Internatona Journa of Computer and Eectrca Engneerng, Vo., No. 4, Augut, 793-863 Some Numerca Meod for Temperature and Ma Tranfer Smuaton on e Dehydraton of Her Md. Rau Iam, Memer, IACSIT and Norma Aa Atract Advance n her aed product preervaton and technooge are very gnfcant n order to reduce pot-harvet oe. The dynamc maematca mode of concurrent heat and moture tranfer are eng etahed for e muaton of temperature and moture dtruton nde e her matera durng dehydraton potenta of her n a a-haped od. Maematca modeng preent e exchange of heat and ma tranfer etween matera and dryng ar. Fnte-dfference meod (FDM aed on Crank-Ncoon wa ued to dcrete a paraoc type parta dfferenta equaton (PDE. The key purpoe of tudy to utrate e muaton of tropca her dehydraton rough ome numerca meod uch a Jaco, Gau-Sede and Red-Back Gau-Sede. Th tudy focue on e mpementaton of equenta agorm on e muaton. 3D geometrc vuazaton y COMSOL Mutphyc and graphca numerca reut of FDM approxmaton n ma and heat tranfer demontrate e reut of tudy. The contruton of tudy a fourhng and modfed maematca muaton n repreentng e concrete proce of dehydraton n her product aed ndutry. Mot erma and moture mode are emprca raer an eoretca. Therefore, e novety of paper e et ource of erma and moture data for e commerca tropca her dehydraton derved from e maematca mode n order to avod hgh prototype cot and to mprove naccurate condton and proce parameter w e advancement of dryer technooge. The computatona patform aed on Inte Core Quad proceor w MATLAB oftware. The performance anaye of Numerca meod are preented n term of executon tme, computatona compexty, numer of teraton, error, accuracy, and convergence rate. Index Term Paraoc Equaton, dehydraton, tropca her, teratve meod, heat and ma tranfer. I. INTRODUCTION The potentaty of Hera ector ha een dentfed a e arget contrutor to e grow of e Maayan economy. Maayan her are of uperor quaty and utae for e Manucrpt receved Novemer, 9. Th work wa upported n part y Mntry of Scence, Technoogy and Innovaton (MOSTI, Maaya under Grant 78363. Md. Rau Iam wa w e Facuty of Informaton Scence and Technoogy (FIST, Mutmeda Unverty, 7545 Meaka, Maaya. He currenty workng a a Reearch Atant n Inu Sna Inttute, Facuty of Scence, Unverty Technoogy Maaya, 83 UTM Skuda, Johor. (Correpondng auor moe: 6-6-48986; e-ma: md.rau.am5@mmu.edu.my. Dr. Norma Aa w Inu Sna Inttute, Facuty of Scence, Unverty Technoogy Maaya, 83 UTM Skuda, Johor. She workng a a Senor Lecturer a we a a Reearcher n e maematc department, UTM. (Phone: 6-755-364; Moe: 6-7-9994. 73 oca market. Maaya ha over pant at poe medcna vaue. Demand for hera product ke Medcna pant and her aed product uch a pegaga, kacp fatema, ma kacg (oca name for heay, eauty and youngerne, are on e re a conumer are ecomng more hea and eauty concou. The Medcna pant and her aed product need to e proceed to proog er hef fe. Hera producer erefore have to e aware of advance n Medcna pant and her aed product proceng and pot harvet technooge n order to effcenty reduce pot-harvet oe. It neceary to dry e her aed product to a certan eve after harvet. Dryng remove e water or moture from e her aed product o at actera, yeat and mod cannot grow up and po e her product epecay for e purpoe of torage year and year. It ao ued to reduce e cot or dffcuty of packagng, handng and tranportaton. Smuaton reut and nformaton of dryng knetc of her product uch a dryng rate, tme-temperature-moture content dtruton, a we a eoretca and emprca approache to moture movement, very eenta for e preventon of quaty degradaton and for e achevement of fat and effectve dryng. A greater part of dryng R&D effort reae nowaday to e agrcutura egment []. Nowaday, e ue of technoogy ha een a mut n amot a of ndutre n Maaya to mprove er ervce and productvty n order to fuf e cutomer demand. Dryng procee are wdey ued n her preervaton ut a centfc approach ha not o wdey een apped, o raer emprc rue are often ued to et up ndutra producton, partcuary n ma-medum frm. The core pont of her dryng proce water remova up to partcuar moture content to prevent her from mcroa poage and deteroraton reacton and to ncreae e product hef fe [5]. It a compex procedure reatng concurrent heat and ma tranfer phenomena. The formuaton of uffcent maematca mode to optmze e proce-eadng can e enhanced product quaty and a reducton n proce cot. Improvng peed and product quaty requre a reducton n decon atency whch decreae e amount tme t take peope to hare nformaton and make crtca decon, a aong a vaue chan of upper, partner and cutomer. Seectng an approprate dryng mode to evauate e dryng dtruton very mportant to get et predcton of dryng knetc. In e dehydraton proce, t mportant to know e temperature and moture dtruton n e matera and t
Internatona Journa of Computer and Eectrca Engneerng, Vo., No. 4, Augut, 793-863 change durng dehydratng; e preented maematca mode ae to predct. The governng dfferenta equaton decrng moture content and temperature dtruton were oved numercay. The maematca mode ung PDE w e hepfu to etmate e dryng rate at any moture condton of e matera and to etmate dryng tme for partcuar tak durng dehydraton of her aed product. Computer program wa deveoped to ove e et of fnte dfference equaton. Computer muaton a powerfu too for achevng meaurement of change n temperature and moture durng dehydraton proce. Smuaton reut and nformaton of dryng knetc of her matera uch a tme, temperature, moture content dtruton, a we a eoretca approache to moture movement, very eenta for e preventon of quaty degradaton and for e achevement of fat and effectve dryng. Such nformaton w e very uefu to optmze producton procee of her dred. The ncreang deveopment of computer program had a great mpact on e quaty evauaton of agrcutura product. Inventon of e computer ao nfuenced e fed of numerca anay, nce nowaday onger and more compcated cacuaton coud e done. However, e oectve of tudy are: ( To derve muaton of moture and temperature veru tme n producng dehydraton of her product aed on convecton-dffuon mode ung parta dfference equaton (PDE and ( To provde ome meod for ovng e paraoc PDE equaton; and to anay performance of each meod preented n term of temperature and moture content vaue. The maorty of erma property mode are expermenta raer an hypoetca; pecfcay mot of em are aed on tattca curve fttng reatvey an hypoetca dervaton concernng ma and heat tranfer tudy. Water treated a a nge, homogeneou part of e her product n modeng. It coud e dagreed at e erma properte of water n e her depend on how t confgured or ound wn e product [6]. In fact of ntegraton technooge n her producton, t neceary to muate more often n order to contro prototype cot and to muate etter n order to get proce parameter w e needed accuracy. Hence, ome modeng tude are eenta on heat and ma tranfer feature to enhance dryng condton and proce parameter []. The hgh contruton of paper uccefu modfed e maematca muaton n repreentng e actua proce of dehydraton n commerca her ndutry n term of heat and ma tranfer nde tropca her matera. Accuracy greater an -5 % rarey requred for mot engneerng heat tranfer cacuaton performed n commerca her dehydraton [6]. Th happen ecaue of e error durng wrongy condered oundary condton uch a e temperature and veocty of ar woud overhadow error caued y mprece erma properte. One way to get e ource of erma property data are predcton and muaton equaton aed on temperature and phyca tructure (denty, ze and confguraton of vod pace. The orgnaty of tudy to preent 74 greatet ource of erma and moture property data for commerca tropca her dehydraton rough heat and ma tranfer equaton aed on temperature and moture apect to evade hgh prototype cot. It ao can mprove dryng condton and proce parameter a we a evouton of dryer technooge w needed accuracy. II. MATHEMATICAL SIMULATION MODELING Dryng knetc can e modeed maematcay aed on Fck aw of dffuon. The muaton of varou product dryng ytem nvove ovng a et of heat and ma tranfer equaton. Marou et a. [9] decred tranport phenomena a foow:. Heat tranfer : Convectve heat (energy tranfer from e ar to e food urface (externa heat tranfer Conductve heat tranfer wn e food (nterna heat tranfer and ar,. Moture tranfer : Moture tranport wn e food toward t externa urface (nterna ma tranfer The frt dryng proce heat tranfer to e product from e heatng ource and e econd ma tranfer from e nteror of e matera to t urface and from e urface to e urroundng ar. The heat and ma tranfer equaton are preented n e mode eow are governed y e foowng PDE. In mode, e moture tranport are y dffuon n ony one drecton; from e nteror of e product to e ar ampe nterface, and evaporaton take pace at e nterface. Shrnkage of her product durng dryng an notceae phyca ncdent, whch occur concurrenty w moture dffuon. Thee mode had een preented y Md Azharu Karm and Hawader [7]. To mpfy e mode, Md Zaharu Karm and Hawader [8] were made e foowng aumpton:. Moture movement and heat tranfer are one-dmenona. No chemca reacton perform durng dryng, to e prece matera, ar and moture erma and chemca properte are contant wn e range of temperature condered.. The matera ecome hrnkage after dryng progree.. Unform dtruton of ar rough e dryer. Ma tranfer equaton can e wrtten a: M u = D t, ( and mary, e heat tranfer equaton can e wrtten a: T u = α t ( W e foowng nta (IC and oundary condton (BC of equaton ( and ( are gven eow: IC: M x = M,, = T x = T = BC: At ; = and at, moture aance D um x = h ( M M (. eff = m e
Internatona Journa of Computer and Eectrca Engneerng, Vo., No. 4, Augut, 793-863 and = and at, heat aance x = ( k ρ c p ut = h( T T h ρ( M M hfg (. a m e TABLE : PARAMETERS OF MASS AND HEAT TRANSFER EQUATION Notaton haf ckne of dryng pecmen (m c p pecfc heat (J/kgK D dffuon coeffcent (m/ h convectve heat tranfer coeffcent (W/mK hfg enapy of evaporaton (J/kg ma tranfer coeffcent (m/ hm k erma conductvty (W/m K L ckne of e dryng pecmen (m M t T u x Sucrpt moture content of pecmen (g/g dry tme ( temperature ( C hrnkage veocty (m/ dtance from e centre of e dryng pecmen(m S nta, reference ar a equrum e effectve eff matera (her ampe m mo III. DISCRETIZATION Dcretzaton nvoved w e tranformaton of contnuou dfferenta equaton nto dcrete dfference equaton approprate for numerca computng. A dcrete form can e found y ung FDM. Betta G., et a [4], Amendoa and Queroz [3], Tarz and Hamduahpur [], Ahmet Kaya et. a. [], Md Zaharu Karm and Hawader [7][8] and Queroz and Nera [] were oved er dehydraton mode ung FDM. In tudy, Crank-Ncoon cheme wa ued to decrte e dffuon and convecton term for e equaton ( and (. Suequenty, ome teratve meod were apped to ove o e equaton. In order to muate e ma and heat tranfer numercay, e Crank-Ncoon FDM meod wa apped to dcrete e equaton ( and (. Wang and Brennan [3], Md Zaharu Karm and Hawader [8], Ahmet Kaya et a. [] utzed mpct Crank-Ncoon cheme w e numerca procedure n er experment. The dryng matera condered a a n a of ckne, L( at a unform nta temperature, T and moture content, M accordng to Md Zaharu Karm & Hawader [8]. For meod, e muated matera (tota ckne, L are ced up nto N ampe and e tme (tota duraton T are pt nto N ampe: h= x = /N and k= t = T/N. Accordng to Crank-Ncoon cheme (where, repreent poton and, repreent tme, e dervatve of dffuon term for e equaton ( and ( can e wrtten a; M D M, M, M, M, M, M, D = ( Δx ( Δx (. T α T, T, T, T, T, T, α = ( Δx ( Δx (. And e dervaton of convecton term for o equaton are; u M, M, M, M, u = (.3 ( Δx ( Δx u T, T, T, T, u = (.3 ( Δx ( Δx The governng equaton decrng dryng charactertc were oved numercay. Phyca properte of e tropca her condered for e experment, were adopted from Md Zaharu Karm & Hawader [7]. A computer program wa deveoped y MATLAB oftware to ove e et of PDE. A. Iteratve Meod Iteratve meod can e performed to ytem a many a, varae. Thee arge ytem are to ove e PDE. Startng from a prmary gue, teratve meod form conecutve etmate at meet to e prece outon ony n e mt. A convergence condton tated n order to make a decon whe an adequatey prece outon ha (expectanty een found. There are many veron of teratve cheme for ovng e PDE, we focu e mpementaton of ome popuar teratve over here ung ome equenta programmng, uch a Jaco, Gau-Sede, and Red-Back Gau-Sede Meod [4]. A ref decrpton of each meod gven eow. B. Jaco Iteraton Meod (JB The Jaco teraton meod attruted to Car Jaco. Jaco teraton a mpe and fundamenta pont teratve meod. Jaco meod compute e vaue of moture or temperature y ovng for each component of x n term of oer y ( k ( k, =,, 3, m. (3 x = ( a x / a C. Gau Sede Iteraton Meod (GS The Gau Sede meod an enhanced veron of e Jaco meod deveoped y e Car Fredrch Gau and Phpp Ludwg von Sede. The Gau Sede (GS meod compute e vaue of moture or temperature y ( k ( k ( k x = ( a x a x / a, =,, 3,..m (4 < > D. Red-Back Gau Sede Iteraton Meod (RBGS The Red-Back Gau Sede (RBGS meod contan R B u doman, Ω and Ω. There ext a communcaton R B etween Ω and Ω. The cacuaton of meod hown y e equaton eow: R grd cacuaton at Ω : 75
Internatona Journa of Computer and Eectrca Engneerng, Vo., No. 4, Augut, 793-863 ( k ( k ( k = ( a x a x a, (5 x / < > B grd cacuaton at Ω : ( k ( k ( k x = ( a x a x / a, (6 < > For every meod aove, ( k x e unknown current vaue n x durng e k teraton, =,, N and k =,, ( k x e unknown n x durng e, N and k =,, x ( e nta vaue for e k teraton, =, unknown n x durng e k teraton, =,, N and k =,, a e coeffcent of A n e row and e vaue a. ( k x and coumn A e teratve meod were eng repeated a proce over and over unt an approxmaton of e outon wa reached. The toppng crteron at wa ued for a e meod, depended on a convergence toerance, ε uch ( k ( k at x x ε. Equaton ( and ( wa oved for e current moture content, M ( k and temperature, ( k ( k T n term of x hown aove. Round No Start Inta condton Boundary condton t t t = Δ Numerca Meod under conderaton Stoppng crteron met? New M End Fgure : Sequenta agorm of paraoc equaton B. MATLAB Program Baed on agorm aove, programmng n MATLAB wa deveoped to ove e equaton. Fgure how a part of e program. Ye and T Count IV. ALGORITHM AND PROTOTYPE A. Procedure Fgure how e fow of cacuaton to muate temperature and moture ehavor nde her matera durng dehydraton proce. The tem count repreent e numer of teraton taken to fuf e toppng crteron. Meanwhe, round decared a numer of tme tep n order to get new M and T vaue. Fgure : A part of MATLAB program 76 V. NUMERICAL RESULT AND DISCUSSION In ecton, ome numerca reut are preented at utrate e ehavor of e meod preented n ecton 3. The patform for computaton aed on
Internatona Journa of Computer and Eectrca Engneerng, Vo., No. 4, Augut, 793-863 Inte Core Quad proceor w wndow XP operatng ytem and MATLAB R8a oftware. An anay of e ome teratve meod are codered. In order to evauate e capate and performance of oe teratve meod of e equenta agorm, numerca reut are demontrated n Tae oe were otaned from e muaton of e data confguraton. TABLE : DATA CONFIGURATION c p D hfg k L M t u 5.4(J/kg K 6.6x - 3586(J/kg.87(W/m K 4mm 4 kg/kg 8.3(m/ Fgure 5: Evouton of Moture content nde her matera durng dehydraton w tme; T=4 c, v=.3m/ A. Geometrc Vuazaton Of The Mode Dehydraton The COMSOL Mutphyc oftware wa ued to vuae e 3D geometry of e heat and moture tranfer equaton n ovng e dehydraton proem a hown n Fgure 3 and Fgure 4. Fgure 6: Evouton of temperature nde her matera durng dehydraton w tme; T=4 c, v=.3m/ Fgure 3: 3D Temperature vuazaton on e tropca her (t=8 Fgure 4: 3D Moture vuazaton on e tropca her (t=8 Smuaton of e dehydraton The graphca numerca reut of moture content and temperature ung JB,GS and RBGS are dpayed eow. Fgure 5 how e moture dtruton and Fgure 6 how e temperature dtruton durng dehydraton. The o dtruton were wn e ampe of tropca her matera durng dryng at 4ºC w ar veocty.3m/. From e o fgure preented aove, oerved e paraoc curve of e moture content and temperature ehavour. For a e outon meod under conderaton, how e moture content and temperature were ook ke contant ecaue er change were very tte and ecame arge dfferent change after 44 econd for moture and 6 econd for temperature. At e egnnng of e dehydraton proce e evouton wa practcay contant and unform unt e at perod t tarted dfferent. Even e muaton reut dd not eem much dfferent for a e teratve meod, e performance of every meod wa dfferent. The numerca anay n e next ecton w proof at. B. Performance evauaton In ecton, e reut of Numerca anay nvoved e tudy of ome teratve meod of computng numerca data n tropca her dehydraton. The anaye of performance nvove e convergence and e accuracy of e numerca muaton data. Tae 3 how e convergence condton for every teratve meod n term of tme executon, numer of teraton, computatona compexty and convergence rate. It ao how, e accuracy meod wa determned y computng Root Mean Square Error (RMSE etween e new and e prevou teraton. The formua gven a e foowng, RMSE = N ( ( k ( k x x / N 77 The comparon wa done for e.e -5 toerance rate and
Internatona Journa of Computer and Eectrca Engneerng, Vo., No. 4, Augut, 793-863 5 data ze. TABLE 3: NUMERICAL ANALYSIS FOR EACH METHOD IN MASS AND HEAT SIMULATION Numerca Anay N=5, Toerance =.e-5 Tme Executon( Jaco. 3 Ma Smuaton Gau Sede. 975 Red Back Gau Sede. 88 Jaco. 395 Heat Smuaton Gau Sede. 79 Red Back Gau Sede. 8 Iteraton 99 6 55 3 8 6 Convergence Rate com puta ton a com pex ty mut pcat on addt ona Aoute Error.6.56.58.5 664 456.549 45e-5 RMSE.353 86e-5 78 48 795 6 9.866 3e-6 5.6 7e-6 495 4 3348 8 9.376 58e-6 7.675 67e-6 5 34 448 7.49 4e-6.4 4e-6 66 8.676 3e-6 4.335 89e-6 36 9 8.6 4e-6.833 59e-6 C. Convergence Comparon Convergence comparon among Jaco, Gau-Sede and Red Back Gau-Sede teratve meod are made n term of e executon tme and e numer of teraton at t take to converge. Fgure 7: Convergence anay among e numerca meod for ma and heat muaton In Fgure 7, e convergence n term of executon tme and numer of teraton how at eer n ma or heat muaton, RBGS meod perform fater an JB and GS meod. RBGS provde e owet numer of teraton and e hortet tme of executon to converge foowed y JB meod and GS meod. The executon tme depend on e numer of teraton and computatona compexty. Fgure 7 how at JB take hghet executon tme compared to GS and RBGS n o muaton. Durng e muaton of moture content rough dehydraton, JB need 44 teraton more an RBGS to converge. Whe GS ony need more 5 teraton compared to RBGS. In contrat durng temperature muaton, aough RBGS gve e owet teraton to converge, ut e dfference etween RBGS, GS and JB are not o much an ma muaton. Computatona compexty refer to e numer of armetc operaton nvoved n numerca muaton. The computatona compexty of each teratve meod ncreang y e numer of teraton. Tae 3 how, JB produced e hghet numer of operaton n mutpcaton and addton. It foowed y GS and RBGS. The reut ao how at RBGS meod ha e fatet rate of convergence among oer meod, oe took under conderaton n tudy. RBGS ha.48% fater an JB and ony.6% fater an GS n term of convergence rate. The reut aove proved at RBGS meod e aternatve teratve meod w e owet computatona compexty a we a e mnmum tme of executon, numer of teraton and convergence rate. D. Accuracy performance The accuracy meod wa determned y computng root mean quare error. The owet vaue of root mean quare error ndcate e mot accurate meod. Aoute error ao can decre e accuracy of each meod. From e tae 3, t hown at RBGS provde maet vaue of RMSE a we a aoute error. VI. CONCLUSION AND DISCUSSION A maematca muaton mode ung e one dmenona paraoc equaton regardng e moture and temperature ehavor of tropca her durng dehydraton ha een preented. Three teratve meod uch a Jaco, Gau-Sede and Red Back Gau-Sede are tuded. Accordng to e Tae 3 and Fgure 7, t proved at e RBGS meod e et meod to ove heat and ma tranfer equaton numercay foowed y Gau Sede and Jaco meod. The reut of numerca anay uch a tme executon, numer of teraton, computatona compexty, root mean quare error and rate of convergence ha proved at dehydraton mode capae to muate ma and temperature dtruton rough numerca meod approach. Concernng e evouton of ntegraton technooge n e producton of her aed product epecay tropca her, t neceary to muate more often n order to avod hgh cot and to get etter proce condton and parameter w e derae accuracy. The contruton of tudy to uccefuy modfy e maematca muaton n repreentng e genune proce of dehydraton at e her ndutry. It ao tme conumng and capae to reduce e rk of rea experment n e actua proce. The future contruton of tudy can e e ue of parae agorm to ove e mode of dehydraton. Parae agorm w mprove numerca computaton partcuary whe dehydraton nvove w huge data ze. The computatona tme and compexty ncreae durng huge data ze muaton/cacuaton. Hence, parae computaton ecome an ogaton. ACKNOWLEDGMENT The auor acknowedge e Inu Sna Inttute, Unverty Technoogy Maaya and Mntry of Scence, Technoogy and Innovaton (MOSTI, Maaya for e fnanca upport under Reearch Grant 78363. 78
Internatona Journa of Computer and Eectrca Engneerng, Vo., No. 4, Augut, 793-863 REFERENCES [] Ahmet Kaya, Orhan Aydn and Irahm Dncer, Numerca modeng of heat and ma tranfer durng forced convecton dryng of rectanguar mot oect, Internatona Journa of heat and ma tranfer, vo. 49(7-8, 6, pp. 394-33. [] Ahmet Kaya, Orhan Aydn and Irahm Dncer, Expermenta and numerca nvetgaton of heat and ma tranfer durng dryng of hayward kw frut (Actnda Decoa Panch, Journa of Food Engneerng, vo. 88(3, 8, pp. 33-33. [3] Amendoa, M. and Queroz, M.R., Maematca meodooge for cacuatng e ma dffuon coeffcent of anana durng dryng, Revta Braera de Engenhara Agrcoa e Amenta, vo. (6, 7, pp. 63-67. [4] Gampaoo Betta, Mamano Rnad, Davde Barant and Roerto Man, A quck meod for erma dffuvty etmaton: Appcaton to evera food, Journa of food Engneerng, vo. 9(, 9, pp. 34-4. [5] Curco, S., A FEM anay of tranport phenomena occurng durng vegetae dryng, Proceedng of e COMSOL Conference 9 Mano, 9. [6] Gavra, C., Heat and ma tranfer n convectve dryng procee., Proceedng of e COMSOL Conference 8 Hannover, 8. [7] Md Azharu Karm & Hawader, M.N.A, Dryng charactertc of anana: eortca modeng and expermenta vadaton, Journa of Food Enggneerng, vo. 7, 5, pp. 35-45. [8] Md Azharu Karm & Hawader, M.N.A, Maematca modeng and expermenta nvetgaton of tropca frut dryng, Internatona Journa of Heat and Ma Tranfer, vo. 48, 5, pp. 494-495. [9] Marou Z. B., Kranoud C. T., and Marno-Kour D.. Heat and ma tranfer modeng n ar dryng of food, Journa of food engneerng, vo. 6 (, 995, pp. 3-3. [] Muumdar, A.S., Some recent deveopment n dryng technooge approprate for poarvet proceng, Internatona Journa of Poarvet Technoogy and Innovaton, 6. [] Queroz, M.R. and Nera, S.A., Theoretca and expermenta anay of e dryng knetc of anana, Journa of food Engneerng, vo. 47,, pp. 7-3. [] Tarz, H.B. and Hamduahpur, F., Maematca modeng of dryng ed on a urface evaporaton ource term for couped energy and ma tranfer, Internatona Journa of Energy Reearch, vo. 3, 7, pp. 455-464. [3] Wang, N. and Brennan, J.G. A maematca mode of mutaneou heat and moture tranfer durng dryng of potato, Journa of Food Engneerng, vo. 4, 995, pp. 47-6. [4] Norma Aa, Md. Rau Iam and Nur Syazana Roy, A dynamc PDE over for reat cancerou ce vuazaton on dtruted parae computng ytem, n Proc. of The 8 Internatona Conference on Advance n Computer Scence and Engneerng (ACSE 9, Phuket, Thaand, 9, pp. 38-43. of evera Internatona Journa w hgh mpact factor and aocaton w ome Internatona conference and workhop organzed y Inu Sna Inttute. Her reearch nteret ncude Indutra Computng, Numerca Computaton, and Scentfc Computng & Hgh Performance Computng on Dtruted Parae Computer Sytem. Md. Rau Iam receved h Bacheor of Computer Appcaton (BCA degree from e Indra Gandh Natona Open Unverty, New Deh, Inda, n 4 and M.Sc n Informaton Technoogy degree from Mutmeda Unverty, Meaka, Maaya. Currenty he workng a a Reearch Atant at Inu Sna Inttute, n Scence Facuty of Unverty Technoogy Maaya, Johor. H reearch nteret ncude Dtruted Parae Computng, Numerca Computaton, Pattern Recognton, Image Proceng, Computer Von, and Artfca Integence. Dr. Norma Aa otaned her PhD (Indutra Computng: Parae Computng from Natona Unverty of Maaya n 4 and her M.Sc degree n Indutra Computng and BSc n Maematc from e ame Unverty n 997 and 99 repectvey. Currenty, he a Senor ecturer at e Maematc Department n Facuty of Scence, Unverty Technoogy Maaya (UTM and e Reearcher Head of Hgh Performance Computng Group a we n Inu Sna Inttute, UTM. She ha puhed over paper n evera referred Internatona ourna, conference, workhop, ecture note and ook chapter. She a revewer 79