Modelisation and Simulation of Heat and Mass Transfers during Solar Drying of Sewage Sludge with Introduction of Real Climatic Conditions

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1 Jornal o Alied Flid Mechanics, Vol., No., , 7. Aailable online a ISSN , EISSN DOI:.8869/acadb.jam Modelisaion and Simlaion o Hea and Mass ransers dring Solar Dring o Sewage Sldge wih Inrodcion o al limaic ondiions N. Ben Hassine,, X. hesnea and A. H. aaar aboraor o Mahemaics and Phsics, Uniersi o Perignan Via Domiia, 5 aene Pal Ald 6686 Perignan ede 9, France. aboraor o Energeics and hermal and Mass ransers, Facl o Sciences o Bizere, Uniersi o arhage, Jarzona 7, nisia. orresonding Ahor Benhassinenidhal@gmail.com (ceied Jl, 6; acceed Noember, 6) ABSRA Sewage sldge resens a real roblem wih he rban and indsrial eanding. So, he dring echniqe is indisensable in he sldge reamen rocess o minimize is olme and is realorizaion. For cos and enironmenal reasons, he solar dring is becoming increasingl aracie or small and medim wasewaer reamen lans. hereore, he aim o his work is he modelisaion o solar drer o residal sldge. he model sdied is a recanglar agriclral greenhose. In he lower ar, he sldge (assimilaed o a oros medim), acs as an absorber. I is sbjeced o a orced laminar low. he ransers in he greenhose and he oros medim are described reseciel b he classical eqaions o orced conecion and he Darc- Brinkman-Forchheimer model. he imlici inie dierence mehod is sed o discreize he goerning dierenial eqaion. he algebraic ssems obained are soled sing he Gass, homas and Gass-Seidel algorihms. In order o comlee he model and o deermine he dring rae we associae a model o he sewage sldge dring kineics. his work is realized wih he meeorological daa o he aaoine region in he soh o nisia. his daa hae ndergone saisical reamen sing he i and Jordan mehod. In order o show he adanages o solar dring, we eseciall sdied he arios ranser modes, he dring kineics and he drer erormance. Kewords: Hea and mass ransers; Forced conecion; Solar dring; Sewage sldge; Drer erormance. NOMENAURE c F Da Dh D e H Hr k Ms Pr q Sc mass racion Forchheimer coeicien Darc nmber hdralic diameer aor dision coeicien hickness o he sldge channel heigh relaie hmidi ermeabili o oros medim channel lengh laen hea o aorizaion dr mass Prandl nmber solar radiaion densi nold nmber Schmid nmber emerare ems longidinal eloci ranserse eloci X dx d α λ ρ ν φ Ω ψ s Sbscri longidinal coordinae Waer conen dr base ranserse coordinae dring rae hermal disii hermal condcii densi kinemaic iscosi orosi o oros medim orici sream ncion absorion coeicien o he sldge ransmiance o he greenhose lid

N. Ben Hassine e al. / JAFM, Vol., No.,. 65-659, 7. oros ambien w wall Serscri dimensionless ariable. INRODUION For a long ime solar dring has been sed o dr ood rodcs o reain hem.

2 N. Ben Hassine e al. / JAFM, Vol., No., , 7. oros ambien w wall Serscri dimensionless ariable. INRODUION For a long ime solar dring has been sed o dr ood rodcs o reain hem. his e o dring has he adanage ha i is no eensie and i does no harm he enironmen. In recen decades, his e o dring is again ineresing wih he high cos o dring and he enironmenal concerns. Indeed, he oic o dring has been he sbjec o seeral research sdies, he irs scieniic works are hose o Sherwood (99 a, b, 93). He has sdied he mechanism o dring and he eaoraion o waer rom solid maerials where he has ideniied or cases. In wo cases he eaoraion ron is locaed on he solid srace and in he oher wo cases he eaoraion ron moes inside. Aerwards, he has shown ha he dring rae is no consan dring he rocess. hen, He has shown ha dring rocess consiss o wo hases, in he irs he dring rae is consan, while dring he second hase he dring rae is decreasing. He also noed ha he decreasing hase is sli ino wo ars. In anoher work, Sherwood (936) roosed a classiicaion o he Dring mode according o he shae o he cre o he dring l deending on he waer conen and he concaiies orienaion. In order o deermine a nmerical model o rban sldge dring, Vaelaire e al. (), Amado e al. (6) and Slim (7) hae condced eerimenal sdies b aring he dieren oeraing condiions (emerare, hmidi and eloci o he ambien air and solar radiaion). For he irs work, he hae roosed a macroscoic aroach in erms o cre o kineics and dring oenial. his aroach gros a se o eernal condiions ino a single arameer. In he second work he ahors hae roided a nmerical model o he dring kineics based on he conce o he characerisic cres. In he hird, Slim (7) has roosed a nmerical model o he sldge dring ha akes ino accon he ariable climaic condiions. In heir work, Vaelaire and Piggali (), ao e al. (6) and Fon e al. () hae ocsed on he henomenon o shrinkage, he crack ormaion and he skin laer. B sding he srcre o he sldge he hae obsered he zigzagging orm o he cracks inside he samles and he deelomen o a skin laer dring he shrinkage. Also he hae conclded ha hese henomena hae an imoran inlence on he dring rae. éonard e al. (5) hae sdied eerimenall he inlence o air emerare, eloci and hmidi dring conecie dring o wo dieren sewage sldges. he hae shown ha he emerare is he main oeraing arameer aecing he dring kineics. B inerreing he eolion o dring rae deending on he waer conen, he hae conirmed he eragranlar limiaions dring he dring rocess. More recen sdies hae elored arios aroaches o sole he roblem o conecie dring o hin ilm. Among hese aroaches, we noe REA aroach (acion Engineering Aroach), his engineering aroach has been sed b Prano e al. (4). he comarison o he resls obained b his model wih eerimenal daa shows is eecieness. Hang e al. (5 and 6) hae sed wo models o redic he hin laer sldge dring. hese models are he Back- Proagaion (BP) and he Generalized gression Neral Nework (GRNN) model. he showed ha he BP model is more recise or he redicion o he waer conen o he sldge, whereas or he redicion o he sldge emerare, he hae shown ha i is alid or he one or he oher o he models according o he oeraing condiions. As a resl, in his work we roose a modelisaion o solar drer or sewage sldge wih ariable climaic condiions dring he da. he case o sewage sldge dring wih he meeorological condiions o he aaoine region was sdied o redic he drer eicienc and he oimal eriod o dring in hese condiions.. PROBEM POSIION he Fig. schemaicall shows he greenhose made o a horizonal channel where he er wall is ransaren o he solar radiaion. he boom is a oros medim, which has he characerisics o sewage sldge. his sldge is eosed o a orced laminar low wih a arabolic eloci roile a he emerare, he relaie hmidi Hr, he mass racion and he consan ressre P a he inle. Fig.. Geomeric conigraion. nin order o simli he roblem, he ollowing In order o simli he roblem, he ollowing assmions are made: he ransers are laminar and wo-dimensional; he lid is Newonian and incomressible; he iscos dissiaion is negleced; 65

3 N. Ben Hassine e al. / JAFM, Vol., No., , he Sore and Dor eecs are negleced; he Bossinesq aroimaion is reained; he air waer aor mire is a erec gas; he air-sldge is a local hermodnamic eqilibrim; he oros medim is isoroic. 3. ONSERVAION EQUAIONS o generalize he resls, he eqaions are wrien in dimensionless orms. he ariables sed o obain he dimensionless ariables are he channel heigh and he inle condiions (he eloci, he emerare and he moisre conen). 3. In he Greenhose Mass conseraion () X-momenm conseraion P () Y-momenm conseraion P (3) Energ conseraion Pr (4) Secies conseraion (waer aor) Sc (5) Wih: ; D ;Sc ;Pr U H Where all he air roer,,d,, are ariable. 3. In Poros Medim In order o ensre he momenm conseraion in he oros medim we se he Darc-Brinkman- Forchheimer model (Swai e al., ). In order o oercome he diicl osed b he bondar condiions o imose on he ressre, he momenm eqaion is wrien sing he sream ncion-orici ormlaion (Nogoo e al., 978). In his ormlaion he conini eqaion is saisied aomaicall. So he ranser eqaions in he oros medim are: Sream ncion eqaion (6) Vorici eqaion F Da Da (7) Energ conseraion Pr (8) Wih: H k ;Da ;Pr U H ; 4. INIIA AND BOUNDARY ONDIIONS 4. Iniial ondiions Iniiall (=) he emerare, he ressre and he waer aor concenraion are niorm in he channel. Inside, he oros medim, he emerare and he waer conen are also niorm. 4. Bondar condiions For he channel: A he inle ; ; ; 6 A he ole

4 N. Ben Hassine e al. / JAFM, Vol., No., , 7. ; ; ; A he er srace ; ; ; For he oros medim: A he righ and le walls ; ; A he boom wall ; ; For he lid-oros medim inerace: he longidinal comonen o he eloci is obained b ensring he conini o he shear sresses. For he sream ncion and he orici, he bondar condiions are: ; ; he hea balance is gien s: H s q D in erace Assming ha he air-oros media inerace is ermeable onl or he waer aor, he eloci a he inerace is wrien as: Ms dx S U d (9) Assming ha he air-waer aor mire is a erec gas and ha he air-oros medim inerace is a a local hermodnamic eqilibrim. he mass racion a he inerace, w, can be calclaed rom: Sc () w w 5. MEEOROOGIA DAA REAMEN AND DRYING KINEIS MODE 5. Meeorological Daa reamen Meeorological daa are colleced sing a saion insalled in a locaion whose coordinaes are: laide 3 58'6,76''N, longide and 9'6,47''E alide o m (amsl). his saion belongs o he EnerMENA rojec. Meeorological daa hae been recorded or a eriod o ears. he hae ndergone saisical analsis o deermine he monhl ical da. Indeed, we sed he mehod o i and Jordan (96). his mehod soses ha he sk is isoroic and ha he inensi o he dise sk radiaion is assmed o be niorm oer he whole sk. I consiss o esimae he monhl ariaion o meeorological ariables b a ical da. Eer da o he monh is he same ha his da. he model eqaions hae been nmericall ranslaed sing a Forran rogram o aciliae calclaions. he solar radiaion eolions dring he ical das or he Janar,.Aril, Jl and monhs are shown on ig.. solar radiaion (W/m²) Jnar Aril Jl ime (hors) Fig.. Solar radiaion eolion dring he ical das. 5. Dring kineics Model o deermine he dring rae, we ado a dring kineics model or he sewage sldge, dedced rom he resls o Amado (6). his model is based on he conce o characerisic cre (Van Meel 957). he dring rae can be wrien: dx dx Xr () d d dx Where: is he consan hase rae. d 3 Xr A Xr A Xr A 3 Xr is he redced dring rae. X Xeq Xr is he redced waer conen. X X cr eq 654

5 N. Ben Hassine e al. / JAFM, Vol., No., , 7. For sewage sldge, he moisre conen a eqilibrim is gien b he ollowing eression (Oswin 946): n Hr Xeq k () Hr A, A, A3, k and n are deermined eerimenall b Amado (7). he ales are resened in able. able Model arameers Parameers Vales A.37 A -3.3 A3.9 k.938 n RANSFERS PARAMEERS AND DRYER EFFIIENY 6. Hea and Mass ransers Parameers he solar radiaion ha reaches he srace o he sldge is decomosed in wo modes. One is he sensible hea ranser ia he air emerare gradien, Qs; he oher is he laen hea ranser ia he waer eaoraion, Ql. so he oal hea ranser rom he srace o he sldge can be eressed as ollows: Q Qs Ql w (3) he local Nssel nmber close o he sldge srace is deined as: Dh Qs Dh Ql N Ns N l w b w b Where he Ns and Nl are he local Nssel nmbers or sensible and laen hea ranser, reseciel and he are deined in dimensionless orm as: N s w b w Dh U N w w b he Sherwood nmber is eressed as: Dh w Sh w (4) D w b he dimensionless orm is wrien as: U D h w Sh w D w b Where he sbscri b, denoes he blk qaniies. he local blk emerare b and he mass racion b are deined reseciel as ollows: U d U d b ;b (5) U d U d 6. Drer Eicienc Parameers he sd o he solar drer eicienc roides a means o assessing js how a drer oeraes nder cerain condiions. Drer eicienc is deined as he raio o energ reqired o eaorae he waer o he energ slied o he sldge and is calclaed rom he ollowing mahemaical ormla: Qea (6) Qs Where:. Qea m. dx m Ms is he mass o waer eaoraed in d ime. Q S q s s where S is he srace o he sldge. 7. NUMERIA RESOUION AND VAIDAION 7. Nmerical solion For he wo media (lid and oros), he ranser eqaions are discreized b sing an imlici inie dierence mehod. he nmerical resolion is realized b he Gass and homas algorihms in he lid medim and b he homas and Gass-Seidel algorihms in he oros medim. he considered mesh is reglar and recanglar in he wo media. o sd he mesh deendence we resened in he Fig. 3 he eolion o he sensible Nssel nmber (a) and he eolion o he laen Nssel nmber (b) dring dring ime. he resls show ha rom a nodes nmber eqal o 8 in he X-direcion, 8 in he Y-direcion or he channel and 4 in he Y- direcion or he oros medim, he ariaions on he eolions o sensible and laen Nssel nmber are minimms. hereaer, in or simlaions we ado his mesh. 7. Validaion he comaional code has been alidaed or he wo media. We hae comared or resls wih hose o Mohamad (3) in he case o hea ranser b orced conecion in a horizonal channel illed wih a oros medim whose walls are mainained a consan emerare (Fig. 4). For he low, we hae comared or eolion o aerage Nssel nmber wih ha obained sing he correlaion deeloed b Sieder and ae (936) in he case o a laminar low in a horizonal dc where he walls are a a consan emerare (Fig. 655

6 N. Ben Hassine e al. / JAFM, Vol., No., , 7. 5). For he wo cases, he maimm dierence does no eceed 4%. 6 5 H. Amado (6) Presen sd Xs (kg waer/kg Ms) 4 3 N S (a) N Dring ime (hors) Dring ime (hors) (b) Fig. 3. Mesh sensiii or sensible Nssel nmber (a) and laen Nssel nmber (b). N mo A.A. Mohamad (3) Presen sd 7. E-6 E-5 E-4 E-3.. Da Fig. 4. Nssel nmber as a ncion o Darc nmber ime (hors) Fig. 6. Eolion o waer conen s a ncion o dring ime a =33.68 K, Hr=63.59%, U=.79 m/s and q=78 W/m². We hae also alidaed he model o he dring kineics sed in or simlaions. For his, we hae comared or resls wih hose o Amado (7) in he ollowing condiions; =33.68 K, Hr=63.59%, U=.79 m/s and q=78 W/m² (Fig. 6). his comarison shows an acceable agreemen and allows s o alidae he sed model. 8. RESUS AND DISUSSION 8. Hea and Mass ransers We hae resened one monh or each season. So, Janar is he winer eriod, Aril is he sring season, Jl indicaes he smmer eriod and is he amn season. he resls resened were obained a m o ical da o monhs. he eolion o Nssel and Sherwood nmbers close o he sldge srace are resened on Fig.7, Fig.8 and Fig 9. On hese igres we can see ha he mass and hea ransers are more imoran a he greenhose inle. his is de in ac ha, a he inle, he dierence beween he emerare and mass racion a he sldge srace and blk qaniies o he air in is icini are imoran (Fig ). Aer he enrance zone, he air emerare and hmidi increases, so, he emerare and mass racion gradiens close o he sldge srace decreases. I ollows ha he Nssel and Sherwood nmbers decrease along he greenhose Presen sd Sieder and ae (936) Janar Aril Jl N mo 4 3 N S Gz Fig. 5. Nssel nmber as a ncion o Graez nmber Fig. 7. ocal sensible Nssel nmber as a ncion o monhs close o he sldge srace. 656

7 N. Ben Hassine e al. / JAFM, Vol., No., , 7. N Janar Aril Jl oncerning he disribion o he Sherwood nmber along he sldge srace (Fig. 9), we noe ha i is similar o ha o he sensible Nssel nmber. he similari beween he wo eolions can be elained b he ac ha or he air he ales o Prandl and Schmid nmbers are er close Fig. 8. ocal laen Nssel nmber as a ncion o monhs close o he sldge srace. We recall ha he climaic condiions are oimm dring he smmer. Dring his eriod, he disribion o sensible Nssel nmber decreased comared o he winer season eolion, where climaic condiions are a heir minimm (Fig. 7). his is de o he ac ha in he smmer he emerare o he air in he icini o he sldge ndergoes a larger increase han ha o he srace o he sldge (Fig..a). hereaer, he emerare gradien close o he srace decreases, which imlies a decrease o he sensible Nssel nmber. We also noe ha he sensible Nssel nmber decreases when going rom a cold season o anoher warmer. m (a) m Janar Aril Jl Janar Aril Jl Sh Janar Aril Jl (b) Fig.. Disribion o emerare gradiens (a) and mass racion gradiens (b) along he sldge srace Fig. 9. ocal Sherwood nmber as a ncion o monhs close o he sldge srace. As regards he eolion o he laen Nssel nmber we ind he inerse henomenon. he laen Nssel nmber increases wih he warmer climae. I is a is maimm dring he smmer and minimm in he winer (Fig. 8). his is de o he mass racion gradien which increases wih climaic condiions. Indeed, wih a warm climae, he emerare o he sldge srace is more imoran han ha o a cold climae. his imlies an increase o he mass racion on he sldge srace and hereaer o mass racion gradien (Fig..b). We noe ha he hea ranser b laen mode increases rom one season o anoher warmer. We can also see ha he laen Nssel nmber is more imoran han he sensible one, which means he redominance o ransers b laen mode. 8. Dring kineics We resen on Fig. he ime eolion o he waer eaoraion rae dring he ical da o each monh. Firsl we ind ha he waer eaoraion rae ollows, mainl, he dail eolion o he solar radiaion. I is a his maimm or minimm a he same ime ha he solar radiaion. On anoher hand, i shows as eeced, ha he waer eaoraion rae is maimm in Jl, which corresonds o he smmer eriod, and minimm in Janar which is reresenaie o he winer season. Dring he ical da o Janar (he winer season), he qani o waer eaoraed is eqal o.49 lier/da/m². his qani increases or he ical da o Aril and is eqal o 4.69 lier/da/m² (sring season). Dring he Jl ical da (he smmer eriod) i reaches a maimm eqal o 6.63 lier/da/m². In amn and dring he ical da, he qani o waer eaoraed is lower han ha recorded in sring and smmer; i is eqal o.8 lier/da/m². 657

8 N. Ben Hassine e al. / JAFM, Vol., No., , 7. Monh aailable energ (KWh/m²/da) able Drer erormance or he ical das slied energ (KWh/m²/da) Eaoraion energ (KWh/m²/da) Drer eicienc (%) m (liers/hor/m²) (-dx/d) (kg waer/kg Ms.h) ime (hors) Janar Aril Jl Fig.. ime eolion o he aerage waer eaoraion rae or arios ical das Janar Aril Jl ime (hors) Fig.. ime eolion o he aerage dring rae or arios ical das. As shown in Fig. he dring eriod has an inconesable eec on he kineics. As he waer eaoraion rae, here is a high decrease in he dring rae dring he winer eriod. I increases wih a warmer enironmen and reaches is maimm dring he smmer. his eolion is idenical o ha o solar radiaion; i is acceleraed wih his aariion and decreases o a sbsaniall consan ale dring he nigh. 8.3 Drer Eicienc o be objecie in or sd we deermine he drer eicienc or ical das. his is enables s o deermine he oimal eriod o dring. On he able we hae reresened he aailable energ, he slied energ, he eaoraion energ and he drer eicienc as a ncion o he ical das. he aailable solar energ is a is maimm dring he smmer, seciicall in Jl where i is close o 8 KWh/m²/da, while he minimm is achieed dring he winer eriod when he aerage ale does no eceed 3.5 KWh/m²/da. his is de o he climaic condiions and he draion o snshine in he aaoine region ha are oimal in he smmer. Also, we noe ha he eolions o he slied energ and he eaoraion energ, whaeer he monh, ollow ha o he aailable solar energ. he hae a arabolic shae wih a maimm recorded arond he Jl. As eeced, he solar eicienc o he greenhose is also maimm dring he smmer das. Dring his eriod, as we hae shown on Fig., he waer eaoraion rae increases nder he eec o climaic condiions. Hence, i ollows an increase o dring eicienc. 9. ONUSION In his aer, we resen a modelisaion o solar drer o residal sldge. he ransers in he air low are modeled b he classical Naier-Slokes eqaions or he orced conecion and b he Darc-Brinkman-Forchheimer model in he sldge considered as a oros medim. he dring kineics model o sewage sldge is based on he conce o he characerisic cre. his work is comleed b a nmerical sd o he solar dring o sewage sldge wih he climaic 658

9 N. Ben Hassine e al. / JAFM, Vol., No., , 7. condiions o he aaoine region in he soh o nisia. he mos signiican conclsions o his work are: he comarisons beween or resls and hose o he lierare shows he alidi o or modelisaion. he hea ranser b laen mode is redominan; he laen Nssel nmber is more imoran han he sensible Nssel nmber. here is a similari beween he eolion o sensible Nssel and Sherwood nmbers. his similari is de o he ac ha or waer aor he Prandl and Schmid nmbers are close. he waer eaoraion rae and he dring rae increase wih a warmer climae and ollow he eolion o he solar radiaion. he dring eicienc aries nder he eec o climaic condiions; i increases when he climaic condiions are oimal and decreases when he are minimal. In ac, he maimm drer eicienc is recorded dring he smmer monhs while he minimm o erormance is obained dring he winer. REFERENES Amado, H. (7). Modélisaion d Séchage Solaire sos Serre des Boes de Saion d Eraion Urbaines. Ph. D hesis, UP Srasborg. Amado, H.,. Beck, R. Mose, Vasile, A. G. Sadowski and J. B. Pole (6). Analsis o he onecie Dring o sidal Sldge rom he Eerimen o he Simlaion. Waer Pollion VIII: Modeling, Monioring and Managemen, Fon, R., M. F. Gomez-Rico and A. Fllana (). Skin eec in he hea and mass ranser model or sewage sldge dring. Searaion and Priicaion echnolog 77, Hang, Y. W. and M. Q. hen (5). Ariicial neral nework modeling o hin laer dring behaior o mnicial sewage sldge. Measremen 73, Hang, Y. W., M. Q. hen and. Jia (6). Assessmen on hermal behaior o mnicial sewage sldge hin-laer dring ho air orced conecie dring. Alied hermal Engineering 96, 9-6. éonard, A., S. Blacher, P. Marcho, J. P. Pirard and M. rine (5). onecie dring o wasewaer sldge: Inlence o air emerare, sericial eloci and hmidi on he kineics. Dring echnolog 3, i, B. Y. H., R.. Jordan (96). he inerrelaionshi and characerisic disribion o direc, dise and oal radiaion. Solar Energ 4, -9. Mohamad, A. A. (3). Hea ranser enhancemens in hea echangers ied wih oros media ar I: onsan wall emerare. Inernaional Jornal o hermal Sciences, 4, Nogoo, E. F., B. M. Berkosk and W. J. minkowcz (978). Alicaion o Nmerical Hea ranser. Mc Graw-Hill Book oman. Oswin,. R. (946). he Kineics o Package ie. Inernaional hemical Indsr 65, Prano, A. and X. D. hen (4). A simle and eecie model or modeling o conecie dring o sewage sldge: he reacion engineering aroach (REA). Procedia hemisr 9, Sherwood,. K. (99a). he dring o solids I. Ind. Eng. hem. (), -6. Sherwood,. K. (99b). he dring o solids II. Ind. Eng. hem. (), Sherwood,. K. (93). he dring o solids III. Ind. Eng. hem. (), Sherwood,. K. (936). he air dring o solids. rans. Am. Ins. hem. Engrs. 3, Sieder, E. N. and G. E. ae (936). Hea ranser and ressre dro o liqids in bes. Indsrial and engineering chemisr 8(), Slim, R., (7). Ede e onceion d n Procédé de Séchage ombiné de Boes de Saions d Eraion ar Energie Solaire e Pome à hale. Ph. D. hesis, Ecole des Mines de Paris. Swai, M., R. D. Praia, B. Krishnend and G.. laek (). Forced conecie low and hea ranser oer a oros lae in a Darc- Forchheimer oros medim in resence o radiaion. Meccanica 47, ao,., X. F. Peng and D. J. ee (6). Skin laer on hermall dried sldge cake. Dr. echnol. 4, Van Meel, D. A. (957). Adiabaic conecion bach dring wih recirclaion o air. hemical Engineering Science 9, Vaelaire, J. and J. R. Piggali (). Analsis o he dring o residal sldge: rom he eerimen o he simlaion o a bel drer. Dr. echnol. (4-5), Vaelaire, J., J. M. Bongioanni, P. Mosqes and J. R. Piggali (). hermal dring o residal sldge. Waer s. 34(7),

ME 321: FLUID MECHANICS-I

ME 321: FLUID MECHANICS-I 8/7/18 ME 31: FLUID MECHANICS-I Dr. A.B.M. Toiqe Hasan Proessor Dearmen o Mechanical Engineering Bangladesh Uniersi o Engineering & Technolog BUET, Dhaka Lecre-13 8/7/18 Dierenial Analsis o Flid Moion