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Kumar, Chandan & Karim, Azharul(2019)Microwave-convective drying of food materials: A critical review.Critical Reviews in Food Science and Nutrition, 59(3), pp. 379-394.

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https://doi.org/10.1080/10408398.2017.1373269

1

110867Microwave‐ConvectiveDryingofFoodMaterials:ACriticalReview1

C.Kumara1,M.AKarima2

aChemistry, Physics and Mechanical Engineering, Queensland University of 3Technology, Brisbane, Australia 4

5

1. Abstract:6

Microwave convective drying (MCD) is gaining increasing interest due to its7

uniquevolumetricheatingcapabilityandabilitytosignificantlyreducedryingtimeand8

improvefoodquality.Themainobjectiveofthispaperistodiscuss,criticallyanalyze9

andevaluatetherecentadvancesinMCDandsuggestthefuturedirectionsinthisfield.10

The main focus of this paper is the mathematical modelling and experimental11

investigationsinmicrowaveconvectivedryingoffoodmaterials.Recentdevelopments12

inmthamaticalmodellingofMCDisdiscussedandexistingexperimentalsetupandtheir13

advantagesanddisadvantagesarediscussedandanalysed.Longdryingtimeisaconcern14

infoodindustries.ReductionsindryingtimebyapplyingMCDcomparedtoconvection15

drying are calculated and discussed. It was apparent that the proper integration of16

mathematicalmodellingandexperimentaltechniqueisthebestwaytomaximizethe17

advantages of this dryingmethod. Although there is a plethora of research is being18

carried out in this topic, there is still need for research to develop fundamental19

modellingtooptimizetheprocessparametersandscaleupthistechnologyforindustrial20

application.Overall,thereviewprovidesanin‐depthinsightintothelatestdevelopment21

ofMCDanditsmathematicalmodellingapproachesandwillhopefullyservetoinspire22

futureworkinthefield.23

24

Keywords: Food Drying, Microwave, Drying time, Modelling, Food quality,25

Experimentalsetup,Energyefficiency26

1Correspondingauthor:Tel+61415489441,Email:c.kumar@qut.edu.au

2

2. Introduction:27

Energyefficiency,productqualityanddryingtimearethreemainconcernsinfood28

drying. Drying research evolved to optimize these three parameters. Based on the29

availabledryingtechnologies,dryingmethodscanbedividedintofourgenerations.First30

andsecondgenerationincludedifferentconvectivedryingmethods.Cabinet,kiln,belt,31

conveyordryerareconsideredas the firstgeneration,andsprayanddrumdrierare32

considered as second generation drying. Then the freeze and osmotic drying are33

consideredasthethirdgeneration.MicrowaveandRFrelateddryingarereferredtoas34

innovative and fourth generation drying technology (Malafronte et al., 2012; Vega‐35

Mercado,MarcelaGóngora‐Nieto,&Barbosa‐Cánovas,2001).Microwaverelateddrying36

is gaining increasing interest due to the following reasons: (a)volumetric heating:37

microwaveenergyheatsupvolumetricallyandpumpsmoisturetosurfacetheproduct38

thuscasehardeningoftheproductcouldbeeliminated(I.W.Turner,Puiggali,&Jomaa,39

1998); (b)increase drying rate:microwave increase diffusion of heat andmass thus40

significantly reduce thedrying time (Mujumdar,2004;M.Zhang,Tang,Mujumdar,&41

Wang,2006);(c)qualityimprovement:qualityofthedriedproductcanbeimprovedby42

combining microwave with other drying method(Dev, Geetha, Orsat, Gariépy, &43

Raghavan, 2011); (d) applying MW energy in a pulsedmanner to maximize drying44

efficiencywhen the process ismass transfer controlled; (e) Boundwatermolecules45

whicharedifficulttoremovecanalsobeexcitedbymicrowaves(Gunasekaran,1999).46

Inordertoimprovetheperformance,microwaveisgenerallycombinedwithhotair47

drying, freeze drying, vacuumdrying, spouted bed drying and osmotic drying. Since48

freezeandvacuumdryinginvolvehighercapitalandoperatingcost,convectiondrying49

ismostwidelycombinedwithmicrowave(Andrés,Bilbao,&Fito,2004).Moreover,the50

maindrawbacksofconvectivedryingarelongerdryingtimesandformationofacrust51

on the surface due to the elevated temperature. Microwaves can mitigate these52

problemsbyincreasingthediffusionrateandsupplyingenoughmoisturetothesurface.53

Thus,combiningmicrowavewithconvectiondryingcansignificantlyshortenthedrying54

timeandimproveproductqualityandenergyefficiency(M.Zhangetal.,2006).Internal55

heat generatedby themicrowave increasepressurewithin thepores anddrives the56

moisture to the surface. The convective air takes themoisture by evaporation, and57

sometimesevaporativecoolingoccursatthesurface(Kumar,Millar,&Karim,2016)..58

3

There have been tremendous progress in experimental investigation and59

mathematical modelling of MCD in the last few decades. However, there is no60

comprehensive review of the recent advances in this field to analyze the progress61

systematically and prospect future direction. This paper presents a comprehensive62

reviewof the currentdevelopments inMCDof foodmaterials.Thiswork focuseson63

mathematicalmodellingofMCD,experimentalmethodsanddryingtimesavingsinMCD,64

First,areviewonMCDmethodwascriticallydiscussedbycategorizingtheliterature65

intotwobroaddivisions:(1)continuousmicrowave‐convectivedrying(CMCD)and,(2)66

intermittent microwave‐convective drying (IMCD). In this section, the drying time67

savingsandfoodqualityinMCDarediscussed.Thenthecurrentexperimentalprocess68

andtheiradvantagesandlimitationwerepresentedanddiscussed.Finally,anextensive69

review of the mathematical models available for MCD are critically analysed with70

relevantanalysisandreasoning.71

3. Principleofmicrowaveheating72

Microwavereferselectromagneticradiationinthefrequencyrangeof300MHz‐73

300GHz with a wavelength 1mm‐1m. Electromagnetic energy propagates through74

spacesbymeansoftime‐varyingelectricandmagnetic fields(HaoFeng,Yin,&Tang,75

2012).Microwavepenetrates thematerialuntilmoisture is locatedandheatsup the76

materialvolumetrically thus facilitateshigherdiffusionrateandpressuregradient to77

driveoffthemoisturefrominsideofthematerial(I.W.Turner&Jolly,1991).Thereare78

two main mechanisms of MW heating; dipolar reorientation and ionic conduction.79

Water molecules are dipolar in nature and try to follow the electric field which80

alternatesatveryhighfrequency.Foracommonlyusedmicrowavefrequencyof245081

MHz,theelectricfieldchangesdirections2.45billiontimesasecond,makingthedipoles82

movewithit(Kumar,2015).Suchrotationofmoleculesproducesfrictionandgenerate83

heatinsidethefoodmaterial(M.Zhang,Jiang,&Lim,2010).Foodmaterialsespecially84

fruits and vegetables contain about 80%of dipolarwater, therefore,microwave can85

generatesignificantvolumetricheat.Thesecondmajormechanismisionicconduction.86

Theions,particularlyinsaltyfoods,migrateundertheinfluenceofelectricfieldmigrate87

andgenerateheat.Figure1showsthetwoheatingmechanisminthefrequencyregion88

usedinindustryforheatinganddrying.89

4

90

Figure1:Schematicdiagramdepictingthedipolarandioniclossmechanismsand91

their contributions to the dielectric properties as a function of frequency (Metaxas,92

1996b).93

4. Continuousmicrowave‐convectivedrying(CMCD)94

Anextensivecompilationof literatureregardingmicrowaveassistedconvective95

dryingof food ispresented in Table1. ThesecondcolumnofTable1represents the96

drying time savings for different studies when compared to convective drying. The97

percentageofdryingtimesavingswerecalculatedbydividingthereductionindrying98

timecomparedtoconvectivedryingwiththetotalconvectiondryingtime.Asubstantial99

dryingtimesavingwasreportedby(Sadeghi,MirzabeigiKesbi,&Mireei,2013),where100

theyreportedthattheconvectiondryingoflemonsliceat500Ctook1850min,whereas101

microwaveconvectivedryingwithspecificmicrowavepower2.04W/g tookonly44102

min.Thisisanenormoussavingindryingtime,accounting97%.Anotherconsiderable103

dryingtimesavingwasreportedbyMcMinnetal.(2003)whichisapproximately96%104

forlemonslicedryingusingMCD.OthersignificantdryingtimesavingsusingMCDwas105

reportedbyPrabhanjanetal.(1995)forcarrot(82%),Bantleetal.(2013)forclipfish106

(90%),Gowenetal.(2008)forsoybean(62.5%).Nevertheless,thedryingtimesavings107

maydifferwiththemicrowavepowerlevel.Thehigherthemicrowavepower,themore108

thedryingtimesavings.However,thehigherpowerlevelcandamageoroverheatthe109

product and eventually degrade the food quality. Therefore, the microwave power110

5

shouldbetakenintoconsiderationwhenapplyingCMCDdrying.Insummary,itcanbe111

concludedthatsubstantialreductioninthedryingtime(25–90%)havebeenachieved112

inMCDdryingwhencomparedwithconvectiondrying(Cinquanta,Albanese,Fratianni,113

LaFianza,&DiMatteo,2013;Izli&Isik,2014;Prabhanjanetal.,1995). However,as114

mentioned earlier, heat sensitive food materials like banana may char due to115

overheating. In thatcase, themicrowaveshouldbeappliedcarefully toavoidquality116

degradationinCMCD.117

Table1:Summeryofmicrowaveassistedconvectiveheatinganddryingoffoodmaterial118

Material Drying time saving

(Maximum)

Modelling of power

distribution

Reference

Apple N/A N/A (Marzec, Kowalska, & ZadroŻNa, 2010)

Apple cylinders N/A N/A (Andrés et al., 2004)

Apple cube 50% N/A (Chong, Figiel, Law, & Wojdyło, 2014)

Apple and

Mushroom

N/A N/A (Funebo & Ohlsson, 1998)

Beetroot 75% N/A (Figiel, 2010)

Carrot N/A Lamberts law (Sanga, Mujumdar, & Raghavan, 2002)

Carrot cubes 82% N/A (Prabhanjan et al., 1995)

Chinese jujube 61% N/A (Fang et al., 2011)

Clipfish 90% N/A (Bantle et al., 2013)

Cooked soybeans 62.5% N/A (Gowen et al., 2008)

Corn N/A N/A (Nair, Li, Gariepy, & Raghavan, 2011)

Cranberries N/A N/A (Sunjka, Rennie, Beaudry, & Raghavan,

2004)

Garlic N/A Lambert’s law (Abbasi Souraki & Mowla, 2008)

Garlic cloves 65% N/A (Sharma, Prasad, & Chahar, 2009)

Gel N/A Maxwell* (Pitchai, Birla, Subbiah, Jones, &

Thippareddi, 2012)

Green peeper N/A Empirical (H. Darvishi, M. H. Khoshtaghaza, G.

Najafi, & F. Nargesi, 2013)

6

Material Drying time saving

(Maximum)

Modelling of power

distribution

Reference

Green pepper N/A Empirical (H. Darvishi, M. H. Khoshtaghaza, G.

Najafi, & F. Nargesi, 2013)

Lemon slice 97% Empirical (Sadeghi et al., 2013)

Mashed potato N/A Maxwell* (Chen et al., 2014)

Minced beef N/A Lambert’s Law* (Campañone & Zaritzky, 2005)

Moringa oleifera

pods (Drumsticks)

79% N/A (Dev et al., 2011)

Mushrooms N/A N/A (Argyropoulos, Heindl, & Müller, 2011)

Oyster mushroom 80% Empirical (Bhattacharya, Srivastav, & Mishra, 2013)

Pineapple N/A N/A (Botha, Oliveira, & Ahrné, 2011)

Pistachios N/A Empirical (Kouchakzadeh & Shafeei, 2010)

Potato N/A Maxwell’s Equation (Malafronte et al., 2012)

Potato 96% Lamberts law (McMinn et al., 2003)

Potato spheres N/A Maxwells (Gulati, Zhu, Datta, & Huang, 2015)

Pumpkin slices 76% N/A (Ilknur, 2007)

Swede, potato,

bread, and

concrete

N/A N/A (Holtz, Ahrné, Rittenauer, & Rasmuson,

2010)

Sour Cherries N/A N/A (Wojdyło, Figiel, Lech, Nowicka, &

Oszmiański, 2014)

Tomato N/A N/A (Swain, Samuel, Bal, & Kar, 2013)

Tomato slice 85% Empirical (Workneh & Oke, 2013)

Two-percent agar

gel

N/A Lambert’s and

Maxwell’s*

equations

(Yang & Gunasekaran, 2004)

Wheat seeds N/A Lambert’s Law (Hemis, Choudhary, & Watson, 2012)

*‐heatingonly(nomasstransfer);N/A‐Notavailable119

Microwaveassisteddryingalsoapplied tonon‐foodmaterial likewood(Lehne,120

Barton,&Langrish,1999),kaolin(Kowalski,Musielak,&Banaszak,2010),brick(I.W.121

Turner&Jolly,1991),agglomeratedsand(Hassini,Peczalski,&Gelet,2013)andfound122

7

tobehelpfulintermsofenergyefficiencyandproductquality.Regardingqualityofnon‐123

foodmaterials,MCDdriedproductsresultedinsuperiorqualitywhencomparedtohot124

airdrying(Argyropoulosetal.,2011;Cinquantaetal.,2013).Jindaratetal.(2011)also125

foundthatusingmicrowaveenergyindryingofanon‐hygroscopicporouspackedbed126

reduceddryingtimebyfivetimeswhencomparedtoconvectivedryingmethod.From127

theabovediscussion,itcanbesaidthatMCDisapotentialoptiontoachieveabetter128

qualityofdriedfoodandareductionindryingtime.129

The third columnofTable1 indicates the availability ofmodellingworkof the130

relevantstudyandtypesofmodel,i.e.whethertheyappliedLambert’slaworMaxwell’s131

equationformicrowavepowerabsorption.Moredetailsofthemodellingworkincluding132

Lambert’sLawandMaxwell’sequationarediscussed in themodellingsectionof this133

paperpresentedinsection7.134

However,supplyingcontinuousmicrowaveenergytoheatsensitivemateriallike135

foodmaycauseunevenheatingoroverheatingorevencreatehotspotsandcoldspots136

(Kumar, Joardder, Karim, Millar, & Amin, 2014). Heat and mass transfer should be137

carefullybalancedtoavoidsuchoverheating(Gunasekaran,1999).Thisproblemcould138

beovercomebyapplyingmicrowaveenergyintermittently.Intermittencyalsoallows139

limiting the temperature rise and moisture redistribution which improves product140

qualityandenergyefficiency(Soysal,Ayhan,Eştürk,&Arıkan,2009a).141

5. IntermittentMicrowave‐ConvectiveDrying(IMCD)142

Table 2 summarizes the studies relevant to Intermittent Microwave‐Convective143

Drying (IMCD). Intermittentapplicationofmicrowaveenergy in convectivedrying is144

more advantageous than continuous application and can overcome the problems of145

overheatingandunevenheating.Thishasbeendemonstratedindifferentstudiesshown146

on Table 2. For instance, Soysal et al. (2009a) reported that IMCD of red pepper147

producedbettersensoryattributes,appearance,color,textureandoverallliking,than148

MCD and commercial drying. Soysal et al. (2009b) compared IMCD and convective149

dryingfororeganoandfoundthattheIMCDwas4.7–11.2timesmoreenergyefficient150

comparedtoconvectivedryingandwasabletoprovidebetterqualitydriedfood.151

152

8

Table2:Summary of intermittent microwave assisted convective heating and drying of food material 153

Material Modelling of power

distribution

Single phase or

multiphase models Reference

Bananas N/A N/A (Ahrné, Pereira, Staack, &

Floberg, 2007)

Carrots, mushrooms N/A N/A (Orsat, Yang, Changrue, &

Raghavan, 2007)

Carrot Slices N/A N/A (D. Zhao et al., 2014)

2% agar gel Lambert’s Law* Single Phase (Yang & Gunasekaran,

2001)

Dill leaves Empirical N/A (Esturk & Soysal, 2010)

2% agar gel N/A* N/A* (Gunasekaran & Yang,

2007a)

Mashed potato Maxwell’s* Single Phase (Gunasekaran & Yang,

2007b)

Oregano N/A N/A (Soysal et al., 2009b)

Pineapple N/A N/A (Botha, Oliveira, & Ahrné,

2012)

Red pepper N/A N/A (Soysal et al., 2009a)

Sage(Salvia

officinalis) Leaves N/A N/A

(Esturk, 2012; Esturk,

Arslan, Soysal, Uremis, &

Ayhan, 2011)

Apple Labmert’s Law Single Phase (Kumar, Joardder, Farrell,

Millar, & Karim, 2015)

Apple Labmert’s Law Multipahse (Kumar, Joardder, Farrell,

& Karim, 2016)

AdvantagesofIMCDintermsofimprovingenergyefficiencyandproductquality,154

andsignificantlyreducingdryingtimehavebeenfoundinmanyotherproductssuchas155

Oregano(Soysaletal.,2009b),Pineapple(Bothaetal.,2012),RedPepper(Soysaletal.,156

2009a),SageLeaves(Esturk,2012;Esturketal.,2011),Bananas(Ahrnéetal.,2007),157

andCarrotsandMushrooms(Orsatetal.,2007).158

9

ThesecondandthirdcolumnofTable2presentsanoverviewofmodellingstudies159

regardingIMCD.Itcanbeseenfromthetablethatthereareverylimitedstudyregarding160

modellingofIMCD,whichhasbeendiscussedmoredetailsinsection7.161

6. ExperimentsinMCDdrying162

ThissectiondiscussestheexperimentalproceduresusedinliteratureforMCD.163

The limitation and strength of the experimental facilities are analysed and164

recommendations for future experimental setup and challenges in scaling up MCD165

experimentalfacilityaresuggested.166

The main components of an MCD drying test facility are: 1 variable power167

microwavegenerator(magnetron),2.waveguide,3.microwavecavityand4.Aheating168

source forhotair supply (Tulasidas,1995).Microwavegeneratorcanbeavarietyof169

devices such asmagnetrons, klystrons, power grid tubes, travelingwave tubes, and170

gyrotrons,butthemostcommonlyusedsourceisthemagnetron,whichismoreefficient,171

reliable, and available at lower cost than other sources (National Research Council,172

1994).Microwavegeneratedinmagnetronisguidedthroughwaveguidestothecavity173

wherethematerialsareplaced.At thesametimehotairneedstobesuppliedtothe174

cavitytocombinewiththeconvectivedrying.TheMCDdryingsetupscanbeclassified175

intotwomaincategoriesbasedonthecavitytype:singlemodecavityandmultimode176

cavity(Chandrasekaranetal.,2011).177

6.1 Experimentalprocesswithsinglemodecavity178

Singlemodecavitiesareusedwhenprecisefocusatagivenlocationisneeded.179

Forthesecavities,thetransverseelectric(TEorH)wavesandtransversemagnetic(TM180

orE)wavesarecommonlyusedwhicharedesignedeitherrectangularorcircularcross181

section.Theelectric intensity inthedirectionofpropagation iszero fortheTEwave182

whereasfortheTMwave,themagneticintensityinthedirectionofpropagationiszero183

(Chandrasekaran, Ramanathan, & Basak, 2012). Single mode applicators are used184

extensivelywheretheloadconditionscanbekeptconstant(andthusrepeatedtuningis185

not required). These conditions are present in heating a fluid stream, for example,186

whereby the fluid flowsthroughtheapplicatorsuchthat itspropertiesarerelatively187

constant.188

10

AbasicsinglemodeapplicatorsetuphasbeenshowninFigure2.Thewaveguide189

circulator(as inFigure2) isa three‐portdevice ideallyhavingnopowerattenuation190

capability.Becausecirculatorsarenotdesignedtoabsorbpower,aseparate“dummy”191

loadisconnectedtothecirculatorandusedtoabsorbreversepowerthatmayotherwise192

damagethemagnetron(Gerling,2000).193

194

Figure2:Basicsinglemodeapplicatorsetup(Gerling,2000)195

Impedancematchingisusuallyachievedusingthreemanualstubtuners,which196

are used to alter the capacitance of the waveguide system (Gerling, 2000). As an197

example,twostrawberriesofslightlydifferentshapewouldrequiredifferentstubtuner198

settings (position and penetration depth) for optimum impedance matching.199

Furthermore, the same strawberry at different drying stages (and thus different200

moisture contents)may require a drastic change in stub tuner settings to keep the201

strawberrymatchedwith the load. Failure tomatch two impedances results inpoor202

microwavepowercouplingwiththeload.203

Therearemanyotherstudiesthatusedspeciallydesignedsinglemodeapplicator204

intheirstudy(Holtz,Ahrné,Karlsson,Rittenauer,&Rasmuson,2009;Holtzetal.,2010;205

Malafronteetal.,2012).Thedryingequipment(asshowninFigure3)comprisedofa206

straightaluminiumwaveguide (8643mm) fittedwithanair‐cooledmagnetron (2.45207

GHz,2M244‐M16,Panasonic,Cwmbran,U.K.).Thedryingcavitywassituatedinsidethe208

waveguide.Betweenthemagnetronandwaveguideathree‐stubtuner(stainlesssteel)209

11

wereincorporated,andthefarendofthewaveguidewasadjustable,enablingthelength210

ofthewaveguidetobeadjusted.211

212

Figure3.Microwaveconvectivedryingequipment.Schematicimageand213dimensionsofthedryer(applicator)(Malafronteetal.,2012)214

Jindaratetal.(2011)analysedenergyefficiencyofmicrowaveconvectivedrying215

usingaTE10modemicrowaveconvectivedryerforporouspackedbed.Figure4shows216

the experimental setup using a rectangular waveguide with dimension of 110mm217

⤬55mm. The isolator was used to trap microwave reflection from sample to save218

magnetron.The temperatureatvariouspointofsamplewasmeasuredby fiberoptic219

probes.220

12

221

222

Figure4.Schematicofexperimentalfacility:(a)equipmentsetup;(b)223microwavemeasuringsystem.(Jindarat,Rattanadecho,&Vongpradubchai,2011)224

Inconclusionofsingleofcavitydiscussion,itcanbesaidthattheexperimental225

setupwithasinglemodelcavityaremainlydesignedforstudyingthephysicsinvolved226

ratherthanbeingoptimizedforadryingprocess.Inthesesetups,couplingmicrowave227

powertoaloadrequirestherespectivecompleximpedancesbetweentheloadandthe228

microwavepowersourcetobematched.Thisisthegreatestdisadvantageofasingle229

mode applicator, since the complex impedance of the load changes with geometry,230

chemical composition and temperature (Gerling, 2000). Precision control or target231

heatingcanbeachievedwithsinglemodeapplicator.However,multimodeapplicatoris232

beingwidelyusedintheindustrialsystem.233

6.2 Experimentalprocesswithmultimodemodecavity234

Multimode microwave applicators are closed volume, totally surrounded by235

conductingwallsandhavealargecavitytopermitmorethanonemode(pattern)ofthe236

electric field (Funebo & Ohlsson, 1998). Unlike single mode applicators, multimode237

applicators are less sensitive to product position or geometry (Chandrasekaran,238

13

Ramanathan,&Basak,2013).Figure5showsamultimodecavitywithhotairinletand239

outlet fordryingofpumpkin (Wang,Wang,&Yu,2007).Manydrying researchused240

modifiedhouseholdmicrowaveovenasmultimodeapplicator.Wangetal.(2007)used241

alaboratorymicrowaveovenwithanoutletattheupperleftsideoftheoventoallow242

exhaustofmoistairasshowninFigure5.Onedish,containingthesample,wasplaced243

atthecenterofaturntablefittedinside(bottom)themicrowavecavity.Moistureloss244

wasrecordedat5minintervalsduringdrying,measuredbytakingoutandweighingthe245

dishonthedigitalbalance(JY1000,1000±0.01g).However,takingthesampleoutmay246

causesomeerrorinmoisturemeasurement.Themajorlimitationofthisstudywasthat247

therewasno temperaturemeasurement of the sample. Therefore, itwas difficult to248

monitortheoverheatingofthesamples.249

250

251

Figure5:Multimode applicatorwithmode stirrer and turntable(Wang et al.,2522007).253

Figure 6 shows a modified microwave (900 W, 2450MHz), having an inside254

chamberwithdimensionsof(345x335x220)whichwasusedtodryOregano(Soysalet255

al.,2009b;Soysaletal.,2009a).Tworectangularopening(10x8cm2)wasmadeonthe256

14

backandtopwalltosupplyandexithotairrespectively.Theheatedairwasforcedinto257

thedryingchamberbya radial fan (100W,180m3/h).Apotentiometerwasused to258

controlthespeedofthefan.Continuousmonitoringoftheweightwasdonewithadigital259

balance(SartoriusTE3102S,Germany,3100±0.01g)thatwasplacedundertherotating260

glasstray(diameter:314mm,mass:1150g).Aprogrammable logiccontroller(PLC)261

systemwasusedtocontroltheintermittencetime,thefanandtheglassturntable.The262

temperature of the air inside the air duct was measured using a PT100 platinum263

resistancetemperaturesensor.Theglassturntableonwhichthematerialwasplaced264

continuously turned (5 rpm) during the drying procedure to obtain a uniform265

distributionofthemicrowaveenergyinthematerial,andtoassurehomogenizeddrying.266

Thisdryingsystemisimpressivebecauseitisequippedwithtemperature,moisture,and267

airvelocitymeasurementsystem.However,onelimitationcouldbetheunevenairflow268

distributioninthedryingchamber.Astheairentersatthebottomandexitatthetop,269

this may result in uneven airflow or poor airflow distribution over the product.270

Moreover,thetemperaturedistributioncanbeuneveninmicrowavesoitisbetterto271

usethermalimagingcamerainmultimodecavityratherthanpointmeasurementusing272

thermocouple.273

274

Figure 6: Experimental microwave–convective drying system: 1. microwave275drying chamber; 2, rotating glass tray; 3, tray rotating rod; 4, digital balance; 5, PID276controlunitandsolid‐staterelay;6,airentrance;7,wiremesh;8,moistairexitopening;2779,temperaturesensor;10,airduct;11,electricheaters;12,fan;13,fanspeedadjuster;27814,digitalwattmeter;15,PLCcontrolunit(Soysaletal.,2009b;Soysaletal.,2009a).279

15

UpritandMishra (2003)usedamodifiedprogrammabledomesticmicrowave280

oven(IBM,ModelElectron),withamaximumoutputof625Wat2450MHzandcavity281

(dryingchamber)dimensionsof300x240x210mmasshowninFigure7forsoy‐fortified282

paneerdrying.Moisturelossinthesamplewasmeasuredbyon‐lineweightrecording283

at 3 min interval. The temperature and relative humidity of the exhaust air were284

measuredperiodicallyusingadigitalhygrometer(ALMEMO,Germany).Thematerialis285

assumedtoreachequilibriummoisturecontentwhenthematerialacquiredaconstant286

weight.Theypaidspecialattentiontoavoidcharringoftheproductwhichisdifficult287

withoutmeasuringthetemperatureoftheproduct.Becausemicrowaveheatingisfast288

and volumetric, their visual inspection may not be sufficient to predict the289

commencementofcharring.290

291

Figure7.Schematicofmicrowaveconvectivedryer(Uprit&Mishra,2003)292

293

Andrés et al. (2004) performed experiments in a specially designed hot air–294

microwaveovenequippedwithcontinuousmicrowaveenergy(Figure8).Theyvaried295

microwavepowerandairtemperaturewithconstantairvelocityat1m/s.296

16

297

Figure8.Schematicillustrationofthecombinedhotair–microwavedrying298equipment(Andrésetal.,2004).299

Ahrnéetal.(2007)Thedryingexperimentswereperformedinadryer(Figure300

9)speciallydesignedintheframeworkoftheEuropeanUnionprojectICA4‐CT‐2002‐301

10034byP.O.RismanincollaborationwithSIKandconstructedbyTIVOXmachineAB302

(TIVOXMaskinAB,Sweden).Itcanbeoperatedwithatemperatureof40‐800Candair303

velocity of 0.3‐0.8m/s. The product temperature was measured by fiber‐optic304

temperaturesensors (ReFLexTM,Neoptix,Canada)placed in four samples locatedat305

differentpositionsofthedryer.Thefiberoptictemperatureprobesgivetemperatureat306

a point which may sometimes deceive in microwave heating experiments since307

microwavegeneratesunevenheatingwithhotspotandcoldspotinthesample.Instead308

of point measurement, Kowalski, Musielak et al. (2010) used a thermal imager to309

measure2Dsurfacetemperature(Figure10)whichcanprovidemoredetailinformation310

ofsurfacetemperatureofthesample.311

312

Figure9.Schematicrepresentationofthemicrowaveconvectivedryer.(Ahrné313etal.,2007)314

17

Kowalski,Musielaketal.(2010)usedamicrowaveovenwithcavitydimensions315

300x400x450 which can supply maximum power of 600W. They found that316

temperaturewashigherinthemiddleofthesample.Intheirsetup,airwith220Cwas317

suppliedwithinstalledmechanicalventilationsystem.However,fromFigure10,itisnot318

clearwheretheventilationsystemwasplacedandhowefficientlyitworked.Airflowis319

importantbecausereducedairflowmayresultsmoistureaccumulationatthesurfaceof320

thesamplewhichreducesdryingrateanddegradessampletextureforfoodapplication.321

322

Figure10.Theexperimentalset‐up:(a)microwave‐convectivedryerand(b)323determinationofthetemperaturedistribution324

Incontrast,Fuetal.(2005)developeddryertooperateatanairvelocityof1‐325

3m/stoprovidesufficientairflowtothedryingchamber(Figure11).Theairwasdrawn326

withanaxialfanthroughcuttingventonthemicrowavewall.However,oneshouldmake327

surethat themicrowave leakageis lessthantheallowable limit(5mW/cm2)through328

thatvent.329

18

330

Figure 11.Apparatus for convective and microwave finish drying (Fu et al.,3312005)332

Temperatureandmoisturearethetwomainparametersneedtobemeasured333

accuratelyduringthedryingprocess.Theefficacyofanexperimentalsetupdependson334

howaccurately these twoparameterscanbemeasured.Additionally, theairvelocity335

distributionplaysanimportantroleindryingratebecauseitaffectstheheatandmass336

transfercoefficientwhichisessentialformodelling.337

The major problem with multimode applicators is non‐uniformity of the338

microwavefieldintheloadwhichcausesnon‐uniformheatdistribution.Thisproblem339

canbeminimisedbyprovidingamodestirrer(rotatingmetalbladedfan)orturntable340

(Schiffmann, 1995). The effect of mode stirrers in a multimode microwave heating341

applicatorareinvestigatedbyKurniawanetal.(2015)using3DCOMSOLMultiphysics342

Simulation.Theyhavefoundthatthetemperaturedistributionismoreuniformforthe343

casewithmodestirrerscomparedtothatobtainedwithoutmodestirrers.Implementing344

intermittency inmicrowave application is another technique to reduce non‐uniform345

heatingofsample.346

In summary, the experimental facilities for a MCD should be equipped with347

continuous weight monitoring, temperature monitoring such as thermal imaging348

camera,andhaveuniformairflowdistributioninthechamber.Inaddition,thesafetyof349

thesetupisanothercriticalissue.Becausethemicrowaveleakagecancausedamageto350

human cell and tissues and cause cataracts. Therefore, the design of vent or any351

19

perforationshouldbecarefullyhandledwhiledesigningandmanufacturingmicrowave352

assisteddryer.353

7. MathematicalModellingofMCD354

Mathematicalmodels can be used to predict the internal temperature that is355

difficult to measure and control the microwave power to avoid overheating. As356

discussedinsection3thatmicrowavegeneratevolumetricheatinsidethesampleand357

thisheatgenerationneedstobeaddedinenergyequationwhenmodellingMCDprocess.358

Thus the theoretical investigationofMCD consists of twoparts. The first part is the359

calculationofmicrowavepowerabsorptionthatconvertedintoheatandthesecondpart360

issolvingtheconjugateheatandmasstransferfordrying.Thissectiondiscussesboth361

microwavepowerabsorptionandheatandmasstransferduringMCDdrying.362

7.1 ModellingofMWpowerabsorption363

InMCDmodel,heatgenerationanalysisiscrucialforaccurateestimationofthe364

temperature of the sample. Volumetric heat generation depends on the dielectric365

propertiesofthematerial,andthefrequencyandintensityoftheappliedmicrowave.366

There is plethora of studies regarding calculation of power distribution or heat367

generationduetomicrowave.Inthepreviousstudieselectromagneticfieldinsidethe368

product was assumed to be (i)uniform; (ii) exponentially decayed; (iii)decayed369

followingempiricalrelations;(iv)decayedfollowingLambert’srelationand(v)decayed370

calculated by solving electric field equations (Maxwell’s equations). Among them,371

Lambert’sLawandMaxwell’sequationsaremostcommonlyusedinmicrowaveassisted372

drying.373

374

7.1.1 Lambert’sLaw:375

Microwaveenergydistribution in foodproductswithbasic geometries (slabs,376

spheres, and cylinders) is calculated by using Lambert’s Law. Especially in drying,377

applicationofthislawismorecommon(AbbasiSouraki&Mowla,2008;J.R.Arballo,378

Campanone,&Mascheroni,2012;Hemisetal.,2012;Khraisheh,Cooper,&Magee,1997;379

Mihoubi & Bellagi, 2009; Salagnac, Glouannec, & Lecharpentier, 2004; Zhou, Puri,380

Anantheswaran,&Yeh,1995).381

20

Lambert’s Law considers exponential attenuation of microwave absorption382

withintheproduct,viathefollowingrelationship.383

x)(-20expP=xP (1)

Here, the incident power at the surface (W), α is he attenuation constant384

(1/m), and x represents the distance from surface (m). The measurement of 0P is385

generallyobtainedviaexperimentation.386

Theattenuationconstant, isgivenbythefollowingequations387

2

1'

''1

'2

2

1

(2)

where isthewavelengthofmicrowaveinfreespace( cm24.12 at2450MHz388

andairtemperature200C)andε'andε"arethedielectricconstantanddielectricloss,389

respectively.390

Thevolumetricheatgeneration, micQ (W/m3)inEquation(3)isthencalculated391

by:392

V

PQ mic

mic , (3)

where,Visthevolumeofapplesample(m3).393

However,Lambert’sLawdoesnotaccuratelypredicttheheatingsituationand394

electricfielddistribution(Chandrasekaranetal.,2012;V.Rakesh,Datta,Amin,&Hall,395

2009).Recently,Kumaretal.(2015)developedmathematicalmodelforIMCDdrying396

usingLambert’slawandhighlightedthelimitationsofLambert’slaw.Theymentioned397

thatthemicrowaveabsorptionshouldreducewithdecreasingmoisturecontent,butthe398

Lambert’s Law fails to take this into account, giving highest power at the surface399

irrespectiveofmoisturecontent.400

Duringthe1970sand1980smostofthepowerabsorptioncalculationwasbased401

onLambert’slaw.However,duringtheearly1990s,theoreticalfoundationofcombined402

electromagneticandthermaltransportusingMaxwell’sequationshasbeenestablished.403

Chandrasekaran, Ramanathan et al. (2012) reviewed the comparison between404

21

Lambert’slawandMaxwell’sequation;theyreportedthatMaxwell’sequationgiveexact405

andmoreaccuratesolutionformicrowavepropagationinsamples.406

7.1.2 Maxwell’sEquations407

Maxwell’sequationsareasetofpartialdifferentialequationsofelectrodynamics408

whichrepresentafundamentalunificationofelectricandmagneticfieldsforpredicting409

electromagneticwavepropagation.Physicistandengineersusecomputersrangingfrom410

simpledesktopmachinestomassivelyparallelsupercomputingarraysforsolvingthese411

equationstoinvestigatewaveguiding,radiation,scattering,andheating(H.Zhao,1997).412

Maxwell’s equations that govern the propagation and microwave heating of413

materialaregivenbelow:414

t

BE

(4)

cJt

DH

(5)

0. B (6)

D. (7)

WhereEiselectricfielddistribution(V/m),Diselectricfluxdensitydistribution415

(C/m2),Hismagneticfielddistribution(A/m),Bismagneticfluxdensitydistribution416

(W/m2), currentdensity(A/m2),ρisvolumechargedensity(C/m3).417

InfrequencydomaintimeharmonicMaxwell’sequationscanbewrittenas418

0''''

1 2

Ei

cE

(8)

where Eistheelectricfieldstrength(V/m), f isthemicrowavefrequency(Hz),419

c isthespeedoflight(m/s), ' , '' , arethedielectricconstant,dielectriclossfactor,420

andelectromagneticpermeabilityofthematerial,respectively.421

422

Theheatgenerationduetomicrowave, mQ (W/m3),givenby(COMSOL,2012),423

mlrhm QQQ . (9)

22

Here, rhQ istheresistiveloss(W/m3)and mlQ isthemagneticloss(W/m3).For424

foodproductsthemagneticlossesarenegligible,i.e. 0mlQ (Chenetal.,2014).425

Theresistivelosscanbecalculatedas(Chenetal.,2014;Wentworth,2004)426

*5.0 EJQrh

(10)

where *EistheconjugateofE

andtheelectriccurrentdensity J

(A/m2)isgiven427

by,428

EfEJ

02 , (11)

where, istheelectricalconductivity(S/m), isthedielectriclossfactorand429

0 ispermittivityinfreespace.430

Substitutingtheaboveintoequation(12),themicrowaveheatgenerationdueto431

canbewrittenas,432

2

0 EfQm (12)

whichconformswiththeheatgenerationsequationderivedbyMetaxas(1996a).433

7.2 Dielectricproperties:434

Dielectricpropertiessuchasdielectricconstantanddielectriclossfactordefine435

how materials interact with electromagnetic energy. These properties of materials436

definehowmuchmicrowaveenergywillbeconvertedtoheat(Chandrasekaranetal.,437

2013). As can be seen from the heat generation formulation above, the dielectric438

properties of the material are one of themost important parameters in calculating439

microwaveheatgenerationduringdrying(Sosa‐Morales,Valerio‐Junco,López‐Malo,&440

García,2010).Therefore,theevaluationofdielectricpropertiesiscriticalinmodelling441

andproductandprocessdevelopment(Ikediala,Tang,Drake,&Neven,2000).442

7.3 HeatandmasstransfermodellinginMCD443

Heatandmasstransfermodel isnecessaryforevaluatingtheeffectofprocess444

parametersonenergyefficiency anddrying time, andoptimizing thedryingprocess445

23

(Kumar,Karim,Joardder,&Miller,2012a;Kumar,Karim,&Joardder,2014).Developing446

aphysicsbaseddryingmodelforagriculturalproductsisachallengingtaskduetothe447

complexstructuralnatureofagriculturalproductsandchangesinthethermo‐physical448

properties during drying. Moreover, the heat generation due to microwave in MCD449

makesthemodellingmorechallenging.Therefore,someassumptionsareindispensable450

if mathematical models are to be developed, but these should be carefullymade to451

represent thephysical phenomenaduring theprocess. In this section, themodelling452

approachesofheatandmass transfer inMCDarediscussed, and their limitationare453

highlighted.TheMCDdryingmodelsavailable in literaturecanbeclassified into two454

categories:empiricalmodels,fundamentalmodels.Thefundamentalsmodelsagainthen455

categorizedintothreedivisionsbasedontheirwatertransportmechanisms:1)single456

phase,2)doublephaseand3)multiphasemodelsasshowninFigure12.Inthefollowing457

sections,themodelbasedontheseclassificationarediscussedandanalysed.458

459

Figure12.Generalclassificationofmicrowavedryingmodels460

461

7.3.1 Empiricalmodel462

TheempiricalmodelsaregenerallyderivedfromNewton’slawofcoolingandFick’s463

lawof diffusions (Erbay& Icier, 2010). These are simpler to apply and oftenused to464

describethedryingcurve.Thedryingconstantandcoefficientsintheempiricalmodels465

are developed with regression analysis. Page model and exponential model are466

frequently used in microwave convective drying. Table 1 and Table 2 present the467

24

empiricalmodelofCMCDandIMCDavailableintheliterature.Therearemanydifferent468

empirical model often referred as thin layer drying models such as Newton, Page,469

Henderson Pabis, Logarithmic, two term, two‐term exponential, and Wang and Sing470

models.Theacceptabilityofthesemodelsareusuallydeterminedbythecoefficientof471

determinationR2, and the reducedvalueofmean squareofdeviationχ2.Theydonot472

providephysical insightintotheprocess.Also,thesemodelsareonlyvalidforspecific473

process condition and material. In contrast to empirical models, the physics‐based474

models can capture the inherent drying mechanism better (Chou, Chua, Mujumdar,475

Hawlader,&Ho,2000;Chua,Mujumdar,&Chou,2003;Ho,Chou,Chua,Mujumdar,&476

Hawlader,2002).The theoreticalmodelsoften canbeused forwide rangeofprocess477

parameterandcanbeusedforparametricanalysisandoptimization.478

7.3.2 Singlephasemodel479

Thesinglephasemodelsconsideronlyonephaseinfooddomaini.e.liquidwater480

diffusionthroughthesolidmedia.Theseareoftencalleddiffusion‐basedmodelsandare481

verypopularbecauseoftheirsimplicityandgoodpredictivecapability(JavierR.Arballo,482

Campañone,&Mascheroni,2010;Kumaretal.,2012b;Perussello,Kumar,deCastilhos,483

&Karim, 2014).Maybe due to this reason,most of themodel related tomicrowave484

assisted drying are single phase. Thesemodels assume conductive heat transfer for485

energyanddiffusivetransportformoisture.486

Thesinglephasemodelconsidersonlydiffusivewatertransportasshowninthe487

equation(13).488

489

0u)(-Deff

www cct

c (13)

490

where,cwisthemoistureconcentration(mol/m3), effD istheeffectivediffusion491

coefficient(m2/s)anduistheconvectiveflow.Theeffectivediffusioncoefficient, effD ,in492

thosemodelshastobedeterminedexperimentally.Thusthismodelcanbesaidassemi‐493

empiricalmodel.494

TheenergybalancewascharacterizedbyaFourierfluxwithaheatgenerationterm495

duetomicrowaveheating, micQ (W/m3).496

25

micp QTkt

Tc

).( (14)

where,Tisthetemperature(0K), isthedensityofsample(kg/m3), pc isthespecificheat497

(J/kgK), and k is the thermal conductivity (W/mK). Theheat generation, micQ (W/m3),498

wascalculatedusingLambert’sLaw.499

Incaseofmicrowaveheatingordrying,theeffectivediffusivityincreasesdueto500

volumetric heating which cause pressure driven flow. This pressure driven flow is501

lumpedtogetherwithdiffusionincaseofsinglephasemodels.Thereforeitcanbesaid502

thatalthoughthismodelcanprovideagoodmatchwithexperimentalresults,itcannot503

provideanunderstandingofothertransportmechanismssuchaspressuredrivenflow504

and evaporation. This is because all water are lumped in one parameter, diffusion505

coefficient,cannotprovideindividualcontributionofthewaterflux.Thedrawbacksof506

thesekindsofmodelsarediscussedindetail intheworkofZhangandDatta(2004).507

Lumping all thewater transport asdiffusion cannotbe justifiedunder all situations.508

Therefore,multiphasemodelsconsideringtransportofliquidwater,vapour,airinside509

thefoodmaterialsareconsideredtobemorerealistic.510

7.3.3 Doublephasemodel511

Double phase models consider two species, namely water vapour and liquid512

waterformasstransferduringthemodellingprocess.Thesemodelsarecomparatively513

more realistic and comprehensive than single‐phase models because of the514

incorporationofevaporationorphasechangebetweenliquidwaterandwatervapour.515

Thegeneralgoverningequation fordoublephasemodel ispresented inEq (15)and516

(16).517

Liquidphaseofwater: Rcuc-Dt

cllll

l

(15)

Vapourphaseofwater:

Rcuc-Dt

cvvvv

v

(16)

Herethe lc and vc aretheconcentrationofliquidwaterandwatervapour, lD and518

vD arethediffusioncoefficientforliquidwaterandwatervapourand lu and vu arethe519

convectiveflowofliquidwaterandvapour.TheRistheproductionorconsumptionof520

26

species (i.e. evaporation or condensation). Malafronte et al. (2012) estimated the521

evaporationrateas,522

0

)( vsatc cTckR when,

vsat

vsat

cc

cc

(17)

WhereRT

TMPTc v

sat

)()( and vapour pressure was calculated from Antoine’s523

equation.524

There are some two phase models in MCD drying process. For example,525

Malafronte et al. (2012) developed a two phase models for combined microwave526

convective drying. The strong point of the model is that they took moisture and527

temperaturedependentdielectricproperties.Moreover,theysolvedbothheatandmass528

transportequationsandMaxwell’sequationsintransientregime.Marraetal.(2010)529

alsodevelopedatwophasemodelforcombinedmicrowaveconvectivedrying.Themain530

strongpointoftheirmodelisthattheyconsideredconjugateapproachofheatandmass531

transfer,whichenabledtocalculaterealisticheatandmasstransfercoefficientwithout532

requiringempiricalaveragebasedcalculations. Jindaratetal. (2011)alsoconsidered533

twophasetransport.However,thedeformationorshrinkagehavenotbeenconsidered534

inallthesemodels.Moreover,theavailablemodelconsideringtwophaseneglectedthe535

Darcyorpressuredrivenflowi.e.bulkflow.Multiphasemodelsdiscussedbelowhave536

consideredbulkflow.537

7.3.4 Multiphaseporousmediamodel:538

The multiphase models consider all phases inside the food materials namely water, air, 539

water vapour and solid matrix. Multiphase models can be categorised into two groups: 540

equilibrium and non-equilibrium approach of vapour pressure. In equilibrium formulations, the 541

vapour pressure, vp , is assumed to be equal with equilibrium vapour pressure, eqvp , , and vice 542

versa. There are some multiphase models considering equilibrium approach applied in vacuum 543

drying of wood (Ian W. Turner & Perré, 2004) and convection drying of wood and clay 544

(Stanish, Schajer, & Kayihan, 1986) (Chemkhi, Jomaa, & Zagrouba, 2009), microwave 545

spouted bed drying of apple (H. Feng, Tang, Cavalieri, & Plumb, 2001) and large bagasse 546

stockpiles (Farrell et al., 2012). Some multiphase porous media models combine the liquid 547

water and vapour equations together to eliminate the evaporation rate term (Farrell et al., 2012; 548

27

Ratanadecho, Aoki, & Akahori, 2001; Suwannapum & Rattanadecho, 2011). By doing this, the 549

concentrations of liquid water and vapour cannot be determined separately (Kumar, Joardder, 550

et al., 2016). 551

However, equilibrium condition may be valid at surface with lower moisture content 552

because equilibrium condition may not be achieved due to lower moisture content at the surface 553

during drying. Therefore, the non-equilibrium approach is a more realistic representation of 554

the physical situation during drying (J. Zhang & Datta, 2004). Moreover, the non-equilibrium 555

formulation for evaporation can be used to express explicit formulation of evaporation, thus 556

allowing calculation of each phase separately. Furthermore, non-equilibrium multiphase 557

models are computationally effective and applied to wide range of food processing such as 558

frying (Bansal, Takhar, & Maneerote, 2014; Ni & Datta, 1999), microwave heating (Chen et 559

al., 2014; V. Rakesh, Seo, Datta, McCarthy, & McCarthy, 2010), puffing (Vineet Rakesh & 560

Datta, 2013) baking (J. Zhang, Datta, & Mukherjee, 2005), meat cooking (Dhall & Datta, 2011) 561

etc. However, application of these non-equilibrium models in drying of food materials is very 562

limited. 563

TherearesomemultiphasemodelsinMCDprocess.Mostrecently,Kumaretal.564

(2016) developed multiphase model for IMCD of apple. They considered non‐565

equilibrium approach and applied Lambert’s law to calculate microwave heat566

generation.Dinčovetal. (2004)developedaFinitevolumemultiphaseporousmedia567

model where the coupling was achieved by considering dielectric properties as a568

functionofmoisture and temperature. Zhuet al. (2015)developeda comprehensive569

multiphase model of microwave drying of sphere. The governing equation used to570

developthemultiphasemodelaresummarisedinTable3(Kumar,Joardder,etal.,2016).571

Table3.Summaryofgoverningequationsusedinmultiphasemodelling572

Physics and Phases Governing Equations Eq. No.

Hea

t and

Mas

s T

rans

port

Mas

s T

rans

port

Wat

e Liquid water evapc

w

wrww

w

wrwwww Rp

kkP

kkS

t

,,

(18)

Gas

Vapor evapvgeffgg

v

grgvgvgg RDSP

kkS

t

,

,(19)

Air va 1 (20)

Gas pressure evap

g

grggg RP

kkS

t

,

g (21)

28

Ene

rgy

Energy mevapfgeffthwwggeffpeff QRhTkhnhn

t

Tc

).( ,

(22)

Nom

encl

atur

e

Sym

bols

=porosity, S=saturation, =density, k= permeability, P=gas pressure, = viscosity, P=gas

pressure, c= concentration, D=Diffusion coefficient, =mass fraction, T=Temperature, n

= flux, kth= thermal conductivity, h= latent heat, E=Electric field, f= microwave frequency, c= speed of light, Qm= microwave heat generation, Revap=evaporation of liquid water, p= pressure,

m = magnetic permeability, ' = dielectric constant , '' =dielectric loss factor, 0=permittivity in free space,

Subscript

w=water=vapor, g=gas, eff=effective, m=microwave, r=relative=capillary, evap=evaporation, m=microwave

573

8. Challengesandfuturedirectionforresearch574

Themajorchallengeinmicrowavesystemisthenon‐uniformityofelectricfield.575

Future research should involve addressing this problem focusing on obtainingmore576

uniform electric filed distribution thus to obtain uniform temperature andmoisture577

distribution.Onepotentialsolutioncouldbeusingmultiplemagnetronatappropriate578

locationofthechamber.Mathematicalmodellingandsimulationwouldbeessentialto579

do such investigations. The plant based food materials are hygroscopic in nature,580

containingfreewaterandboundwater.Thetransportmechanismsoffreewaterand581

boundwateraredifferent.Therefore,thefuturemodellingstudyofMCDshouldinclude582

aseparatemechanismforthetransportoffreeandboundwater.Moreover,themodels583

shouldbeabletopredicttheeffectofprocessparametersondryingkinetics,thenthe584

models can be used to optimize the process and suggest an appropriate strategy of585

applyingMCDtoavoidoverheatingandgainingmaximumfoodqualitywithminimum586

energyusage.587

9. Conclusion588

The present study provides an overview of MCD process focusing on drying589

kinetics,experimentalprocessandmathematicalmodelling.Moreover,thecomparative590

study of drying time betweenmicrowave assisted drying and convective drying for591

differentmaterialsarecalculatedanddiscussed.Itisclearthatdryingtimesavingcan592

beupto90%byapplyingmicrowave.ConsideringthishugedryingtimesavingofMCD,593

there is enourmous potential of this process in industrial applications. The critical594

29

review of experimental facilities showed that the experimental facilities should be595

equippedwith real timemoistureand temperaturemeasurementof the sample, and596

shouldhaveuniformairflowdistribution.Theriskandsafetyissuesofcreatingventfor597

airflowinmicrowavecavitywasinvestigated.Althoughthesetupwithasinglemode598

cavity can provide an understanding of physics, their performance is sensitive to599

product position and geometry. In contrast,multimode cavities are less sensitive to600

productpositionorgeometrybutprovidesunevenheating.However,theseunevenheat601

canbeminimizedbyapplyingmicrowaveintermittently,providingturntableormodel602

stirrersandbysuitablecavitydesign.Continuousmicrowave‐convectivedrying may603

overheat and damage quality which can be overcome by intermittent microwave‐604

convective drying by applying appropriate power level and pulse ratio. The605

mathematical modeling can help to optimize intermittency and power level of606

microwaveforbetterproductqualityandenergyefficiency.Onemajordisadvantageof607

microwave application is the non‐uniform heating due to standing wave pattern. A608

comprehensivemultiphasemathematicalmodelcanalsohelp inselectingmagnetron609

size, position and cavity shape in order to obtain more uniform heating pattern.610

Therefore,thefutureresearchshouldfocusonscalingupandoptimizingthistechnology611

forindustrialapplications.612

10. References613

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Ahrné, L. M., Pereira, N. R., Staack, N., & Floberg, P. (2007). Microwave Convective Drying of Plant 617Foods at Constant and Variable Microwave Power. Drying Technology, 25(7‐8), 1149‐1153. 618doi:10.1080/07373930701438436 619

Andrés, A., Bilbao, C., & Fito, P. (2004). Drying kinetics of apple cylinders under combined hot air–620microwave  dehydration.  Journal  of  Food  Engineering,  63(1),  71‐78.  doi:10.1016/s0260‐6218774(03)00284‐x 622

Arballo, J. R., Campanone, L. A., & Mascheroni, R. H. (2012). Modeling of Microwave Drying of Fruits. 623Part  II:  Effect  of  Osmotic  Pretreatment  on  the Microwave  Dehydration  Process.  Drying 624Technology, 30(4), 404‐415. doi:10.1080/07373937.2011.645100 625

Arballo, J. R., Campañone, L. A., & Mascheroni, R. H. (2010). Modeling of Microwave Drying of Fruits. 626Drying Technology, 28(10), 1178‐1184. doi:10.1080/07373937.2010.493253 627

Argyropoulos, D., Heindl, A., & Müller, J. (2011). Assessment of convection, hot‐air combined with 628microwave‐vacuum  and  freeze‐drying methods  for mushrooms  with  regard  to  product 629quality.  International  Journal  of  Food  Science  &  Technology,  46(2),  333‐342. 630doi:10.1111/j.1365‐2621.2010.02500.x 631

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Bansal, H. S., Takhar, P. S., & Maneerote, J. (2014). Modeling multiscale transport mechanisms, phase 632changes  and  thermomechanics  during  frying.  Food  Research  International,  62,  709‐717. 633doi:10.1016/j.foodres.2014.04.016 634

Bantle, M., Käfer, T., & Eikevik, T. M. (2013). Model and process simulation of microwave assisted 635convective  drying  of  clipfish.  Applied  Thermal  Engineering,  59(1–2),  675‐682. 636doi:http://dx.doi.org/10.1016/j.applthermaleng.2013.05.046 637

Bhattacharya,  M.,  Srivastav,  P.,  &  Mishra,  H.  (2013).  Thin‐layer  modeling  of  convective  and 638microwave‐convective drying of oyster mushroom  (Pleurotus ostreatus).  Journal of  Food 639Science and Technology, 1‐10. doi:10.1007/s13197‐013‐1209‐2 640

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