Modelling of Diffusion Process in Porous Bricks

Transcription

1 hp:// Modellng of Dffson Process n Poros Brcs KRNIATI ORNAM, MASYKR KIMSAN, LA ODE NGKOIMANI 3, EDI CAHYONO 4 Deparmen of Archecre, Hal Oleo nversy, Jl.H.E.A Moodomp Kamps Ha Bm Trdharma, Andonoh Kendar INDONESIA Deparmen of Cvl Engneerng, Hal Oleo nversy, Jl.H.E.A Moodomp Kamps Ha Bm Trdharma, Andonoh Kendar INDONESIA 3 Deparmen of Physcs, Hal Oleo nversy, Jl.H.E.A Moodomp Kamps Ha Bm Trdharma, Andonoh Kendar INDONESIA 4 Deparmen of Mahemacs, Hal Oleo nversy, Jl.H.E.A Moodomp Kamps Ha Bm Trdharma, Andonoh Kendar INDONESIA rna.ornam@yahoo.co.d Absrac: - We consder dryng process of brcs made of sol and celllose mxre. The parcle szes of he sol are abo μm, whch are consdered o be clay. We apply a dffson ype eqaon o model he dryng process. The model s based on macro modelng, where he parcle and pore szes are consdered mch smaller compared o he sze of nals o measred he mosre conen of he area nsde he brcs. The model s a nonlnear dffson eqaon where he dffson rae depends on he mosre conen. The solon s comped analycally applyng a fne dfference mehod for one and wo dmensonal cases. The smlaon shows ha he dryng process of wo dmensonal case s slghly faser han of he one dmensonal case. The case s he dffson o he sde wall of wo dmensonal case where hs wall s does no exs n one dmensonal case. Key-Words: - Dffson eqaon, dryng process, macro modelng, mosre conen, pore sze, dffson rae. Inrodcon Ths paper examnes dffson process n brcs prodced radonally n home ndsry n Kendar Indonesa. I s a connaon of []. The brcs prodcon s dvded no 4 (for) smple sages.e. moldng, dryng, brnng, and nloadng. 500 brcs can be prodced n a day, and reqres approxmaely 3 (hree) wees o accomplsh he process. Based on seve analyss and aerberg lm es, he sol s classfed as sly clay wh sand. In moldng process, clay s mxed wh waer a specfc composon, hen molded n sandardzed shape le box. Ths s followed by dryng process n open ar wh drec snlgh for (wo) wees. Afer ha, hose brcs are brned by arrangng hem wh a hole n he mddle for he frewoods. Ths process aes 5 o 6 hors for each brnng process ha can reach more or less a hosand brcs. Then, he brned brcs wll be nloaded afer 4 o 5 days. A hs sage, mos of he brcs cold be broen, especally hose on he oer pars, as a resl of pachy hea ransfer from nsde o osde of hose brcs. Recen modelng on hea ransfer s repored n [, 3, 4, 5]. Hence here s conseqence for economc vale ha can be obaned from he brcs mare. Brcs are mos preferred bldng maerals de o s cheap and reasonable prce, good hermal nslaor properes, and ha hey are exposed and can be prodced locally hrogh home ndsry. Neverheless, brcs prodcon n home ndsry had enconered classc saon where he level of prodcvy s an o he prevos perod and ends o decrease as a conseqence of modes echnqe of prodcon process. In addon, envronmenal mpacs e.g flood and eroson mgh ense resled from he excavaon of he sol and loggng. There are some reqremens for brc o be sed as maeral consrcon n [6]. How hea ransfer wors on brc srface wll deermne he qaly of he brcs. Some nnovave fllers and desgn e.g. sawds, reed, corn, cocon wase, and hollow brc desgn [, 7, 8] demonsraes good performance snce he compressve srengh s hgher han he convenonal model. Typcally, 0% of brcs are consdered broen,.e. no meeng he compressve srengh reqremen (> 6 MPa), followng he brnng ISSN: X 87 Volme, 06

2 hp:// process sng frewood, snce here s pachy hea ransfer []. In erms of shrnage, abo 4% sze redcon n lengh, wdh and hcness from he begnnng nl he las sage [9]. Frhermore, he densy of brcs s vared beween.6 and.8 g/cm 3. By nowng he dffson process n poros brcs, s expeced ha effcency and effecveness mgh be measred, where mgh generae essenal mpac on prodcon cos. Ths sdy s essenal o ndersand he dffson of fld nsde he brc, no only drng he dryng process, b also afer he brc s lzed n he bldng consrcon. I s becase some dangeros fld may nflrae no he brc and poros maerals as no concree sded n [0]. Dffson n poros maeral s presened n []. Problem Formlaon The brc szes are cm n lengh, cm n wdh and 6 cm n hcness. A frs, s assmed ha he mosre conen (MC) n he whole body s smlar (rgh afer moldng process). Then, he mosre conen a brc s srface wll be smlar wh eqlbrm mosre conen (EMC), and nsde he brcs, he mosre conen wll decrease gradally. Moreover, a nfne me, he mosre conen n he brcs s dencal wh he ar mosre conen. To address he problem, frsly, s presmed ha he hcness of brcs s relavely small compared o s lengh and wdh. Therefore, he one dmensonal analyss s performed o examne he dffson process. Thenceforh, wo dmensonal analyss s condced based on conecre ha he hcness and wdh are relavely small compare o he lengh. These wo analyss are hen evalaed o compare her mosre conen. Shold hey share almos smlar vales, may be deermned ha hree dmensonal analyss s no reqred and he complee behavor s precsely clear. On he oher hand, frher analyss on hree dmensonal bass s necessaed o be carred o. 3 Mahemacal Model For wrng he mahemacal model, we wll se symbols presened he Table. The symbols are n he lef colomn and he physcal meanng are n he rgh. Table. Symbols and he physcal meanng sed n modelng Symbol Meanng x : Spaal varable y : Spaal varable z : Spaal varable : Temporal varable : Sae varable represenng mosre conen K : Dffson rae x : Paral dervave wh respec o x x : Paral dervave of wh respec o x : Graden The model s based on macro modelng, where he pore sze, parcle sze are assmed mch less sgnfcans compared o he sze of do nder consderaon. Hence, or mahemacal model has he form K ) 0 x d, x : 0 y d,, 0. () 0 z d3, (,, y, z For consan dffson rae, () s nohng else b he hea eqaon, where he dervaon of can be fond n many classcal sandard exboos. In [3] he dervaon for more general K has been dscssed. Ths allows he applcaons for nonlnear dffson sch as on wood dryng. Some maerals sch as wood show ha he dffson rae depends on he mosre conen. Some ypes of concree are almos mpermable when hey are compleely dry. I means ha he dffson rae become close o zero. Ofen, n some applcaon we may neglec he y and z componen of he spaal varables. Ths may happen f he hcness of he doman s mch smaller han he wdh and he lengh. For one ISSN: X 88 Volme, 06

3 hp:// dmensonal case, () has he form x K( x, 0 x d, 0. () Drng he dryng process of brcs, he EMC of he srondng ar acs as he bondary condon. EMC depend on he hmdy of he ar. If he process happens n an oven or n a laboraory, he EMC may be se a ceraned vale. On he oher hand, he nal condon s he MC of he brcs for example 00%. and Tables shold be nmbered as follows: Fg., Fg., ec Table, Table,.ec. If yor paper devaes sgnfcanly from hese specfcaons, or Pblshng Hose may no be able o nclde yor paper n he Proceedngs. When cng references n he ex of he absrac, ype he correspondng nmber n sqare braces as shown a he end of hs senence []. 4 Nmercal Mehod Whle we do no solve he model explcly, we solve nmercally. We apply a fne dfference mehod for (). Eqn () can be wren n he form x K( xx. (3) dk( where. d Sppose x N x d, x ( ) x, and ( ). We wre dfference for (3) s x ( x, ). A fne ) /. (4) For compaon, he bondary condon s se 0. for any, and he nal condon N x for N x. The wo dmensonal case, () becomes x K( xx y K( yy. (5) Fg. Mosre conen a 0 for one dmensonal and wo dmensonal case Wrng y ( ) x, fne dfference for (5) s x, y, ) (. A ),, x, ) y, /. / (6) For compaon, he bondary condon s se for any ha s 0. for N y, and, N x, 0. for N x. The nal N y condon for N, and N. y 5 Resl and Dscsson Implemenng a fne dfference (4) n a program, we ge for any and. In hs compaon, d 6, x 0., , and N x 3. Fg shows he vale of n he nerval of 0 x d 6 for several vale of. The crve a he op represens he vale of a Observe ha a pons close o he bondary he vale of decrease mch faser. The crve a he boom s he vale of a 0. The decrease of he vale becomes slower han a Oher crves are orderly n me from he op o he boom. The smlar daa are sed for he compaon of wo dmensonal case. Moreover, as addonal d, x 0., , and N y 56. Fg x ISSN: X 89 Volme, 06

4 hp:// shows he vale of n he regon of 0 x d 6 and 0 y d for several vale of. The crve a he op represens he vale of a y 5. 5 and The crve a he boom s he vale of a y 5.5 and 0. Smlar phenomenon s observed as for he case one dmensonal case. However, comparng he crves a 0 for one dmensonal case and wo dmensonal case we observe he dfference. The vale of he wo dmensonal case decrease slghly faser compared o he one dmensonal case. The dffson process wo he sde wall n wo dmensonal case s responsble for hs. Fg. Mosre conen a several me for wo dmensonal case Fg. 3 Mosre conen a 0 for one dmensonal and wo dmensonal case 6 Conclson We have dscssed dryng process of brcs made of sol and celllose mxre. We apply a dffson ype eqaon o model he dryng process. The model s based on macro modelng, where he parcle and pore szes are consdered mch smaller compared o he sze of nals o measred he mosre conen of he area nsde he brcs. The model s a nonlnear dffson eqaon where he dffson rae depends on he mosre conen. Whle he analycal solon of he nonlnear model s sll dfffcl o oban, he solon s comped analycally applyng a fne dfference mehod for one and wo dmensonal cases. The smlaon shows ha he dryng process of wo dmensonal case s slghly faser han of he one dmensonal case. The case s he dffson o he sde wall of wo dmensonal case where hs wall s does no exs n one dmensonal case. References: [] K. Ornam, M. Kmsan, and E. Cahyono, Evalaon of Alernave Desgn of Hollow Brc wh Sawds as Fller for Home-Made Indsry, Energy, Envronmenal and Srcral Engneerng Seres, Vol. 3, pp , 05. [] E. C. Romão, J. A. Marns, and L. F. M. de Mora, Three-Dmensonal Hea Condcon n Ml-Conneced Domans sng GFEM wh Hexaedrals of 7 Nodes, Inernaonal Jornal of Mahemacs and Compers n Smlaon, Vol. 6, pp , 0 [3] L. Vase, V. Dolnay, Smlaon Mehods for he Hea Dsrbon Sysems, Inernaonal Jornal of Mahemacs and Compers n Smlaon, Vol. 5, pp , 0. [4] M. Sřínsá, J. Sřínsý, V. Sla, J. Senčí, S. Malý, G. Te, Mahemacal Models for he Predcon of Hea Flx from Fre Balls, WSEAS Transacons on Hea and Mass Transfer, Vol. 9, pp , 04. [5] M. G. Adyan, A. Ghaher Sole Transfers Modelng In Layered Poros Meda sng Dfferenal Qadrare Mehod (DQ), WSEAS Transacons on Hea and Mass Transfer, Vol. 9, pp , 04. [6] ASTM C67-4, Sandard es mehods for samplng and esng brc and srcral clay le. Amercan Assocaon Sae Hghway and Transporaon Offcal Sandard. [7] ASTM C6-5, Sandard specfcaon for facng brc (Hollow masonry ns made from clay or shale). Amercan Assocaon Sae Hghway and Transporaon Offcal Sandard. [8] ASTM C65-4, Sandard specfcaon for hollow brc (Hollow masonry ns made from clay or shale). Amercan Assocaon Sae Hghway and Transporaon Offcal Sandard. ISSN: X 90 Volme, 06

5 hp:// [9] K. Ornam, M. Kmsan, L. O. Ngoman and E. Cahyono, Physcal and mechancal properes of reed fller modfed brc, Proceedng of he Celebes Inl Conference on Dversy a Walaceas lne Kendar Indonesa, May, 05. [0] P. Lehner, P. Konečný, P. Ghosh and Q. Tran, Nmercal analyss of chlorde dffson Nmercal analyss of chlorde dffson, Inernaonal Jornal of Mahemacs and Compers n Smlaon, Vol. 8, pp , 04. [] M. B. K. Moorhy, T. Kannan, K. Senhlvadv, Sore and Dfor Effecs on Naral Convecon Hea and Mass Transfer Flow pas a Horzonal Srface n a Poros Medm wh Varable Vscosy, WSEAS Transacons on Hea and Mass Transfer, Vol. 8, Isse 4, pp , 03. [] E. Cahyono, L Hamm, LD. Ngoman J Safan Ineracon of Drople Dffsons Governed by -D Poros Medm Eqaon, Appled Mahemacal Scences, Vol. 8, No. 7, pp , 04. [3] E. Cahyono, Y. Soeharyad and Mhsar, A smooh dffson rae model of wood dryng: a smlaon oward more effcen process n ndsry, Jrnal Ten Indsr Vol. 0, No., pp. -0, 008. ISSN: X 9 Volme, 06