Analytical Investigation of Microwave Heating. Mohammad Robiul Hossan and Prashanta Dutta

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1 Pcdgs f h ASME Iaal Mchacal Egg Cgss & Exps IMECE Nvb -8 Vacuv Bsh Cluba Caada IMECE-3 Aalycal Ivsga f Mcwav Hag Mhaad bul Hssa ad Pashaa Dua Schl f Mchacal ad Maals Egg Washg Sa Uvsy Pulla WA USA ABSAC Mcwav hag s vy ppula ad wdly usd f wag up fdsuffs qucly. Hwv -uf pau dsbu bad f cwav hag s a aj lg fac f s applca usd h fd dusy. h apd dcay f cd cwav ad h pal xsc f sadg wav a spsbl f -uf hag. hf s pa sudy h cuplg bw cwav ppaga ad gy asf h sys pdc pau dsbu. I hs pap a clsd-f aalycal slu s psd pdc h pau dsbu wh a cyldcal shap fdsuff ud cwav hag by slvg a usady gy qua. h splfd Maxwll s qua s slvd f lcc fld dsbu; Pyg h s plyd calcula cwav pw f lcc fld. h suls shw ha h pau h bdy s vy ssv s ad. hs aalycal slu ca b usd vsga h fluc f vaus paas cwav hag.. INODUCION I cwav hag h lcagc fld plas h lculs f dlcc aals ad cas dpl s ha caus hs lculs a. h lcula fc sulg f hs dpla a causs ha ga h bdy []. Du hs al ha ga capably cwav hag ca pvd pp s f pau wh h lw hal cducv pduc spcally fd s. Hwv h pau dsbu wh h fd s usually hghly -uf f cwav chqu s plyd f hag []. h uv hag s paly causd by h -uf dsbu f cwav gy h fdsuff du facs such as dlcc lss pa dph hcss shap ad s f h pduc [3]. I a xpal sudy Saa ad Wag cfd h fluc f dlcc pps f aal pau dsbu [4]. Guasaa ad Yag pd ha h pulsag cwav pvds uf hag ha cuus cwav [5]. Fuawaash ad Suu [6] pd sadg wav s spsbl f uf hag sall s fdsuff whl apd dcay f cd wav s spsbl f lag s fdsuff. h xss a ub f ucal ws sudy cwav hag [7-9]. Ayappa al. [7] pd ha shap cs dgs f sapl ca facla apd hag. Icas fa c ad duc su c a ca pvd fas hag a [9]. Saaa al. [] cducd dal aalyss f cwav hag f D l-wa uls slab suppd by cac allc ad cps plas. h sudy suggss ha allc supp ca pv hag ffccy ad duc -ufy. l f dff paas such as gy cps dlcc paas ad d f cd cwavs w als xsvly sudd [9-]. Ms f h al suds w dvd dal aalyss f cwav hag by xpal ucal hd. Flscha [] cad u a aalycal vsga f pdcg pau D bf slab. Hwv s f h fdsuff qus w h dsal aalyss f gy qua accualy pdc h pau dsbu wh h bdy. Cspdg Auh: l Fax Eal: dua@al.wsu.du Cpygh by ASME Dwladd F: hp://pcdgs.asdgalcllc.as.g/ /9/6 s f Us: hp://

2 I hs w w dvlpd a cpl aalycal slu f pdcg pau dsbu wh h cyldcal shap fdsuff. h s f h pap s gad as fllws. A gal ahacal dl f cwav hag s psd alg wh buday cds assups ad appxas. h a splfd f f Maxwll s qua s slvd sa h lcagc fld ad cwav pw absp. Nx h gy qua s slvd by gal asf chqu ad a clsd-f slu f pau qua s bad. Fally w ps a fw psav suls basd hs aalycal xpsss. h a w appachs calcula cwav pw absp: Pyg h ad ab s law. Mcwav pw fula by ab law s apppa f buly ad hc sapl [7] wh all flcs a gally glcd. O h h had Pyg h s gal ad ca b usd f sall fd s such as uggs. I pdcg pau Pyg h s uch accua ha ha f ab s law spcally h buday g [8]. Hc hs sudy Pyg h s usd calcula h vluc ha suc f h gy qua.. Assups h assups f hs aalycal w a: Fd sys s la ad bys la aal csuv laws; Elcualy cd s sasfd wh h sys; h agc pably ca b appxad by s valu f spac; v Dlcc pps a pau dpd; v Uf pla EM cwav pg; v hal pps a pau dpd. Sla assups ca b fud h al ws [7 ]. Fg.: Mcwav hag f a cyldcal fd f bh p ad b sufacs.. HEOY AND MAHEMAICA MODE Mcwav hag ca b dscbd by w ss f dffal quas: lcagc fld qua ad gy qua. h lcagc cwav s gvd by Maxwll s quas [3] B E a D H b D v c B d wh E s h lcc fld B s agc duc D s h lcc dsplac H s h agc fld sy s h cu dsy ad s h chag dsy. h gvg gy qua f a cyldcal shapd bjc fgu- ud cwav hag s gv by: Q wh s h hal dffusvy s h hal cducvy s h pau fld ad Q s h cwav pw absp. v. Buday Cds: Fgu shws a cyldcal bjc subjcd cwav pg f h p ad b sufacs. hf h gal cuy buday cds f lcc ad agc fld vcs a csdd b sasfd a h p ad b sufac f h bjc. F pau qua h b buday cds a usd a all f sufacs h wh s h al pau h s h cvcv ha asf cffc. Sc hs s a axs-syc pbl syc adabac cd s psd a h cl f gy qua. 3 ANAYICA SOUIONS 3. Mcwav Pw Ga Wh h assups lsd abv; h Maxwll s qua a suc-f da bcs a day dffal qua. I uf pla wav bh lcc ad agc flds a al h dc f ppaga. hus h splfd Maxwll s qua f uf pla wav s gv as [7-]: E E 3 wh s h ppaga csa ad ca b psd as [7] wh Cpygh by ASME Dwladd F: hp://pcdgs.asdgalcllc.as.g/ /9/6 s f Us: hp://

3 3 Cpygh by ASME phas fac a c f ad aua fac a c f Wh h us f buday cds h lcc fld dsbu wh h sys ca b calculad as: E E 4 wh asss cffc ad flc cffc ad h sc pdac [3]. Nw usg h lcc fld dsbu ad h Pyg h h cwav pw dsspa wh h bjc ca b fud as E Q cs cs 5 abl : Igal asf paas. f abl f df f vaus paas. Paas Spac vaabl Spac vaabl asf d d Ivs fula Kl N s cs Egvalus psv s a Nala Igal d d s cs 3. Aalyss f Egy Equa I hs sudy spaa f vaabls ad gal asf chqu s usd slv h gy qua. h gal asf chqu s a aalycal hd slv buday valu pbl whl spaa f vaabls s usd f h buday valu pbl. apply gal asf chqu h gvg qua s splfd Q 6 wh x. H Hal asf s usd v h spac vaabl ad Fu asf s plyd f vg spac vaabl. fd h pp ls ad chaacsc fucs a psav auxlay pbl wh buday cds s slcd f ach asfa. Wh hs w asfas h qua bcs a spl day dffal qua. Nx h fs d dpd day dffal qua s slvd. Fally h vs f ach asf s appld g h clsd-f slu f h pau qua. h pp ls asfs chaacsc fucs a shw h abl wh ad a h gvalus ad h.h cpl slu f gvg ha qua 6 s adly gv by x s cs 4 7 wh cs s d Q s cs Dwladd F: hp://pcdgs.asdgalcllc.as.g/ /9/6 s f Us: hp://

4 abl : Maal pps ad pu paas. Maal pps ad paas Valu Spcfc ha capacy c p /g K 3 hal cducvy W/ K.466 Dsy g/ 3 3 Dlcc cs. 45 MH 3.5 Dlcc lss 45 MH 9.6 Phas fac adas/ 88 Aua fac adas/ 44. flc cffc.73 asss cffc.3 Phas agl adas -3.9 Ha asf cffc h W/ Ial pau C 5 Suudg pau C 5 Icdc cwav I = I B W/c 3. gh f cyld c adus f cyld c.5 fa f lcal axa a f absbd cwav pw ca b fud basd hs paas bf dsgg a bjc f cwav pcssg. h xac lca f axa s spcally pa cas f cwav a f blgcal ssu ad cac clls. 4. ESUS AND DISCUSSION h aalycal slu f lcc fld dsbu cwav pw ga ad pau dsbu wh h fd cyld a valuad wh h aal pps ad paas lsd abl. Fu dff bf cylds wh sa bas da a csdd dsa h gal bhav f h ha asf wh. I cwav hag h lcc fld dsbu cwav pw absp ad pau vaa wh h aal a lad. hf s pa udsad h bhav f lcc fld ad vluc ha ga h sys. h lcc fld dsbu alg h axal dc s psd fgu a f fu dff cass basd h lgh f h cyld. F cvc cpas a ald axal vaabl / s usd hs sudy. suls shw ha h lgh f h fd cyld has a sgfca ffc h lcc fld dsbu. F sall cyld h axu lcc fld sgh s fud a h ddl f h cyld whl f lg cyld h axu fld sgh ccus a h bh d f cyld. h xsc f lcal axa s a sul f sac du h ac f asss ad flc wavs. h ha gad by h cwav clsly fllws h lcc fld dsbu h sys as shw fgu b. Sc w usd a uf pla wav h s vaa lcc fld vluc ha ga h adal auhal dc. h aalycal xpss f pw dsbu qua 5 pvds h fucal lashp ag pw lgh fqucy ad dlcc pps. hf h Fg.: a Elcc fld dsbu b cwav pw dsbu & c avag pw absp dsbu. 4 Cpygh by ASME Dwladd F: hp://pcdgs.asdgalcllc.as.g/ /9/6 s f Us: hp://

5 h avag pw dsy s shw fgu c. F a gv dlcc pps ad cwav fqucy h avag pw dsy s hghs f a cyld lgh f. c bcaus f h fa f w sac pas h lcc fld. h cwav pw absp wh h sys s usd as a ha suc h ha qua. Hc h pw dsbu paly dcas h cwav hag ad h sula pau dsbu. Fgu 3 shws h w dsal pau dsbus f dff lgh cylds a 6 scds. I all cass h pau s h hghs alg h cl f h cyld. Ag all cass h w dsaly f h pau dsbu s vvd f =3.75 c spcally a h bh ds du h psc f sac pas axa pw absp ad hal cvc. h aalyc xpss als dcas ha h pau dsbu h adal dc wll chag sgfcaly wh cvcv ha asf cffc. Fg.3: pau cu f dff lgh cylds. All aal hal ad lcagc pps a psd abl. h pw ad pau dsbu dff lgh cylds dcas ha h gh b a pu lgh f a gv dlcc aal ad fqucy. hs pu lgh wll b lad h sac lgh f a gv dlcc pps ad cwav fqucy. hf a ffc hag sagy f fd pcssg usg cwav ca b dvd f h spaal dsbu f cwav pw ad pau. Fuh aalyss f pau qua Eq. 7 dcas ha h spaal dsbu f ha s als a fuc f hag. h pau dsbu alg h cl f cylds s shw fgu 4. hs fgus val ha h pau cass cally wh ad ala f pau dsbu s fud as a fuc f. Wh h casg h dffc bw h u ad axu pau als cass. Sc hag a s dcly ppal h cwav pw absp pau ss shaply.5 c bf cyld ha ha f h hs as h cass. O h h had h pau ss vy slwly h.5 c cyld. h axu pau dffc 9 sc hag f cyld lgh f.5 c.5 c 3.75 c ad 5. c a 4 C 8 C C ad C spcvly. h hgh pau dffc causs h h ad cld sps ad uv pau wh h sapl. F hs suls s vd ha h ha h pu pw ad h lgh f h cyld slf s a pa paa cl h h sps ad pau ag. 5. CONCUDING EMAKS A clsd f aalyc slu s bad f pau wh a cyldcal shapd bjc f cwav hag f bh sds. hs aalycal sudy suggss ha a slgh chag lgh culd caus a sgfca chag pau vaa wh h sapl. h pu ga f vaus paas f uf hag ca b bad by gus vsga f h fucal lashps gv by h aalycal slu. hs aalycal slu ca b a asy ad ffc l aaly h pac f h paas f xapl dlcc pps pau dsbu wh h aals. 6. EFEENCES. Olva M. E. C. Faca A. S. Mcwav hag f fdsuff ual f Fd Egg Gsy E. O. C.; as S.; as.; Nufy f sufac paus af cwav hag f puly a ual f Mcwav Pw ad Elcagc Egy Cpygh by ASME Dwladd F: hp://pcdgs.asdgalcllc.as.g/ /9/6 s f Us: hp://

6 phaacucal cwav vaccu dyg. Pwd chlgy Saa N.; Wag C. A aalyss f pau dsbu cwav hag f fds wh uf dlcc pps ual f Chcal Egg f apa Guasaa S.; Yag H. Effc f xpal paas pau dsbu dug cuus ad pulsd cwav hag ual f Fd Egg FuawaashY.; Suu. Nucal aalyss f cwav hag f a dlcc Ha asf-asa sach Ayappa K. G.; Davs H..; Caps G.; Davs E. A.; Gd.; Mcwav hag: a valua f pw fulas Chcal Egg Scc Yag H. W.; Guasaa S. Cpas f pau dsbu dl fd cylds basd Maxwll s quas ad ab s law dug pulsd cwav hag ual f Fd Egg Pcu P. A.; Fad A.; Sa X.; Sul I..; Aau Mcwav hag f cd p pas as a fuc f fa c ual f Fd Scc 7 7 N. E57-E63.. Saaa S. K.; Basa.; Sgupa B. hcal aalyss f cwav hag f l-wa ulss suppd cac allc cps plas Iaal ual f Ha ad Mass asf Basa. l f laal ad adal adas ffc cwav pcssg f fd cylds Chcal Egg Scc Flscha G.. Pdcg pau ag fd slabs udgg sh-/hgh-pw cwav hag ual f fd gg Fg.4: pau dsbu alg h cyld lgh a =. a = 3 sc b = 6 sc ad c = 9 sc. All aal hal ad lcagc pps a psd abl. 3. Kl A.; ss S.; Nagy.; Palla E.; Py-Hd K. Mappg f pau dsbu 3. ussy G.; Pac.A.; Fudas ad Idusal Applcas f Mcwavs ad ad Fqucy Flds: Physcal ad Chcal Pcsss Wly Chchs Os M.N. Ha Cduc Wly Nw Y Cpygh by ASME Dwladd F: hp://pcdgs.asdgalcllc.as.g/ /9/6 s f Us: hp://