SQUEEZE FILM CHARACTERISTICS WITH EFFECT OF NON NEWTONIAN COUPLE STRESS FLUID AND PIEZOVISCOUS DEPENDENCY BETWEEN POROUS PARALLEL CIRCULAR PLATES
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1 Intenational Jonal of Ciil Engineeing and Tecnology (IJCIET) Volme 9 Isse 8 Agst Aticle ID: IJCIET_9_8_79 Aailable online at tt:// ISSN Pint: and ISSN Online: IAEME Pblication Scos Indexed SQUEEZE FILM CHARACTERISTICS WITH EFFECT OF NON NEWTONIAN COUPLE STRESS FLUID AND PIEZOVISCOUS DEPENDENCY BETWEEN POROUS PARALLEL CIRCULAR PLATES B. Vijayakma Deatment of Matematics SRM Institte of Science & Tecnology Kattanklat Tamilnad India Sndaammal Kesaan Deatment of Matematics SRM Institte of Science & Tecnology Kattanklat Tamilnad India N. Santanakisnan PG & Reseac Deatment of Comte Science D. Ambedka Goenment Ats College Tamil Nad India ABSTRACT Pieo-iscos deendency lays a significant ole in te field of flid flows like geoysics flid lbication and mico flidics. In tis aticle te sqeee film caacteistics wit effect of Non-Newtonian cole stess flid and ieoiscos deendency between oos aallel cicla lates ae been calclated. Fo distinct ales of ieoiscos aametes te otcome of esse and load caacity ae aoximately ealated and comaed wit Newtonian lbicants and iso-iscos cole stess. De of ieoiscos effect te esse and load caacity wit isoiscos Non Newtonian flid and isoiscos Newtonian is notably lowe tan te esse and load caacity wit ieoiscos Non Newtonian Key wods: Non Newtonian Flid Pieoiscos isoiscos. Cite tis Aticle: B. Vijayakma Sndaammal Kesaan N. Santanakisnan Sqeee Film Caacteistics wit Effect of Non Newtonian Cole Stess Flid and Pieoiscos Deendency Between Poos Paallel Cicla Plates. Intenational Jonal of Ciil Engineeing and Tecnology 9(8) tt:// tt:// 78 edito@iaeme.com
2 B. Vijayakma Sndaammal Kesaan N. Santanakisnan. INTRODUCTION In ecent yeas Magneto ydodynamic lbication as establised a geat deal of inteest. Te stdy of Magneto ydodynamic lbication is lot moe engaged tan tat of ydodynamic lbication. Seeal atos [-] nde aios conditions ae stdied sqeee film beaings nde te action of a tansese magnetic field. Te case of beaing defomation on te caacteistics of sqeee film between ectangla and cicla lates and slide beaing wee stdied by Ramanaia and Sndaammal []. Te stdy of finite MHD jonal beaings was analyed by Malik and Sing [4]. Hama [5] inestigated te Magneto ydodynamic sqeee film and te eslts indicate tat te electomagnetic foces imoe significantly te load sstaining caacity. MHD sqeee film caacteistics between annla disks wee stdied by Lin and et.al [6] and oed tat te imoement in te sqeee film esse was inflenced by magnetic fields. Dynamic caacteistics of Magneto ydodynamic wide slide beaings wit an exonential film ofile wee meased by Lin and L [7] and tey noticed tat te existence of extenally alied magnetic fields signifies te imoement in te film esse. In geneal a significant enance in ales of load sstaining caacity te stiffness co-efficient and daming co-efficient as comaed to te non-condcting lbicant case. Te stdy of sqeee film beaios of diffeent system was caied ot by seeal atos [8-]. Howee tese eseaces ignoed te effects of esse deendency on te flid iscosity. U.P. Sing [] inestigated on sqeee film te case of iscosity esse deendency inoling cicla lates of cole stess flid. Using te exession fo te esse deendent iscosity model o e () Wee o and ae esectiely te coefficient of iscosity te atmoseic iscosity esse film esse and te coefficient of iscosity esse. In tis aticle te combined effects of sqeee film caacteistics between oos aallel cicla lates wit iscosity esse deendency and Non-Newtonian cole stess flid ae been stdied. Te otcome of film esse and load sstaining caacity among diffeent ales of iscosity esse aamete ae ealated aoximately and comaed wit Newtonian lbicants and isoiscos cole stess.. MATHEMATICAL FORMULATIONS Te scematic eesentation of sqeee film lbication wit nomal elocity aoacing eac ote between oos aallel cicla lates is sown in Fig. d dt tt:// 78 edito@iaeme.com
3 Sqeee Film Caacteistics wit Effect of Non Newtonian Cole Stess Flid and Pieoiscos Deendency Between Poos Paallel Cicla Plates Fige Te scematic eesentation of oos cicla late wit sqeee film beaing. Wit te sal assmtion te basic goening eqations is w () 4 () 4 Eqations [-4] ae soled nde te B.C s w wen (5) w wen (6) t Wee te elocity in and diections ae gien by and w te film tickness between te beaing lates is denoted by is te coefficient of iscosity denotes non- Newtonian cole stess flid and eesents te esse. Taking te non dimensional qantities as (4) d R dt R d R dt w w d dt d R dt and tt:// 78 edito@iaeme.com
4 B. Vijayakma Sndaammal Kesaan N. Santanakisnan tt:// 784 Te non dimensional fom te eqation (-4) ae w (7) 4 4 (8) (9) and eqialent B.C s (5) and (6) takes te sae w wen () w wen () Alying te B.C s () and () to Sole te eqation (8) te elocity is gien by Cos Cos () Te atially alteed tye of te Dacy s law in te oos medim is w Wee w ; ae te Dacy s elocity comonents along x and diections indicate te esse in te oos egion is te Electomagnetism of te oos medim and. Using bonday conditions (-) in eqation (7) and integate we get te atially alteed Reynolds eqation of te fom d d f d d ) ( () Wee e e e e f 5 tan 4 (4) Using te etbation metod as << te esse is obtained as... (5) Sbstitting (5) in () omitting second and sccessie owes of we get
5 Sqeee Film Caacteistics wit Effect of Non Newtonian Cole Stess Flid and Pieoiscos Deendency Between Poos Paallel Cicla Plates d d d d f (6) d d f d d (7) d d f d d Using te sitable bonday conditions we sole te eqation (6) and (7) we get d d wen (8) wen (9) Te etbed eslts ae () f f 9 f () Wee f 4 tan () f 6 tan 6 tan () Te load caying caacity can be calclated as follows R W d (4) wic takes te dimensionless fom as follows W W 4 d d (5) R dt. RESULTS AND DISCUSSIONS Using a dimensionless aamete te effect ieoiscos is analyed wit a iscosity esse aamete and te oety of cole stesses. In fige te aiation of te esse is lotted ess adis fo = and.5 wit. &.5. It is fond tat wen = te esse in te case of iso iscos Non Newtonian cole stess is ig and it inceases fo inceasing ales of. It is fonded tat fo all ale of &. 5 te esse in te case of ieoiscos Non Newtonian is ig significantly tan te esse wit isoiscos Newtonian and isoiscos Non-Newtonian flid. tt:// 785 edito@iaeme.com
6 P B. Vijayakma Sndaammal Kesaan N. Santanakisnan Fige dislay te lot of - dimensional aiation of ess fo =.5 α =. and = and.5. It is noted tat fo all ale of te esse in te case of ieoiscos Non Newtonian is ig consideably fo ige ales tan te lowe ales of. = ala= (Iso-Viscos Newtonian Flid) =.5 ala= (Iso-Viscos Non-Newtonian Flid) =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) Fige Vaiation of ess fo isoiscos Newtonian and ieoiscos non- Newtonian flid Fige Te -D aiation of ess fo distinct ales of ieoiscos non Newtonian flid In Fige4 te aiation of ess fo distinct ales of &.5 wit. It is fond tat te film esse in te case of cole stess lbicants is moe in te Newtonian case. Fte te esse gaining moe fo te inceasing ales of. It is fond tat fo all ales of te esse is ig significantly tt:// 786 edito@iaeme.com
7 P Sqeee Film Caacteistics wit Effect of Non Newtonian Cole Stess Flid and Pieoiscos Deendency Between Poos Paallel Cicla Plates ig in ieoiscos Non Newtonian flid tan tat of isoiscos Newtonian as well as isoiscos Non-Newtonian flid. =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) =.5 ala=. (Pieo-Viscos Non-Newtonian flid) =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) =.5ala=. (Poeo-Viscos Non-Newtonian Flid) =.5 ala= (Iso-Viscos Non-Newtonian Flid) = ala= (Iso-Viscos Newtonian Flid) Fige 4 Vaiation of ess fo isoiscos Newtonian and ieoiscos Non Newtonian flid Fige 5 dislay te - D aiation of ess te is sown fo =.5 α =. and = &.5. It is fond te esse in te case cole stess lbicants is ig tan tat of Newtonian case. It is seen tat fo all ale of te esse in te case of ieoiscos Non Newtonian flid is gaining moe significantly tan tat of isoiscos Newtonian and isoiscos Non Newtonian flid Fige 5 Plot of -D aiation of esse ess fo diffeent ales of ieoiscos non Newtonian flid tt:// 787 edito@iaeme.com
8 Load Load B. Vijayakma Sndaammal Kesaan N. Santanakisnan Fige 6 te load sstaining caacity w is lotted against fo distinct ales of &.5 wit. It is noted tat fo te gowing ales of te load sstaining caacity W also inceases =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) =.5 ala=. (Pieo-Viscos Non-Newtonian Flid) Fige 6 Vaiation of W is lotted ess fo PieoViscos Non Newtonian Flid Fige 7 te load sstaining caacity W is lotted against fo.5.5 &. 5. It is seen tat wit inceasing ale of ieoiscos aamete te load sstaining caacity W also inceases =.5 (Pieo-Viscos Non-Newtonian Flid) =.5 (Pieo-Viscos Non-Newtonian Flid) =.5 (Pieo-Viscos Non-Newtonian Flid) ala Fige 7 Vaiation of W is lotted ess α 4. CONCLUSIONS Te aoximate analytical soltion fo esse distibtion and load sstaining caacity is obtained sing Petbation Metod deied. Te following conclsions ae been dawn in te esent teoetical analysis. tt:// 788 edito@iaeme.com
9 Sqeee Film Caacteistics wit Effect of Non Newtonian Cole Stess Flid and Pieoiscos Deendency Between Poos Paallel Cicla Plates Te effect of ieoiscos deendency enances te film esse wit incease ales of cole stess aamete. Also te effect of ieoiscos deendency enances te load sstaining caacity aeciably wit incease ales of te cole stess aamete. REFERENCES [] Skla JB. Hydomagnetic teoy fo sqeee films. Jonal of Basic Engineeing 965; D87:4 4. [] Lin JR. Viscos sea effects on te sqeee-film beaio on oos cicla disks. Intenational Jonal of Mecanical Sciences 996; 9:7 84 [] Ramanaia G and Sndaammal K Wea Vol 8 No [4] Malik M. and Sing D. V. Analysis of finite Magneto ydodynamic jonal beaing. Wea Vol. 64() (98) P. 7. [5] Hama E.A. Te magneto ydodynamic sqeee film. J. Tibol. Vol. () (998) P. 75] [6] Lin J. R. Magneto-ydodynamic sqeee film caacteistics between annla disks. Ind. Lb. Tib. Vol. 5() () P. [7] Lin J. R. and L R. F. Dynamic caacteistics] Fo Magneto ydodynamic wide slide beaings wit an exonential film. J. Ma. Sci. Tec. Vol. 8() () P. 68. [8] Lin JR C LM Liaw WL Mo LJ. Effects of non-newtonian cole stesses on te sqeee film Caacteistics between two diffeent sees. Poc. IMecE Pat J: Jonal of Engineeing Tibology 8; :69 7. [9] Amad N Sing JP. A model fo cole-stess flid film mecanism wit efeence to man joint. Poc. IMecE Pat J: Jonal of Engineeing Tibology 7; : [] Lin JR Hng CR. Combined effects of non-newtonian cole stesses and flid inetia on te Sqeee film caacteistics between a long cylinde and an infinite late. Flid Dynamics Reseac 7; 9:66 [] Nadinamani NB Hiemat PS Gbasaaaj G. Effect of sface ogness on te cole stess Sqeee film between a see and a flat late. Tibology Intenational 5; 8:45 8. [] Sing U P 4 Tkis Jonal of Science and Tecnology Vol 9() 97- tt:// 789 edito@iaeme.com
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