.springer.com/series/8884
William F. Mohs (cid:129) Francis A. Kulacki
Heat and Mass Transfer
in the Melting of Frost
WilliamF.Mohs FrancisA.Kulacki
Christchurch,NewZealand DepartmentofMechanicalEngineering
UniversityofMinnesota
Minneapolis,MN,USA
ISSN2191-530X ISSN2191-5318 (electronic)
SpringerBriefsinAppliedSciencesandTechnology
ISBN978-3-319-20507-6 ISBN978-3-319-20508-3 (eBook)
DOI10.1007/978-3-319-20508-3
LibraryofCongressControlNumber:2015942245
SpringerChamHeidelbergNewYorkDordrechtLondon
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Preface
Animportantproblemintherefrigerationindustryistheformationandremovalof
frostlayersonsubfreezingheatexchangersurfacesofaircoolers.Frostisaporous
structure of ice and air pockets that grows on the finned surfaces of the heat
exchanger. It directly diminishes the performance and efficiency of the entire
cooling system by increasing resistance to air flow and heat transfer. To return
thesystemtopre-frostedperformance,thefrostlayerismeltedbysurfaceheating.
Thismethodisinherentlyinefficient,withthemajorityoftheappliedenergybeing
losttothesurroundingenvironment.
A validated model for heat and mass transfer in frost melting and defrost
efficiencyisdevelopedbasedonlocalconditionsataverticalsurface.Noninvasive
measurements of frost thickness are taken from digitally reduced in-plane and
normal images of the frost layer through time. The visual method eliminates
disturbances caused by contact measurements at the frost–air interface.
Thermophysicalpropertiesandporosityofthefrostarealsoestimatedfromdigital
imageanalysis.Visualdataarecombinedwithtemperatureandheatfluxmeasure-
ments to produce a detailed analysis of the frost and defrost processes. Heat and
mass transfer models are constructed from these measurements, and the defrost
process is analyzed through its distinctly defined stages: vapor diffusion, liquid
permeation,anddryout.
Frost porosity at the start of defrost has a significant impact on the vapor
diffusionstagewhereinalargeportionoftheappliedheattothesurfaceisabsorbed
bythefrostlayer.Frostlayerswithlowporosity(highdensity)absorbmoreofthe
applied heat andexhibithigherdefrost efficiency. Heat andmasstransfer through
sublimationduringthisstageisinsignificant.
Thesecondstageofdefrostisdominatedbymeltingandpermeationofthemelt
liquid into the overlying frost. Digitally computed frost front velocity is found to
varywiththesuppliedheattransferrateandfrostporosity,whichcompareswellto
the visual measurement. Higher heat transfer results in a larger melt velocity and
thus shortened defrost time. Lower frost porosity has the effect of increasing the
defrosttime.Asinthefirststageofmelting,theeffectsofsublimationarefoundto
v
vi Preface
benegligiblecomparedtotheoverallheatandmasstransfer.Defrostefficiencyfor
thisstageisnearly100%withlittleheatlosttothesurroundings.
Evaporation dominates the final stage of defrost. This stage inherently has the
low defrost efficiency because most of the supplied heat is lost through sensible
heat exchange with the ambient air. Latent heat exchange is correlated to an area
reductionof the water droplets, which is expressed by amasstransfer coefficient.
A general improvement in the defrost efficiency can be achieved by limiting the
durationofthefinalstage,butthiscanresultinresidualmoistureonthesurfacethat
willberefrozeninthesubsequentcoolingcycle.
TheauthorsextendtheirappreciationandthankstotheIngersoll-Rand/Thermo
KingCorporation,Bloomington,Minnesota,forthesupportofthisresearchasthe
seniorauthorcompletedhisgraduatestudiesattheUniversityofMinnesota.
Christchurch,NewZealand WilliamF.Mohs
Minneapolis,MN,USA Francis.A.Kulacki
Contents
1 Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Defrost:AnOverview. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 DefrostEfficiency. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 State-of-the-Art. . . . .. . . . . .. . . . . .. . . . .. . . . . .. . . . .. . . . . .. . . 9
2.1 FrostFormationandGrowth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.2 Defrost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
2.3 SystemEffectsofDefrost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
3 Multi-stageDefrostModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
3.1 VerticalSurfaceGeometry. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
3.2 StageIDefrost:Diffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.3 StageIIDefrost:Melting–Permeation. . . . . . . . . . . . . . . . . . . . . . 27
3.4 StageIIIDefrost:DryOut. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.5 ScaleAnalysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41
4 ExperimentalMethod. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
4.1 Apparatus. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 45
4.2 CharacterizationoftheTestChamber. . . . . . . . . . . . . . . . . . . . . . 48
4.3 VisualMeasurementandQuantification. . . . . . . . . . . . . . . . . . . . . 51
4.4 ExperimentalUncertainty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
5 MeasurementoftheDefrostProcess. . . . . . . . . . . . . . . . . . . . . . . . . . 57
5.1 ScopeoftheMeasurements. . .. . . .. . . .. . . .. . . .. . . .. . . .. . . 58
5.2 FrostGrowth. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
vii
viii Contents
5.3 Defrost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
5.3.1 StageIDefrost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3.2 StageIIDefrost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.3.3 StageIIIDefrost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
5.4 Summary. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
References. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
6 SolutionofDefrostModel. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
6.1 StageIDiffusion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
6.2 StageIIMeltingandPermeation. . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.3 StateIIIDefrost. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
6.4 Conclusion. . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . . . . . .. . . . . . 95
Reference. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . . .. . . . . 96
Index. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Chapter 1
Introduction
Abstract Theimpactoffrostformationonrefrigerationperformanceisdescribed,
and several current methods for frost removal are discussed. Defrost efficiency is
generallydefinedforuseateitherthesystemorsurfacelevels.Anexampleofthe
economicimpactofdefrostisgivenforU.S.transportationrefrigerationunits.
Keywords Frostlayer•Defrost•Defrostefficiency
Nomenclature
c Specificheat(J/kgK)
COP Coefficientofperformance(1.1)
E Appliedenergyofdefrost(J)
d
E Lostenergy(J)
loss
m Mass(kg)
T Temperature(K)
Greek Letters
η Defrostefficiency
d
η Surfacedefrostefficiency
d,s
λ Latentheatoffusion(J/kg)
if
Subscripts
C Cold,condensate
f Frost
H Hot
loss Loss
s Surface
©SpringerInternationalPublishingSwitzerland2015 1
W.F.Mohs,F.A.Kulacki,HeatandMassTransferintheMeltingofFrost,
SpringerBriefsinAppliedSciencesandTechnology,
DOI10.1007/978-3-319-20508-3_1
