Scholars Journal of Physics, Mathematics and Statistics

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1 DOI:.76/sjps holas Jonal of Physis aheais and aisis h. J. Phys. ah. a. 7; :5- holas adei and ienifi Pblishes Pblishes n Inenaional Pblishe fo adei and ienifi Resoes IN Pin IN 9-86 Online Effes of Radiaion and heial Reaion on HD Flow Pas Oe Veial Plae wih Vaiable epeae and ass Diffsion U.. Rajp aa a Depaen of aheais and sonoy Uniesiy of Lknow UP India *oesponding ho: U.. Rajp Eail: ajpgaalko@gail.o bsa: In he pesen pape we sdy he effes of adiaion and heial eaion on flow pas an osillaing eial plae wih aiable wall epeae and ass diffsion in he pesene of ansesely applied nifo agnei field and Hall en. he flow odel onsiss of nseady flow of a isos inopessible and eleially onding flid. he plae epeae and he onenaion leel nea he plae inease linealy wih ie. he flid odel nde onsideaion has been soled by Laplae ansfo ehniqe. he odel onains eqaions of oion diffsion eqaion and eqaion of enegy. o analye he solion of he odel desiable ses of he ales of he paaees hae been onsideed. he neial daa obained is disssed wih he help of gaphs and ables. he neial ales obained fo skin-fiion hewood nbe and Nssel nbe hae been ablaed. We fond ha he ales obained fo eloiy onenaion and epeae ae in onene wih he aal flow of he flid. eywods: HD flow adiaion heial eaion aiable epeae Hall en INRODUION he appliaion of hydoagnei inopessible isos flow wih hea and ass ansfe nde he inflene of heial eaion and adiaion is of gea ipoane o any aeas of siene and ehnology. hese hae any appliaions in indsy fo insane agnei aeial poessing HD geneaos ion poplsion HD beaings he hee-diensional fee oneie hannel flow HD pps HD bonday laye onol of e-eny ehiles glass anfaing onol poesses and pifiaion of de oil e. Radiaion hea and ass ansfe effes on oing isoheal eial plae in he pesene of heial eaion was analyed by haasway and handakala []. aniannan e al. [] hae sdied adiaion and heial eaion effes on isoheal eial osillaing plae wih aiable ass diffsion. Radiaion absopion heial eaion and agnei field effes on he fee oneion and ass ansfe flow hogh poos edi wih onsan sion and onsan hea flx was onsideed by Daala e al. []. eini and akinde [] hae woked on HD bonday laye flow de o exponenial sehing sfae wih adiaion and heial eaion. HD bonday laye sagnaion poin flow wih adiaion and heial eaion owads a heaed shinking poos sfae was exained by Ewie e al. [5]. Radiaion effe on nseady HD oneie hea and ass ansfe pas a eial plae wih heial eaion and isos dissipaion was pesened by Balla and Naikoi [6]. alapai and Polaap [7] hae inesigaed nseady HD fee oneion hea and ass ansfe in a bonday laye flow pas a eial peeable plae wih heal adiaion and heial eaion. ingh e al. [8] hae woked on hea ansfe de o peeable sehing wall in pesene of ansese agnei field. heial eaion effe on nseady HD flow pas an iplsiely saed osillaing inlined plae wih aiable epeae and ass diffsion in he pesene of Hall en was sdied by s [9]. he objeie of he pesen pape is o sdy he effes of adiaion heial eaion on flow pas an osillaing eial plae wih aiable wall epeae and ass diffsion in he pesene of ansesely applied nifo agnei field and Hall en. he odel has been soled sing he Laplae ansfos ehniqe. he effes of aios paaees on he eloiy epeae and onenaion as well as on he skin-fiion Nssel nbe and hewood nbe ae pesened gaphially and disssed qaniaiely. HEIL NLYI he geoei odel of he poble is shown in fige-. ailable Online: hp://saspjonals.o/sjps 5

2 Fig-: Physial odel he x axis is aken along he eial plae and axis is noal o i. hs he axis lies in he hoional plane. he agnei field B of nifo sengh is applied pependila o he flow. Iniially i has been onsideed ha he plae as well as he flid is a he sae epeae. he speies onenaion in he flid is aken as. ie > he plae sas osillaing in is own plane wih feqeny and epeae of he plae is aised o w. he onenaion w nea he plae is aised linealy wih espe o ie. he flow odel is as nde: * B g g B D q p k he iniial and bonday ondiions ae : fo eey. : os w w a =. 5 as. Hee and ae he piay and seonday eloiies along x and dieions espeiely - speies onenaion in he flid -he Hall en paaee -epeae of he flid w - epeae of he plae a = heial eaion w -speies onenaion a he plae = B - he nifo agnei field σ - eleial ondiiy. β * - olei oeffiien of onenaion expansion ν- he kineai isosiy ρ- he densiy p - he speifi hea a onsan pesse g-he aeleaion de o gaiy β -olei oeffiien of heal expansion - ie k- heal ondiiy of he flid D-he ass diffsion oeffiien q he loal adian fo he ase of an opially hin gay gas is expessed by * a 6 * a is absopion onsan. onsideed he epeae diffeene wihin he flow sffiienly sall an be whee expessed as he linea fnion of epeae. his is aoplished by expanding in a aylo seies abo and negleing highe-ode es ailable Online: hp://saspjonals.o/sjps 6

3 ailable Online: hp://saspjonals.o/sjps 7 7 Using eqaions 6 and 7 eqaion beoes 6 * a k p 8 he following non-diensional qaniies ae inoded o ansfo eqaions and 8 ino diensionless fo:. ρ μ k μ P D ρ σb θ k 6a R g gβ w w * w w * 9 he sybols in diensionless fo ae as nde: - piay eloiy - seonday eloiy P - Pandl nbe - hid nbe R-Radiaion paaee - ie θ- epeae - onenaion - heal ashof nbe - ass ashof nbe μ- oeffiien of isosiy - agnei paaee. he flow odel in diensionless fo is P R P he oesponding bonday ondiions 5 beoe: θ : fo eey. θ os : a =. θ as. Dopping bas in he aboe eqaions we ge P R P 8

4 he bonday ondiions beoe : θ fo eey. : os θ a =. 9 θ as. Wiing he eqaions 5 and 6 in obined fo sing q= + i q q θ R P P qa Finally he bonday ondiions beoe: : q θ fo eey. : q os θ a =. q θ as. he diensionless goening eqaions o sbje o he bonday ondiions ae soled by he sal Laplae ansfo ehniqe. he solion obained is as nde: e q i 86 P P - e θ e 7 a - R 7 R { ef[ R exp ef[ 6 7 ar P exp R P ] P P P R 8 ] a a a a R R e R a P 7 7 R 9 ef[ e exp a a R P ] P ef[ exp P 5 a a R P a8 R R} ] he expessions fo he sybols inoled in he aboe solions ae gien in he appendix. kin Fiion he diensionless skin fiion a he plae is dq x i y. d he neial ales of τ x and τ y fo diffeen paaees ae gien in able-. Nssel Nbe he diensionless Nssel nbe a he plae is gien by a a a 7 ailable Online: hp://saspjonals.o/sjps 8

5 N R P R R P R R P e P ef[ ] R ef[ ] P R P R. he neial ales of N fo diffeen paaees ae gien in able-. hewood Nbe he diensionless hewood nbe a he plae is gien by h ef[ ] ef[ ] e. he neial ales of h fo diffeen paaees ae gien in able-. REUL ND DIUION he pesen sdy is aied o o exaine he effes of adiaion and heial eaion on he nseady HD flow. he behaio of ohe paaees like agnei field Hall en and heal boyany is alos siila o he ealie odel sdied by s [9]. he analyial esls ae shown gaphially in figes o. he neial ales of skin-fiion hewood nbe and Nssel nbe ae pesened in able- and espeiely. heial eaion effe on flid flow behaio is shown by figes and. I is seen hee ha when heial eaion paaee ineases piay and seonday eloiies deease hogho he bonday laye egion. Figes and 5 indiaes ha effe of adiaion R in he bonday laye egion nea he plae ends o aeleae piay and seonday eloiies. Effe of osillaion on flow behaio is shown by figes 6 and 7. I is obseed ha if phase angle ω is ineased hen eloiies of flid ae deeased hogho he bonday laye egion. Fhe i is obseed ha he epeae and onenaion of he flid nea he plae deeases when adiaion and heial eaion paaees ae ineased figes 8 and 9. kin fiion is gien in able. he ales of τ x and τ y inease wih he ineases in adiaion paaee. Howee boh deease wih heial eaion paaee and phase angle. hewood nbe is gien in able. he ale of h deeases wih he inease in he heial eaion paaee hid nbe and ie. Nssel nbe is gien in able. he ale of N deeases wih inease in Pandl nbe adiaion paaee and ie. Fig-: eloiy fo diffeen ales of ailable Online: hp://saspjonals.o/sjps 9

6 Fig-: eloiy fo diffeen ales of Fig-: eloiy fo diffeen ales of R Fig-5: eloiy fo diffeen ales of R Fig-6: eloiy fo diffeen ales of ω ailable Online: hp://saspjonals.o/sjps

7 Fig-7: eloiy fo diffeen ales of ω Fig-8: epeae θ fo diffeen ales of R Fig-9: onenaion fo diffeen ales of able : kin fiion fo diffeen paaee ω in degee P R ω τ x τ y able : hewood nbe fo diffeen Paaees ailable Online: hp://saspjonals.o/sjps h

8 able : Nssel nbe fo diffeen paaee P R N ONLUION In his pape a heoeial analysis has been done o sdy he nseady HD flow pas an osillaing eial plae wih aiable wall epeae and ass diffsion in he pesene of Hall en adiaion and heial eaion. he esls obained ae in ageeen wih he sal flow. I has been fond ha he eloiy in he bonday laye ineases wih he ales of adiaion paaee. B end is eesed wih heial eaion paaee and phase angle. ha is he eloiy deeases when heial eaion paaee and phase angle ae ineased. I is also obseed ha he peeabiliy paaee and adiaion paaee inease he dag a he plae sfae and deease wih heial eaion paaee and phase angle. hewood nbe and Nssel nbe deease wih inease in adiaion paaee and heial eaion paaee. ppendix: i a a a e e e 8 e bs[ ] bs[ P ] ap R ef[ a ] ef[ a ] ef[ ] P 5 8 ef[ ap R ] P a a 6 ef[ ] 7 ef[ ] R R ef[ ] 9 ef[ ] R ap ef[ ] P P P P R ap ef[ ] ef[ ] ef[ ] P P a ef[ 6 a R exp P P ap R P ] 7 a ef[ 5 exp a a a R R ap a 8 exp 9 exp exp P P P P ap R ai ai exp bs[ ] exp bs[ ] P R e e P ] ailable Online: hp://saspjonals.o/sjps

9 ai ai i 5 e 6 e 7 6 a i a i ef ef 7 ef 5 e ai i a i a i ef e ai i REFERENE. haasway R. & enhil... Hea and ass ansfe effes on oing eial plae in he pesene of heal adiaion. heoeial and pplied ehanis aniannan. haasway R. & hangaaj V. 9. Radiaion and heial eaion effes on isoheal eial osillaing plae wih aiable ass diffsion. heal siene esaaiah D.. ayanaayana P. V. & Venkaaaana.. Radiaion absopion heial eaion and agnei filed effes on he fee oneion and ass ansfe flow hogh poos edi wih onsan sion and onsan hea flx. Inenaional Jonal of ienifi Engineeing and ehnology eini Y. I. & akinde O. D.. HD bonday laye flow de o exponenial sehing sfae wih adiaion and heial eaion. aheaial Pobles in Engineeing. 5. hisian E. J. eini Y. I. & h.. agneohydodynais HD bonday laye sagnaion poin flow wih adiaion and heial eaion owads a heaed shinking poos sfae. Inenaional Jonal of Physial ienes Balla.. & Naikoi. 5. Radiaion effes on nseady HD oneie hea and ass ansfe pas a eial plae wih heial eaion and isos dissipaion. lexandia Engineeing Jonal alapai V. & Polaap P. 5. Unseady HD fee oneie hea and ass ansfe in a bonday laye flow pas a eial peeable plae wih heal adiaion and heial eaion. Poedia Engineeing Dandapa B.. ingh. N. & ingh R. P.. Hea ansfe de o peeable sehing. Wall in pesene of ansese agnei field. hies of ehanis Rajp U.. & a.. Radiaion effes on HD flow pas an iplsiely saed eial plae wih aiable hea and ass ansfe. In. J. of ppl. ah. and eh ailable Online: hp://saspjonals.o/sjps

Effects of Heat Absorption and Porosity of the Medium on MHD Flow past a Vertical Plate

Effects of Heat Absorption and Porosity of the Medium on MHD Flow past a Vertical Plate ailable online.ejae.o Eopean Jonal of danes in Engineeing and ehnology 7 4 4: 87-94 Reseah ile ISSN: 394-658X Effes of Hea bsopion and Poosiy of he Medi on MHD Flo pas a Veial Plae US Rajp and aa a Depaen