PROCESS SIMULATING OF HEAT TRANSFER IN HIGH- TEMPERATURE THERMOCOUPLES

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1 MAEC Web of Confeenes 0006 ( 05) DOI: 0.05/ maeonf/ C Owned by he auhos published by EDP Sienes 05 PROCESS SIMULAING OF HEA RANSFER IN HIGH- EMPERAURE HERMOCOUPLES Yuliana K. Aoshenko Alena A. Byhkova Naional Reseah omsk Polyehni Univesiy 6050 omsk Russia Absa. Numeial eseah of inegal haaeisis of poess of heaansfe in sensiive elemens of R A and B ypes hemoouples in ase of measuemen of high empeaues (moe han 900 K) is exeued. heoeial dependenes of minimum neessay duaion of heaing up of he hemoouple on value of empeaue on bounday of a sensiive elemen ae eeived. I is shown he hemoouple of R ype equies bigge ime of heaing fo obaining saisfaoy auay of measuemens. empeaue fields in sensiive elemens of he speified hemoouples ae eeived. I is shown ha disibuion of empeaue on he hemoouple no linealy and has simila haae fo he eseahed hemoouples.. Inoduion hemoelei effe elaed wih emegene of vaious hemoelei phenomena in iui onduo (Pelie effe Seebek effe). hemoelei effe gain widespead ueny in paie and on is bases design diffeen esoues: hemoelei geneaos hemoelei wames and ooles and ohes. Quesions abou simulaions of hemoelei devies devoed suffiienly lage quaniy of woks (fo example an be disinguish model appoximaion [ ]). he mos widespead example applying effe appeaane of EMF in iui dissimila onduos povided diffeenes empeaues in plaes junions hese onduos aise hemoelei onvee (hemoouple) empeaue. hemoouples ae used boh in omposiion of infomaion-measuing sysems well as in omposiion of onol sysems and hene eliabiliy hei indiaions effe on diely onol of poessing poedues. Heewih simulaions of hemoelei onvees empeaues fom he sandpoin of apabiliies eo esimaes and ohes meologial haaeisis paid vey few aenions. Suh quesions onsideed in [ 6] howeve a poduions poblem in woks [ ] lose sigh of feaues deail of onsuion hemoelei onvees (onsideed only dieion oesponding junion of hemoouples). Engineeing design models hea and mass ansfe ypial hemoelei onvees allows foeas heaing peiod sensos floods hemoouple neessay fo deeminaions indiaions o he exen of limis of eo.. Physial and mahemaial model of hea ansfe In pesen wok solve he poblem of hemal onduiviy fo hemoouple as signifianly heeogeneous sysems (fig. ) inluding hemoouple junion eami nole sainless seel sheah and dieion beween hem fill ou powdes of aluminium oxide. empeaue effe of hemoouple wie wihin he onfines of his model ignoed. Aile available a hp:// o hp://dx.doi.og/0.05/maeonf/050006

2 Figue. Sheme dieion solve he poblem: hemoouple junion; insulaing ap; powde Al O ; meal ove Poblem of ambulaoy hea ansfe a he expense of hemal onduiviy fo elemens inoming dieion solve edues o solve sysem of diffeenial equaions [7]: ρ 0 < < < < H; () ρ 0 < < < < ; < < < < H; () ρ 0 < < < < ; < < < < H; () ρ 0 < < L 0 < < ; < < L < < H. () he bounday ondiions given in able. able Bounday ondiions ; ( <<H); ; (0<< ); ; ( <<H); ; (0<< ); ; ( <<H); ; (0<< ); 0 H R MAEC Web of Confeenes 0006-p.

3 SOR 05 Hee adial oodinae m; axial oodinae m; speifi hea apaiy J/(kg C); densiy kg/m ; oeffiien of hea onduion W/(m C); indexes: hemoouple junion poeive ap; powde of an aluminum oxide poeive ove. Soluion Poedues he aea of he soluion of he ask (fig. ) is boken ino he unifom gid onsising of 00 nodes. he slo pih on adial and axial oodinaes is equal 50 - mm. he sep on a empoal gid hanged in he ange fom 0 - o 0 - wih fo eduion of volume of ompuaion and inease of auay of he deision. Sysems of equaions () () wih he appopiae iniial and bounday ondiions deided using a mehod of finie diffeenes. he soluion of he diffeene analogs of he diffeenial equaions epesening he linea algebai equaions was aied ou by a loal and one-dimensional mehod. he po-ae mehod on he basis of he implii fou-poin diagam [8] was applied o he deision of sysem of he diffeene equaions. Resuls and disussion Compuaional invesigaion podued fo hemoelei onvee empeaue used fo measuemen high empeaue wih he following nominal sai haaeisis of onvesion: R A. Mahemaial modelling wee aied ou a paamees [9 ]: hemoouple junion (ype R): 99 W/(m K); C 95 J/(kg K); 050 kg/m ; hemoouple junion (ype A): 075 W/(m K); C 9 J/(kg K); 905 kg/m ; hemoouple junion (ype B): 787 W/(m K); C 67 J/(kg K); 9776 kg/m ; insulaing ap: 6 W/(m K); C 80 J/(kg K); 800 kg/m ; powde Al O : 657 W/(m K); C 850 J/(kg K); 50 kg/m ; Sainless seel sheah: 5 W/(m K); C 6 J/(kg K); 7900 kg/m. Measuemens of dieion solve (fig. ): H 5 mm L 5 mm. Fis pa pesen eseah aimed a ompaaive analysis of hea ime measuing junion hemoouple o empeaue loaed wihin pemissible vaiaion fom nominal sai haaeisis of onvesion. Pemissible vaiaion fo eseah hemoouples in aodane wih [] pesened in able. able. Values limis of eo measuemen empeaue of hemoouple ype hemoouple R A B Wihin pemissible vaiaion fom nominal sai haaeisis of onvesion K ± 5 wihin he limis of empeaue fom 7 K o 87 K ± wihin he limis of empeaue fom 68 K o 7 K ± 5 wihin he limis of empeaue fom K o 68 K; ± wihin he limis of empeaue fom 68 K o 7 K ± 5 wihin he limis of empeaue fom K o 57 K; ± wihin he limis of empeaue fom 57 K o 07 K A solve he poblem examined opeaions of hemoouple when empeaue measuing fom 900 K o 850 K. Chosen wihin he limis of measuemen oesponds ange of measuemen all hemoouples. Moeove in hosen wihin he limis loaed values of empeaues onsideed onvesion onsan pemissible vaiaions of indiaions hemoouples o linealy dependen fom empeaue measuing fo hemoouples ypes A and B. Wheein speified empeaues haves diffeen values fo hemoouples ypes A and B. Obained dependenes pesened a figue p.

4 MAEC Web of Confeenes Figue. Dependene of hea ime sensos fom empeaue measuing: hemoouple ype R; hemoouple ype B; hemoouple ype A Based on he esuls pesened a piue an be nex findings: ) dependene values of hea ime sensos hemoouples fom empeaue measuing is nonlinea haae and a dieion of empeaues whih oesponding «inonsan» value pemissible vaiaion fom nominal sai haaeisis of onvesion end o «onsan» value; ) hea ime sensos hemoouples ype R a dieion of high empeaues (moe 50 K) exeeds hea ime sensos hemoouples ype A and B by a mean of 85 %. he seond pa of eseah is onneed o deeminaion of influene of duaion of heaing up on a measuemen eo of high empeaues he onsideed hemoouples. he eeived dependenes of he elaive eo of empeaue measuemen aising owing o insuffiien ime of heaing fo hemoouples of ypes R A and B ae givenin fig. -5. Figue. Dependene of he elaive eo of empeaue measuemen fo he hemoouple of R ype: 750 K 500 K 50 K 000 K 0006-p.

5 SOR 05 Figue. Dependene of he elaive eo of empeaue measuemen fo he hemoouple of A ype: 750 K 500 K 50 K 000 K Figue 5. Dependene of he elaive eo of empeaue measuemen fo he hemoouple of B ype: 750 K 500 K 50 K 000 K Follows fom he povided dependenes ha wih he suffiien duaion of heaing up he measuemen eo an be minimied. Besides in he ange of he aken empeaues fom 000 K o 750 K value of empeaue has no essenial impa on a measuemen eo. Follows fom fig. -5 ha haaeisis of poess of heaansfe fo he onsideed hemoouples ae simila. Disibuion of empeaue on a sensiive elemen of he hemoouple of A ype (afe heaing up wihin 0 seonds) is shown in fig p.5

6 MAEC Web of Confeenes Figue 6. empeaue field in a sensiive elemen of he hemoouple of A ype Disibuion of empeaue (fig. 6) no linealy and on axial and adial oodinaes has simila haae. Conlusion he exeued numeial eseahes show ha he hemoouple ype in ase of simila onsuion of a sensiive elemen has no impa on heaansfe in ase of heaing up. he measuemen eo of high empeaues he onsideed hemoouples moe doesn' depend on he aken empeaue and an be loweed a he expense of inease in duaion of heaing of he hemoouple. Aknowledgmens his wok was finanially suppoed by he govenmen gan Siene.9.0/K (he iphe of he fedeal age sienifi and ehnial pogam.0.0). Refeenes. K. Zaboki P.Ziolkowski. Dasgupa J. de Boo E. Mülle. J Eleon mae 7 (0).. Kunesov G.V. Mukhammadeev K.M. Engineeing Physis 9 (009).. G.V. Kunesov K.M. Mukhammadeev Jounal of Engineeing hemophysis 9 (00).. Aoshenko Y. K. Sihak P. A. and Yashuina O. S. EPJ Web of Confeenes (05). 5. Aoshenko Y. K. Sihak P. A. EPJ Web of Confeenes (0). 6. Aoshenko Y. K. Oeova I.P. Sihak P. A. Advaned Maeials Reseah 00 (0). 7. A. Belmiloudi Hea ansfe. Mahemaial Modelling Numeial Mehods and Infomaion ehnology Ineh Rijeka Coaia A. A. Samaskii he heoy of Diffeene Shemes Mael Dekke In. USA Chikin V.S. hemal popeies of maeials: Refeene Guide. Sae Publishing House of physial and mahemaial lieaue Mosow Kinie P.A. hemoouple empeaue Measuemen. N.-Y. L.: Wiley-Inesiene Publ.97.. R.Hulgen R.D. Desai D.. Hawkins M.Gleise K.K. Kelley. Seleed values of he hemodynami popeies of binay alloys Ameian Soiey fo Meals 97.. IEC Inenaional sandad. hemoouples. Pa : oleanes p.6

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