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Energetic performance of regenerators in an active magnetic refrigerator

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(1)Unione Europea. Università degli Studi di Salerno. DIPARTIMENTO DI INGEGNERIA MECCANICA. Dottorato di Ricerca in Ingegneria Meccanica X Ciclo N.S. (2008-2011). “Energetic Performances of Regenerators in an Active Magnetic Refrigerator”. Ing. Armando Tura. Tutor: Prof. Ciro Aprea. Coordinatore: Prof. Vincenzo Sergi. Academic Year 2012.

(2) Summary ! !"! #$%&'()(*+! #&,#! &,-! #&$! .(#$'#/,)! #(! %0$,#$! 1(0$! $22/%/$'#! ,'3! %(1.,%#! 0$20/*$0,#/('! 3$4/%$-! /-! ,'! "%#/4$! 5,*'$#/%! 6$*$'$0,#/4$! 6$20/*$0,#(0! 7"56689! "'! "566! %,'! (.$0,#$! (4$0! ,! :0(,3! 0,'*$! (2! #$1.$0,#;0$-<!,-!)('*!,-!#&$!,..0(.0/,#$!0$20/*$0,'#!/-!/1.)$1$'#$39!=&;-! #&/-!2)$>/:)$!#$%&'()(*+!%,'!:$!;-$3!2(0!-1,))<!$22/%/$'#<!,'3!-/1.)$!0((1! #$1.$0,#;0$! 0$20/*$0,#(0-<! ,-! ?$))! ,-! $22/%/$'#! *,-! )/@;$2,%#/('! .),'#-! 7"56A-89! "%#/4$! 5,*'$#/%! 6$*$'$0,#(0! 6$20/*$0,#/('! $>.)(/#-! #&$! 1,*'$#(%,)(0/%! $22$%#! 3/-.),+$3! :+! 1,*'$#/%! 1,#$0/,)-! ?&$0$:+! ,! 0$4$0-/:)$!#$1.$0,#;0$!%&,'*$!/-!/'3;%$3!?&$'!#&$!1,#$0/,)!/-!$>.(-$3!#(! ,!1,*'$#/%!2/$)39!B+!;-/'*!#&$!1,*'$#/%!1,#$0/,)-!/'!,!0$*$'$0,#(0!,-!#&$! &$,#! -#(0,*$! 1$3/;1! ,'3! ,-! #&$! 1$,'-! (2! ?(0C! /'.;#<! ('$! %0$,#$-! ,'! "%#/4$!5,*'$#/%!6$*$'$0,#(0!7"5689!! "%#/4$! 5,*'$#/%! 6$*$'$0,#(0! 0$20/*$0,#/('! -+-#$1-! -#/))! 0$)+! ('! %(00$),#/('-! :$#?$$'! 2);/3! ,'3! 1,#0/>! 1,#$0/,)! #(! 3$#$01/'$! #&$! &$,#! #0,'-2$0! %($22/%/$'#9! =+./%,)! %('2/*;0,#/('-! (.$0,#$! /'! )(?! 6$+'()3-! ';1:$0! ,'3! &/*&! D0,'3#)! ';1:$0! 0,'*$-9! E(0! #&$! (-%/)),#/'*! 2);/3! 2)(?! #&0(;*&! #&$-$! 0$*$'$0,#(0-! %(00$),#/('-! ,0$! ;-$3! :,-$3! ('! -/'*)$! :)(?! $>.$0/1$'#-9!=&$0$!,0$!),0*$!3/-%0$.,'%/$-!2(0!)(?!6$+'()3-!';1:$0-!,'3! &/*&!D0,'3#)!';1:$0-!:$#?$$'!#&$!%(11(')+!;-$3!%(00$),#/('-<!$4$'!2(0! #+./%,))+! ;-$3! .,%C$3! :$3-<! -;%&! ,-! .,%C$3! -#,/')$--! -#$$)! -.&$0$-! ?/#&! ;'/2(01! 3/,1$#$0! (2! F! 119! =&$0$2(0$<! #&/-! #&$-/-! ,330$--$-! #&$! 3$#$01/',#/('! (2! #&$! &$,#! #0,'-2$0! %($22/%/$'#-! 2(0! (-%/)),#/'*! 2);/3! 2)(?! ?/#&! ,! '$?! ,..0(,%&! ?&/%&! %(1:/'$-! ,'! ,',)+#/%,)! 1(3$)! ?/#&! $>.$0/1$'#,)! 3,#,9! G'! #&/-! ?(0C! 2/'3/'*-! 2(0! ,! .,--/4$! 0$*$'$0,#(0! #$-#! ,..,0,#;-!7D6="8!,0$!3$#$01/'$3!:,-$3!('!#&$01,)!,'3!&+30,;)/%!$22$%#-9! H>.$0/1$'#-!,0$!.$02(01$3!2(0!3/22$0$'#!(.$0,#/(',)!.,0,1$#$0-!/'!0$-.$%#! (2! #&$! )(?! 6$+'()3-! ';1:$0! 0,'*$<! 2(0! 4,0+/'*! 2);/3! 2)(?! 20$@;$'%/$-<! 1,--!2)(?!0,#$-! ,'3!&$,#!)(,3-9!=&$!*$'$0,#$3!$>.$0/1$'#,)!3,#,!,0$!#&$! /'.;#! 2(0! #&$! ,',)+#/%,)! 1(3$)! 2(0! #&$! &$,#! #0,'-2$0! %($22/%/$'#! 3$#$01/',#/('9!=&$!0$-;)#-!,0$!%(1.,0$3!#(!,!%(11(')+!;-$3!%(00$),#/('! 2(0!0$*$'$0,#(0-!)/C$!I,C,(!,'3!H'*$):0$%&#-!%(00$),#/('-9!.

(3) Acknowledgements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

(4) TABLE OF CONTENTS "%0('+1- P+1:()- P;:-%0/.#-. !" !" !"". !"#$%&'()(*+%',-.!%*,+(. ). 1.1 Motivation. !. 1.2 Magnetic Refrigeration F9Q9F!R$+!D,0,1$#$0- F9Q9Q!=$1.$0,#;0$!D0(2/)$!,'3!J(()/'*!D(?$0 F9Q9S!A,+$0/'*. " # # $. 1.3 Thesis Objective. !#. !"#$%&'(/(0#1+&%*!('&2'*1&'#%*,+(%"&,'3(. )/. 2.1 The Magnetocaloric Effect. !". 2.2 Materials. !$. 2.3 AMR Theory. !%. !"#$%&'(4(%"&'0#5('&1&+&'#%,'6(. //. 3.1 Thermohydraulic Optimization of Regenerators. "&. 3.2 Passive Regenerator Testing. "$. 3.3 Previous Work and Literature Review. "%. !"#$%&'(7(0#!',6!,$*!(8#5#+!&(&9.#%*,+6(. /:. 4.1 Regenerator Disposition. "'. 4.2 Length Scales and Volume Averages. "'. 4.3 Macroscopic Balance Equations T9S9F!5,%0(-%(./%!=&$01,)!H'$0*+!B,),'%$. &" %&.

(5) Table of contents. II 6$,)!6$*$'$0,#(0 T9S9Q!E);/3!N$)(%/#/$- T9S9S!5,%0(-%(./%!5(1$'#;1!B,),'%$ T9S9T!L/1$'-/(')$--!D,0,1$#$0-. %% %' %( %(. !"#$%&'(;("&#%(%'#+62&'(!,&22*!*&+%(-&%&'0*+#%*,+(. 7/. 5.1 Analytical Model U9F9F!P();#/('!5(3$). $" )%. 5.2 Determination of the Heat Transfer Coefficient U9Q9F!5(3$)!%(1:/'$3!?/#&!H>.$0/1$'# U9Q9Q!"--;1.#/('-!,'3!D,0,1$#$0- U9Q9S!H>#0$1$!J,-$-!5(3$). $( )' )( )(. !"#$%&'(<(%&6%(#$$#'#%.6(#+-(&=$&'*0&+%#5('&6.5%6(. 7:. 6.1 Test Apparatus. $'. 6.2 Test Section. %!. 6.3 Experimental Procedure. %&. 6.4 Data Processing. %$. 6.5 Experimental Results. %). 6.6 The microchannel regenerator and the internal axial temperature gradient V9V9F!=&$!/'-#0;1$'#,#/('. (! '%. !"#$%&'(>(&=$&'*0&+%#5(&?#5.#%*,+(. <:. 7.1 Friction Factor. ('. 7.2 Nusselt Number. *#. !"#$%&'(@(!,+!5.6*,+6(#+-('&!,00&+-#%*,+6(. >;. '&2&'&+!&6(. >>.

(6) List of Figures E/*;0$!FWFX!5,*'$#(%,)(0/%!$22$%#!(2!Y3!2(0!,!ZWQ!=!,..)/$3!2/$)3!%&,'*$! [F\9!99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!Q! E/*;0$!FWQX!];1:$0!(2!.;:)/%,#/('-!.$0!+$,0![^\9!99999999999999999999999999999999999999!U! E/*;0$!FWSX!=&$!"56!#$1.$0,#;0$!.0(2/)$!,#!.$0/(3/%!-#$,3+!-#,#$![F\9!99999!_! E/*;0$!FWTX!=&$!/3$,)!5JH!,-!%(1.,0$3!#(!*,3()/'/;1!?/#&!,!ZWQ!=!2/$)3! %&,'*$!75,#$0/,)!"8<!,'3!,'(#&$0!1,#$0/,)!?/#&!,!J;0/$!#$1.$0,#;0$!'$,0! QVU!R!75,#$0/,)!B89!9999999999999999999999999999999999999999999999999999999999999999999999999999999999!FZ! E/*;0$!QWF9!Y0,.&/%,)!0$.0$-$'#,#/('!(2!#&$!5JH![FT\9!999999999999999999999999999!FS! E/*;0$!QWQ9!!"!-%&$1,#/%!0$.0$-$'#,#/('!(2!,'!"56!-&(?/'*!#&$!'$#!?(0C! ,'3!&$,#!2);>!,#!,!3/22$0$'#/,)!-$%#/('![S\9!999999999999999999999999999999999999999999999999!FV! E/*;0$!QWS9!M+.(#&$#/%,)!%+%)$!2(0!#&$!1,*'$#/%!0$20/*$0,'#!,#!-(1$!%0(--W -$%#/('!(2!#&$!"56![S\9!999999999999999999999999999999999999999999999999999999999999999999999999999!F_! E/*;0$!TWFX!6$*$'$0,#(0!-/#;,#/('!/'!&+30,;)/%!%/0%;/#!99999999999999999999999999999!Q^! E/*;0$!TWQX!P%&$1,#/%!(2!.(0(;-!1$3/,!999999999999999999999999999999999999999999999999999!SZ! E/*;0$!TWSX!M(#!,'3!%()3!:)(?!2(0!,'!/3$,)!0$*$'$0,#(09!99999999999999999999999999!SS! E/*;0$!TWTX!M(#!,'3!%()3!:)(?!2(0!,!0$,)!0$*$'$0,#(09!999999999999999999999999999999!ST! E/*;0$!VWFX!H>.$0/1$'#,)!,..,0,#;-!999999999999999999999999999999999999999999999999999999999!UZ! E/*;0$!VWQX!P%&$1,#/%!(2!D6="!999999999999999999999999999999999999999999999999999999999999999!UF!.

(7) IV. List of figures. E/*;0$!VWSX!D&(#(*0,.&!(2!,!-/'#$0$3!1/%0(!%&,''$)!.;%C!,'3!-.&$0$-!9999!UQ! E/*;0$!VWTX!P.$%#0,!(2!3/-.),%$1$'#!-/*',)!9999999999999999999999999999999999999999999999!UU! E/*;0$!VWUX!P.$%#0,!(2!&(#!-/3$!#$1.$0,#;0$!-/*',)!;-/'*!1/%0(%&,''$)-!9!UV! E/*;0$!VWVX!P.$%#0,!(2!&(#!-/3$!#$1.$0,#;0$!-/*',)!;-/'*!-.&$0$-!999999999999!U_! E/*;0$!VW_X!P.$%#0,!(2!.0$--;0$!30(.!2(0!,!1/%0(%&,''$)!$>.$0/1$'#!999999!U_! E/*;0$!VW`X!=/1$!,4$0,*$3!#$1.$0,#;0$!3/22$0$'%$!:$#?$$'!&(#!,'3!%()3! -/3$!2(0!:(#&!*$(1$#0/$-9!99999999999999999999999999999999999999999999999999999999999999999999999999!U`! E/*;0$!VW^X!=$1.$0,#;0$!,1.)/#;3$!2(0!1/%0(%&,''$)!$>.$0/1$'#-9!99999999!VZ! E/*;0$!VWFZX!=$1.$0,#;0$!,1.)/#;3$!2(0!.,%C$3!.,0#/%)$!:$3!$>.$0/1$'#-9 !999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!VZ! E/*;0$!VWFFX!D0$--;0$!30(.!(2!&$,#!$>%&,'*$0<!1/%0(%&,''$)-!,'3!-.&$0$-! *$(1$#0+9!99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!VF! E/*;0$!VWFQX!D,0,))$)!.),#$!,'3!-@;,0$!%&,''$)!%(1.,0$3X!2);/3! #$1.$0,#;0$!99999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!VQ! E/*;0$!VWFSX!A,-$0!-/'#$0$3!1/%0(W%&,''$)!0$*$'$0,#(0<!,--$1:)+!?/#&! $'%,-/'*!-&$))<!EBY!,'3!#0,'-3;%$0!)(%,#/('9!=&$!2/*;0$!0$.0$-$'#-!#&$! %;00$'#!$>.$0/1$'#,)!-$#!;.!?/#&!#&0$$!0$*$'$0,#(0!.;%C-!/'-#,))$3!999999999!VT! E/*;0$!VWFTX!7,8!EBY!?,4$)$'*#&!2/)#$0/'*!1$%&,'/-1!7?/C/8!,'3!7:8! D6="!2/:$0!0$2)$%#/('!-.$%#0;1!7UW.(/'#!1$,-;0$1$'#89!9999999999999999999999999!VV! E/*;0$!VWFUX!H>,1.)$!(2!%,)/:0,#/('!%;04$!2(0!2/0-#!*0,#/'*!?,4$)$'*#&! 0$2)$%#/('!0$-.('-$!,-!2;'%#/('!(2!#$1.$0,#;0$!(')+9!9999999999999999999999999999999!V_!.

(8) List of figures. V. E/*;0$!VWFVX!EBY!#$1.$0,#;0$!0$,3/'*!,)('*!0$*$'$0,#(0!%&,''$)9!"P#0/.! %&,0#!(2!#&$!0,?!3,#,!,'3!#/1$!,4$0,*$3!#$1.$0,#;0$!.0(2/)$!-&(?/'*!#&$! ;..$0!:(;'3!,'3!)(?$0!:(;'39!99999999999999999999999999999999999999999999999999999999999999999!V`! E/*;0$!_WFX!5/%0(%&,''$)!20/%#/('!2,%#(0!99999999999999999999999999999999999999999999999999!V^! E/*;0$!_WQX!E0/%#/('!2,%#(0!(2!-.&$0$!*$(1$#0+!9999999999999999999999999999999999999999!_Z! E/*;0$!_WSX!H>.$0/1$'#,))+!(:#,/'$3!];--$)#!';1:$0-!2(0!1/%0(%&,''$)! *$(1$#0+!999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999999!_F! E/*;0$!_WTX!];!,-!2;'%#/('!(2!'ABC!2(0!-@;,0$!%&,''$)-!999999999999999999999999999!_Q! E/*;0$!_WUX!H>.$0/1$'#,)!];--$)#!';1:$0-!4$0-;-!H'*$):0$%&#-!,'3! I,C,(!%(00$),#/('!2(0!-.&$0$-9!9999999999999999999999999999999999999999999999999999999999999999!_S! E/*;0$!_WVX!J(1.,0/-('!(2!];--$)#!';1:$0-!(2!#&$!#?(!*$(1$#0/$-9!999999!_T! ! !.

(9) !. Nomenclature Acronyms "56768! 5JH! ! 56! ! 6=L! ! ]=a! !. "%#/4$!5,*'$#/%!6$*$'$0,#(0!76$20/*$0,#(08! 5,*'$#(%,)(0/%!H22$%#!7,3/,:,#/%!#$1.$0,#;0$!%&,'*$8! 5,*'$#/%!6$20/*$0,#(0! 6$-/-#/4$!=$1.$0,#;0$!L$4/%$! ];1:$0!(2!M$,#!=0,'-2$0!a'/#-!. ! Symbols #! ! 8! ! !! ! -! ! &! ! "! C! *! D! 5! ! 0! E! +! F! 9! G!! ! 'A! 6HI! %! J! K!. J0(--!-$%#/(',)!,0$,b!P;02,%$!,0$,! 5,*'$#/%!2);>!3$'-/#+! M$,#!%,.,%/#+! L/,1$#$0! H'$0*+! 5,*'$#/%!2/$)3!/'#$'-/#+! M$,#!#0,'-2$0!%($22/%/$'#! J;00$'#! =&$01,)!%('3;%#/4/#+! G'3;%#,'%$b!A$'*#&! 5,*'$#/O,#/('! 5,--b!5,--!1,*'$#/O,#/('! ];1:$0!(2!,#(1-! D0$--;0$! H'$0*+!2);>b!&$,#!#0,'-2$0! 6,3/;-! 6$+'()3c-!';1:$0b0$,)!.,0#! H'#0(.+<!$'#0(.+!.$0!;'/#!1,--b!H'#0(.+!*$'$0,#/('b!P#0(C$b! =$1.$0,#;0$! =/1$! I(0C!. ! ! Greek! )( ‫!׫‬ E!. ( ! !. a#/)/O,#/('( D(0(-/#+! B,),'%$b!G-(#&$01,)!%(1.0$--/:/)/#+b!/'#$02,%/,)!,0$,!.

(10) List of figures. J(( M! P! U! W! !. (. =&$01,)!%('3;%#/4/#+( E);/3!#&$01,)!%,.,%/#+! N/-%(-/#+b!1,*'$#/%!.$01$,:/)/#+! L$'-/#+! D$0/(3!. Subscripts GAL! ! 6$2$0$'%$!4,);$! !MGNA! ! J;0/$!.(/'#! !! ! J()3! "! ! M(#! O! ! A(%,#/('! PQR! ! A(?! CNSC! ! M/*&! 8! ! J('-#,'#!2/$)3b!B)(?! TB(!!!!!!!!!!!!!!!!!!!"3/,:,#/%( U! ! B$3! L! ! E);/3! $! ! D0$--;0$b!.,0#/%)$! I! ! P()/3! S! ! Y$'$0,#/('! ENV! ! 5/'/1;1! ETO!! ! 5,>/1;1! 0! ! 5,*'$#/%! GAW! ! 6$4$0-/:)$! NGG! ! G00$4$0-/:)$! B! ! L$1,*'$#/O/'*b!L/-.),%$0! Q! ! d;#$0! *! ! G''$0. VII.

(11)

(12) Chapter 1 Introduction ! 1.1 Motivation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b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d..(0#;'/#/$-! 2(0! /1.0(4$3! .$02(01,'%$! $>/-#! ?/#&! 2;0#&$0! $'*/'$$0/'*! 0$2/'$1$'#-![F\9! ! !.

(13) 2. Chapter 1. 1.2 Magnetic Refrigeration 8TXDSGQMVB( 5,*'$#/%! 0$20/*$0,#/('! $>.)(/#-! ,! .0(.$0#+! (2! 1,*'$#/%! 1,#$0/,)-! %,))$3!#&$!1,*'$#(%,)(0/%!$22$%#!75JH8X!#&$!#$1.$0,#;0$!(2!2$00(1,*'$#/%! 1,#$0/,)-!/-!(:-$04$3!#(!0/-$!;.('!,..)/%,#/('!(2!,!1,*'$#/%!2/$)39!I&$'!,! 1,#$0/,)! /-! 1,*'$#/O$3<! /#-! 1,*'$#/%! 1(1$'#-! ,0$! ,)/*'$3<! )$,3/'*! #(! ,! 0$3;%#/('!/'!/#-!1,*'$#/%!$'#0(.+9!G2!#&/-!.0(%$--!/-!3('$!,3/,:,#/%,))+!,'3! 0$4$0-/:)+! #&$! #(#,)! $'#0(.+! /-! %('-#,'#9! =&;-<! ,! 0$3;%#/('! /'! 1,*'$#/%! $'#0(.+! /-! %(1.$'-,#$3! :+! ,'! /'%0$,-$! /'! ),##/%$! $'#0(.+! 0$-;)#/'*! /'! ,! #$1.$0,#;0$! /'%0$,-$9! 5JH! %,'! :$! 3$2/'$3! ,-! ,3/,:,#/%! #$1.$0,#;0$! %&,'*$! 3;$! #(! 1,*'$#/O,#/('<! (0<! ,)#$0',#/4$)+<! /-(#&$01,)! 1,*'$#/%! $'#0(.+! %&,'*$9! =&/-! .0(.$0#+! /-! ,! -#0('*! 2;'%#/('! (2! 1,*'$#/%! 2/$)3! /'#$'-/#+! ,'3! #$1.$0,#;0$<! ,'3! /-! 1,>/1/O$3! ,#! #&$! 1,*'$#/%! 1,#$0/,)! (03$0/'*!#$1.$0,#;0$<!C'(?'!,-!#&$!J;0/$!#$1.$0,#;0$9!E/*;0$!FWF!-&(?-! Y,3()/'/;1! 5JH! 2(0! ,! Q! =! 2/$)39! G'#$0$-#/'*)+<! -(1$! ,'#/2$00(1,*'$#/%! 1,#$0/,)-! %(()! 3(?'! 0,#&$0! #&,'! ?,01/'*! ;.! ;'3$0! 1,*'$#/O,#/('! [Q\9! !. ! !"#$%&'Ǧ'ǣ!5,*'$#(%,)(0/%!$22$%#!(2!Y3!2(0!,!ZWQ!=!,..)/$3!2/$)3!%&,'*$![F\9! . P;:-$@;$'#)+! ('$! %,'! #&/'C! (2! ;-/'*! 1,*'$#/%! ?(0C! #(! *$'$0,#$! #&$01,)! %+%)$-<! e;-#! ,-! %(1.0$--/('! ?(0C! /-! ;-$3! ?/#&! *,-W%+%)$! 0$20/*$0,#/('! -+-#$1-9! E(0! /'-#,'%$! ,! J,0'(#! %+%)$! %,'! :$! (:#,/'$3! :+! 0$.),%/'*! #&$! ?(0C! (2! %(1.0$--/('! ?/#&! /-$'#0(./%! 1,*'$#/O,#/('9!.

(14) G'#0(3;%#/('!. 3. 5,*'$#/%!0$20/*$0,#/('!?,-!2/0-#!3$1('-#0,#$3!2(0!-;:C$)4/'!%(()/'*!;-/'*! ,! f:,#%&! %(()/'*g! 1$#&(39! =&$! 1,*'$#/%! 1,#$0/,)<! Y3Q7PdT8S`MQd<! 1,*'$#/O$3! ,#! F9U! R! ! ,'3! Z9`! =<! ?,-! ,3/,:,#/%,))+! 3$1,*'$#/O$3<! #&;-! 0$3;%/'*!/#-!#$1.$0,#;0$!#(!Z9QU!R![Q\9!=&$!:,#%&!%(()/'*!1$#&(3!/-!-#/))! ;-$3! 2(0! 0$,%&/'*! $>#0$1$)+! )(?! #$1.$0,#;0$-<! &(?$4$0! /#! %,''(#! :$! %('-/3$0$3!,!#0;$!0$20/*$0,#(0!:$%,;-$!/#!3($-!'(#!,%%(1.)/-&!,!%('#/';(;-! #&$01,)! %+%)$9! "! %+%)/%! .0(%$--! /-! '$%$--,0+! 2(0! ,! .0,%#/%,)! 0$20/*$0,#/('! 3$4/%$9!! ! 0TSVAJNX('ALGNSAGTJNQV("NIJQGY( a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`Q!,!'$?!%('%$.#!?,-!/'#0(3;%$3!:+!B,0%),+!#&,#!:$%,1$! C'(?'! ,-! ,'! "%#/4$! 5,*'$#/%! 6$*$'$0,#(0! 7"5689! a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

(15) 4. Chapter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aP! ],4+! L,4/3! =,+)(0! 6$-$,0%&! J$'#$0! /'! 5,0+),'3<! %('3;%#$3! ,! #$-#! 2(0! 0((1! #$1.$0,#;0$! 0$20/*$0,#/('! ;-/'*! ,! ),+$0$3! 0$*$'$0,#(0! ?/#&! ,! 1/>$3! %(1.(-/#/('! (2! *,3()/'/;1! ,'3! #$0:/;1! [U\9! =&$! 1,*'$#/%! 2/$)3! /'#$'-/#+! ?,-! 4,0/$3! :$#?$$'!Z!,'3!_!=!:+!0,1./'*!#&$!%;00$'#!/'!#&$!-;.$0%('3;%#/'*!1,*'$#! ;.! ,'3! 3(?'<! /'! _Z! -$%('3! %+%)$-9! =$1.$0,#;0$! -.,'-! ;.! #(! UZ! R! ?$0$! (:#,/'$3<! &(?$4$0! #&$! ),+$0/'*! %('%$.#! 2,/)$3! 7),0*$0! #$1.$0,#;0$! -.,'-! ?$0$! ,%&/$4$3! ?/#&(;#! #$0:/;189! I&/)$! #&$! J0+(2;$)-! *0(;.! ,#! #&$! a'/4$0-/#+!(2!N/%#(0/,!:$*,'!?(0C/'*!('!,!0(#,0+!"56!#(!)/@;$2+!',#;0,)! *,-<! #&$! "-#0(',;#/%-! J(0.(0,#/('! /'! %((.$0,#/('! ?/#&! #&$! d,C! 6/3*$! ],#/(',)!A,:(0,#(0+!:;/)#!,'3!#$-#$3!,!1$3/;1!-%,)$!1,*'$#/%!0$20/*$0,#(0! '$,0!#&$!)/@;$2,%#/('!#$1.$0,#;0$!(2!'/#0(*$'![V\9!=&$!3$-/*'!1,3$!;-$!(2! #?(!Q!C*!0$*$'$0,#(0-!0$%/.0(%,#/'*!/'!,!_!=!-;.$0%('3;%#/'*!1,*'$#9!=&$! 3$4/%$! .0(3;%$3! ;.! #(! QU! I! (2! %(()/'*<! ,'3! ;'3$0! '(! )(,3! ,'3! ,! &$,#! 0$e$%#/('!#$1.$0,#;0$!(2!`Q!R!#&$!%()3!$'3!(2!#&$!0$*$'$0,#(0!0$,%&$3!TT! R9! A,#$0<! ,#! #&$! "1$-! A,:(0,#(0+! /'! G(?,<! #&$! "-#0(',;#/%-! J(0.(0,#/('! :;/)#! ,'3! -;%%$--2;))+! #$-#$3! ,! .0((2! (2! %('%$.#! 0$%/.0(%,#/'*! 0((1! #$1.$0,#;0$!3$4/%$!%,.,:)$!(2!.0(3;%/'*!UZZ!I!(2!%(()/'*!.(?$0!,'3!,! %($22/%/$'#! (2! .$02(01,'%$! (2! V! (0! 1(0$! [_\9! "! &$)/;1W/11$0-$3! -;.$0%('3;%#/'*! 1,*'$#! ?/#&! ,! 2/$)3! ;.! #(! _! =! ?,-! ;-$39! G'! F^^`<! 0$-$,0%&$0-! ,#! "-#0(',;#/%-! J(0.(0,#/('! 0$.(0#$3! ,! 0((1W#$1.$0,#;0$! 3$4/%$! ;-/'*! Y3! 0$20/*$0,'#! ,'3! ,! ?,#$0W*)+%()! &$,#! #0,'-2$0! 2);/39! =&$! %(()/'*!.(?$0!(2!#&/-!3$4/%$!?,-!&/*&<!:;#!1(0$!-/*'/2/%,'#)+<!#&$+!?$0$! ,:)$! #(! -&(?! 0$20/*$0,#/('! ?/#&! ,'! ,..)/$3! 2/$)3! ,-! )(?! ,-! F9_! =$-),9! G'! %()),:(0,#/('!?/#&!#&$!"1$-!A,:(0,#(0+<!#&/-!?(0C!/-!'(?!:$/'*!3/0$%#$3! #(?,03-! #&$! 3$4$)(.1$'#! (2! ,! %(11$0%/,)! 0$20/*$0,#(0! '$,0! 0((1!.

(16) 5. G'#0((3;%#/('. #$1.$0,##;0$! ;-/'*! .$01,'$'##! 1,*'$#-9 "! 0(#,#/'**! f1,*'$#//%! ?&$$)g! 1,%&/'$$!3$4$)(.$33!,#!"-#0(',;;#/%-!?,-!(. .$0,#$3!2(0!(4$0!FUZZ!&&!:$#?$$'! QZZF! ,''3! QZZ_! [F\\! ,'3! /#! -#/)))! 0$.0$-$'#--! #&$! :$'%& &1,0C! 2(0! .$01,'$'#! . 1,*'$#! 1,*'$#/%! 0$20/*$0,#(00-9! ! G'! QZZZQ! ,'! "%%#/4$! 5,*''$#/%! =$-#! "..,0,#;;-!?,-!%(1 1.)$#$3!,'3!#$-#$3!:+!#&&$!J0+(2;$)!P+-#$1-!*00(;.!,#!#&$! a'/4$0-//#+!(2!N/%#((0/,9!=&$!3$--/*'!,'3!%(('-#0;%#/('!? ?,-!%,00/$3!(;#!:+!"9! 6(?$!,--!.,0#!(2!&/-!3(%#(0,#$!00$-$,0%&![S\\9!=&$!0$%/.00(%,#/'*!3$44/%$!1,3$! ;-$!(2!,!Q!=!-;.$0%(('3;%#/'*!1 1,*'$#!,'3!#?(!"56--!?/#&!,!1,---!(2!;.!#(! ? 3$-/*'$$3! 2(0! 2)$>//:/)/#+<! ?/#&&! #&$! 1,/'! FSU! *! $,,%&9! =&$! 0$$20/*$0,#(0! ?,-! (:e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`\9! G'! QZZZU! GG6! (0*,,'/O$3! #&$! 2/0-#! G'##$0',#/(',)! J('2$0$'%%$! ('! 5,* *'$#/%! 6$220/*$0,#/('! ,#! 6((1! =$1.$0,,#;0$<! ',1$$3! =&$01,**9! =&/-! :/$$''/,)! $4$'##! &,-! -(! 2,,0! */4$'! ,! -;:-#,'#/,)!1(1$'##;1!#(!#&$!00$-$,0%&!,'3 3!3$4$)(.1 1$'#!,%0(--!##&$!?(0)39! .1$'#! &,-! 2)(;0/-&$33! ,'3! #&$! 5,#$0/,))! 3/-%(4$0++! ,'3! -+-#$$1! 3$4$)(. ';1:$0! (2!0$),#$3!,,'';,))+!.;;:)/-&$3!.,..$0-!&,-!$>..('$'#/,))+! /'%0$,-$3! 7E/*;0$!FWQ89! !. Figgure 1-2:!];1 1:$0!(2!.;:)/%%,#/('-!.$0!+$,,0![^\9!. !.

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(18) 7. G'#0(3;%#/('!. 2/$)3<!#&$!"56!/'%0$,-$-!#&$!#$1.$0,#;0$!-.,'! 1,'+!#/1$-!#&$!,3/,:,#/%! #$1.$0,#;0$!%&,'*$!,-!%,'!:$!-$$'!/'!E/*;0$!FWS9! !. ! Figure 1-3ǣ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

(19) 8. Chapter 1 !. 1.2.1 Key Parameters "! ),0*$! ';1:$0! (2! .,0,1$#$0-! ,22$%#! #&$! :$&,4/(0! ,'3! #&$! .$02(01,'%$! (2! ,'! "56! ,-! /));-#0,#$3! /'! ƒ„Ž‡ ͳǦͳ9! =&$-$! .,0,1$#$0-! %,'!:$!%,#$*(0/O$3!,-!*$(1$#0/%<!1,*'$#/%<!#&$01(2);/3<!(0!(.$0,#/(',)9! G#! /-! ,! %&,))$'*/'*! ,'3! )$'*#&+! #,-C! #(! $>.$0/1$'#,))+! #$-#! #&$! -+-#$1! -$'-/#/4/#+! 2(0! $,%&! 4,0/,:)$9! E;0#&$01(0$! ';1$0/%,)! 1(3$)/'*! &,-! '(#! :$$'! %('-/-#$'#)+! 0$)/,:)$<! ),0*$)+! 3;$! #(! #&$! %(1.)$>/#+! ,'3! #&$! '('W )/'$,0/#+! (2! #&$! .0(:)$1! ,-! ?$))! ,-! ;'%$0#,/'#/$-! ,--(%/,#$3! ?/#&! #&$! 1,#$0/,)!.0(.$0#/$-9 ! Table 1-1.!N,0/,:)$-!/'!,'!"56!-+-#$19! Geometric. Magnetic. Thermofluid/Operational. D(0(-/#+!. E/$)3!/'#$'-/#+!. M$,#!#0,'-2$0!2);/3!. 6$*$'$0,#(0!-&,.$!. "56!1,#$0/,)!. a#/)/O,#/('<!ĭ!. 6$*$'$0,#(0!,-.$%#!0,#/(!. E/$)3!3/-#0/:;#/('!. E0$@;$'%+!. D,0#/%)$!-/O$!. E);>!-&/11/'*!. D0$--;0$!. !. !. M$,#!-/'C!#$1.$0,#;0$!. !. !. J(()/'*!. !. !. D&,-/'*!. ! ! 1.2.2 Temperature Profile and Cooling Power Y/4$'! ,'!"56!,'3! ,!-$#!(2!.,0,1$#$0-!,-!3$2/'$3!/'!ƒ„Ž‡ͳǦͳ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(21) 10. Chapter 1. !. Figure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‹‰—”‡ͳǦͶ9!! ! 1.3 Thesis Objective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

(22) G'#0(3;%#/('!. 11. 2);/3! #0,'-.(0#! -#;3+! 70$*$'$0,#/('8<! ,'3! ,! &+:0/3! -#;3+! #&,#! %(;.)$-! #&$! .0$4/(;-!#?(!2(0!#&$!),+$0/'*!.0(%$--9! "! 4,-#! ,1(;'#! (2! )/#$0,#;0$! $>/-#! #&,#! 3$,)-! ?/#&! #&$! (.#/1/O,#/('! (2! .,--/4$! 0$*$'$0,#(0-! ;-$3! /'! *,-! %(1.0$--/('! 3$4/%$-9! N$0+! 2$?<! &(?$4$0<! 3$,)! ?/#&! &$,#! #0,'-2$0! ;'3$0! (-%/)),#/'*! 2)(?! %('3/#/('-! ;-/'*! ?,#$0! ,-! ,! &$,#! #0,'-2$0! 2);/3! ,-! /'! #&$! .0$-$'#! ?(0C9! d2#$'! #&$! .,%C/'*! *$(1$#0+!#(!:$!%&,0,%#$0/O$3!/-!0,'3(1)+!3/-#0/:;#$3!7-;%&!,-!/'!.,0#/%)$! (0! %0;-&$3! .,0#/%)$! :$3-8! 1,C/'*! 3/0$%#! -/1;),#/('! 2(0! $>#0,%#/('!(2!&$,#! #0,'-2$0!3,#,!3/22/%;)#9!! =&/-! ?(0C! ,/1-! #(! $-#,:)/-&/'*! ,! %)$,0! $>.$0/1$'#,)! ,'3! #&$(0$#/%,)! 1$#&(3()(*+! #(! $>#0,%#! $22$%#/4$! &+30,;)/%! ,'3! #&$01,)! #0,'-.(0#! .0(.$0#/$-9!=&/-!(:e$%#/4$!0$@;/0$-!#&$!2())(?/'*!,%#/4/#/$-X! F9! H>.$0/1$'#,#/('9! =&/-! /'4()4$-! ,'! ,..,0,#;-! 3$4$)(.1$'#<! 3,#,! ,%@;/-/#/('!&,'3)/'*<!,'3!!3,#,!%())$%#/('!:+!4,0+/'*!(.$0,#/'*!.,0,1$#$0-! ,-! 20$@;$'%+<! -#0(C$<! &$,#$0! ,'3! %(()/'*! )(,3! ;-/'*! ,! 1/%0(%&,''$)! ,'3! -.&$0$-!0$*$'$0,#(09!! Q9! D,0,1$#$0! $>#0,%#/('! 7];--$)#! ';1:$0! ,'3! 20/%#/('! 2,%#(08! (2! $>.$0/1$'#,)!3,#,!;-/'*!-/1.)/2/$3!1,%0(-%(./%!#&$01(3+',1/%!1(3$)-9!! S9! N,)/3,#/('!(2!$>.$0/1$'#,))+!2(;'3!.,0,1$#$0-! ?/#&!#&$!,4,/),:)$! )/#$0,#;0$9!! !.

(23) Chapter 2 Magnetic Refrigeration Theory 2.1 The Magnetocaloric Effect 5,*'$#/%! 0$20/*$0,#/('! $>.)(/#-! ,! .0(.$0#+! 3/-.),+$3! :+! %$0#,/'! 1,*'$#/%!1,#$0/,)-X!#&$!1,*'$#(%,)(0/%!$22$%#!75JH89!G'!#&$-$!1,#$0/,)-<! ,! -/*'/2/%,'#! %&,'*$! /'! $'#0(.+! %,'! :$! $22$%#$3! :+! #&$! ,..)/%,#/('! (0! 0$1(4,)! (2! ,! 1,*'$#/%! 2/$)3<! "9! E(0! 1,#$0/,)-! ?/#&! ,! -/1.)$! ! 1,*'$#/%! ?(0C! 1(3$<! #&$! 5JH! 3$.$'3-! (')+! ('! #&$! ,:-();#$! #$1.$0,#;0$! (2! #&$! 1,#$0/,)<! %! ,'3! #&$! 1,*'$#/%! 2/$)3! %&,'*$<! ǻ"! 7?&/%&! $>.0$--$-! #&$! 3/22$0$'%$! "L( W"N8! [FT\9! =&$! 5JH! %,'! :$! /'#$0.0$#$3! ,-! #&$! /-(#&$01,)! $'#0(.+! %&,'*$! (0! ,3/,:,#/%! #$1.$0,#;0$! %&,'*$! ,-! /#! /-! 3$2/'$3! /'! #&$! 2())(?/'*!$>.0$--/('-X! ! !!οܵெ ሺܶǡ ο‫ܪ‬ሻ ൌ ܵ൫ܶǡ ‫ܪ‬௙ ൯ െ ܵሺܶǡ ‫ܪ‬௜ ሻ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9F8! ! !οܶ௔ௗ ሺܵǡ ο‫ܪ‬ሻ ൌ ܶ൫ܵǡ ‫ܪ‬௙ ൯ െ ܶሺܵǡ ‫ܪ‬௜ ሻ!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9Q8!!!! !!!!!!!!!!!!!!!!!!!! H@;,#/('-! 7Q9F8! ,'3! 7Q9Q8! ,0$! *0,.&/%,))+! /));-#0,#$3! /'! E/*;0$! QWF7,8<! ?&$0$!#&$!4$0#/%,)!)/'$!/-!#&$!/-(#&$01,)!$'#0(.+!%&,'*$!,'3!#&$!&(0/O('#,)! )/'$!/-!#&$!/-$'#0(./%!7,3/,:,#/%8!#$1.$0,#;0$!%&,'*$9!B(#&!#0,'-2(01,#/('-! (%%;0!:$#?$$'!#&$!-,1$!6Z%H"[(%;04$-9!!! ! !.

(24) 13. 5,*'$#/%!6$20/*$0,#/('!=&$(0+!. "(\("L(\(XQVIJ((. ǻ60(h(%\%!((. =(#,)!H'#0(.+!. ǻ%TB!h!%\%!!!. 5,*'$#(%,)(0/%!H22$%#!!75JH8!. "(\("N(\(XQVIJ((. ǻ%TB((. %!MGNA( ǻ60((. (a) =$1.$0,#;0$!. (b) =$1.$0,#;0$!. Figure 2-1. Y0,.&/%,)!0$.0$-$'#,#/('!(2!#&$!5JH![FT\9!. ! E/*;0$!QWF7:8!/));-#0,#$-! 'SM !,'3! 'Tad !2(0!,!0,'*$!(2!#$1.$0,#;0$-!/'!#&$! .0(>/1/#+!(2!#&$!J;0/$!#$1.$0,#;0$<!%!MGNA!2(0! 'H Hf  Hi 9!G'!*$'$0,)< Hi /-!-$#!#(!O$0(9!")-(!,!%(00$),#/('!:$#?$$'!#&$!5JH!,'3!1,*'$#/O,#/('!%,'! :$! 3$0/4$39! B+! 4,0+/'*! #&$! 1,*'$#/%! 2/$)3<! ?(0C! /-! .$02(01$3! ,'3! #&$! /'#$0',)! $'$0*+! (2! #&$! -+-#$1! %&,'*$-9! =&;-<! ,! 3/22$0$'#/,)! 4,0/,#/('! /'! /'#$0',)!$'$0*+!%,'!:$!,%%(1.)/-&$3!:+!,!1,*'$#/%!?(0C!/'#$0,%#/('!*/4$'! :+! #&$! .0(3;%#! (2! #&$! ,..)/$3! 1,*'$#/%! 2/$)3<! "<! ,'3! #&$! 4,0/,#/('! /'! 1,*'$#/O,#/('<!E![S\X! ! !. !!!!!!!!!!ߜܹ௠ ൌ ߤ଴ ‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!݉݀ܪ‬7Q9S8!. P/'%$!2(0!,!1,#$0/,)!#&,#!&,-!,!-/1.)$!1,*'$#/%!?(0C!1(3$<!I(\(IZ%H"[<!,! 3/22$0$'#/,)!%&,'*$!/'!$'#0(.+!%,'!:$!?0/##$'!,-X! ! ߲‫ݏ‬. !. ߲‫ݏ‬. ! !!!!!݀‫ ݏ‬ൌ ቀ ቁ ݀ܶ ൅ ቀ ቁ ݀‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ܪ‬7Q9T8! ߲ܶ. ு. ߲‫ܪ‬. ். !.

(25) 14. Chapter 2. ?&$0$!I!/-!#&$!$'#0(.+!.$0!;'/#!1,--9!a-/'*!#&$!3$2/'/#/('!(2!&$,#!%,.,%/#+<! #&$!,:(4$!%,'!:$!0$?0/##$'!,-<! ! !!!!݀‫ݏ‬ሺܶǡ ‫ܪ‬ሻ ൌ. ஼ಳ ሺ்ǡுሻ ். ߲‫ݏ‬. ݀ܶ ൅ ቀ ቁ ݀‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ܪ‬7Q9U8! ߲‫ܪ‬. ். ! G2!,'!/-$'#0(./%!2/$)3!%&,'*$!/-!.0(3;%$3<!#&$!#$1.$0,#;0$!%&,'*$!/-X! !. !. ! !݀ܶ ൌ െ. ். ߲‫ݏ‬. ቀ ቁ ݀‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ܪ‬7Q9V8!. ஼ಹ ሺ்ǡுሻ ߲‫் ܪ‬. ,'3! ;-/'*! 5,>?$))c-! 0$),#/('-! 2(0! #&$! $@;/4,)$'%$! (2! #&$! -$%('3! 3$0/4,#/4$-! !. !. !!݀ܶ ൌ െ. ். ஼ಹ ሺ்ǡுሻ. ቀ. ߲݉ሺܶǡ‫ܪ‬ሻ ߲ܶ. ቁ ݀‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ܪ‬7Q9_8! ு. E0(1!#&/-!-/1.)$!$>.),',#/('<!('$!%,'!3$3;%$!#&,#!,!1,#$0/,)!?/#&!'(! -/*'/2/%,'#! ?(0C! 1(3$-! (#&$0! #&,'! 1,*'$#/%! -&(;)3! &,4$! ,! &/*&! 0,#/(! (2! 1,*'$#/%! $'#0(.+! %&,'*$! #(! #(#,)! $'#0(.+! #(! .0(3;%$! ,! ),0*$! ,3/,:,#/%! #$1.$0,#;0$!%&,'*$9!=&$!5JH!2(0!,!%&,'*$!/'!1,*'$#/%!2/$)3!20(1!Z!#(!"! /-!0$),#$3!#(!H@;,#/('!7Q9_8!:+! ! ு. !!‫ ܧܥܯ‬ൌ െ ‫׬‬଴. ். ஼ಹ ሺ்ǡுሻ. ߲݉ሺܶǡ‫ܪ‬ሻ. ቀ. ߲ܶ. ቁ ݀‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ܪ‬7Q9`8! ு. 2.2 Materials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e$%#/('!#$1.$0,#;0$9!.

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heory =&$!-+-#$1!;'3$0!%('-/3$0,#/('!/-!-&(?'!-%&$1,#/%,))+!/'!E/*;0$!QWQ9! =&$!$'4$)(.$!(2!,'!"56!:$3!/-!-&(?'!?/#&!,!3,-&$3!)/'$!?&/)$!,!-$%#/('! (2!/'2/'/#$-/1,)!#&/%C'$--!/-!30,?'!?/#&!,!-()/3!)/'$9!=&$!:$3!/-!1,3$!;.! (2! ,! .(0(;-! -()/3! 1,#$0/,)! #&,#! /-! #&$! 1,*'$#/%! 0$20/*$0,'#! ,'3! ,! 2);/3! ?/#&/'!#&$!.(0$-!,%#-!,-!#&$!&$,#!#0,'-2$0!1$3/;19!=&$!2);/3!#0,'-2$0-!&$,#! :$#?$$'!,!%()3!&$,#!$>%&,'*$0<!#&$!0$20/*$0,'#<!,'3!,!&(#!&$,#!$>%&,'*$09!  p 89!d4$0!,! =&$!%,.,%/#+!0,#$-!(2!#&$!2);/3!,0$!-&(?'!,-! M 7?&$0$! M !i! mc %(1.)$#$! %+%)$<! &$,#! /-! ,:-(0:$3! ,#! #&$! %()3! $'3! ,'3! 0$e$%#$3! ,#! #&$! &(#! $'39!=&$!"56!-&(;)3!:$!0$%(*'/O$3!,-!#&$!%(1:/'$3!-()/3W2);/3!-+-#$1! [S\9!.

(27) 16. Chapter 2. !. Figure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ǻ%Z%[! %9 "2#$0!,:-(0:/'*!,!&$,#!)(,3!,'3!/'%0$,-/'*!/#-!#$1.$0,#;0$!:+!ǻ%!H! #&$! 2);/3! $'#$0-! #&$! %()3! $'3! (2! #&$! 0$*$'$0,#(0<! ,:-(0:-! &$,#! 20(1! #&$!-()/3!,'3!$>/#-!#&$!"56!,#!,!#$1.$0,#;0$!%]ǻ%"! 39 =&$! "56! /-! 3$1,*'$#/O$3<! #&$! #$1.$0,#;0$! 3$%0$,-$-! 3;$! #(! #&$! 1,*'$#(%,)(0/%!$22$%#<!,'3!#&$!%+%)$!0$.$,#-! !. E/*;0$! QWS! -&(?-! #&$! ,--;1$3! 0$20/*$0,'#! %+%)$! (%%;00/'*! /'! #&$! 3/22$0$'#/,)!-$%#/('!,#!-(1$!)(%,#/('!/'!#&$!"569!=&$!%+%)$!,-!3$-%0/:$3! ,:(4$! /-! $@;/4,)$'#! #(! #&$! .0(%$--! -#,0#/'*! ,#! .(/'#! jTc! ,'3! .0(%$$3/'*! ,).&,:$#/%,))+!#(!0$#;0'!#(!#&$!-#,0#/'*!.(/'#9!!.

(28) 17. 5,*'$#/%!6$20/*$0,#/('!=&$(0+!. !. Figure 2-3.!M+.(#&$#/%,)!%+%)$!2(0!#&$!1,*'$#/%!0$20/*$0,'#!,#!-(1$!%0(--W-$%#/('!(2!#&$! "56![S\9!. ! G#! /-! ,--;1$3! #&,#! #&$! 1,*'/#;3$! (2! #&$! 5JH! 2(0! #&$! .0(%$--! :W%! /-! 3$-%0/:$3! :+! ,! 2/0-#! (03$0! =,+)(0! -$0/$-! ,..0(>/1,#/('! /'! 0$2$0$'%$! #(! .(/'#!,9!G'!#&$!0$4$0-/:)$!%,-$<!#&$!0$-;)#/'*!,0$,!?/#&/'!#&$!=W-!3/,*0,1!/-! $@;/4,)$'#!#(!#&$!1,*'$#/%!?(0C!/'.;#!.$0!;'/#!1,--!2(0!,!%(1.)$#$!%+%)$9!! G2! #&$! 3$#,/)-! (2! #&$! "56! ,0$! /*'(0$3! ,'3! ('$! 2(%;-$-! ('! #&$! ,:-(0.#/('! (2! &$,#! :+! #&$! 2);/3! 2)(?/'*! #&0(;*&! #&$! %()3! 0$-$04(/0<! #&$! %(()/'*!.(?$0!%,'!:$!3$#$01/'$3!20(1<! ! !!!ܳሶ௖ ൌ ‫݉ ׯ‬ሶ௙ ሺ‫ݐ‬ሻܿ௣ ܶ௙ ሺ‫ݐ‬ሻ݀‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!! ݐ‬7Q9^8!. ! ?&$0$! m f (t ) /-!#&$!2);/3!1,--!2)(?!0,#$!,-!,!2;'%#/('!(2!#/1$<!XF!/-!#&$!2);/3! &$,#!%,.,%/#+<!,'3!%L!/-!#&$!2);/3!#$1.$0,#;0$!,#!#&$!$>/#!(2!#&$!"569!E(0!,! %(1.)$#$!%+%)$!#&$!/'#$*0,)!%,'!:$!?0/##$'!,-<! ! ! !!ܳሶ௖ ൌ ሺ݉௙ ܿ௣ ሻοܶ௙ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9FZ8!. ! ?&$0$( ǻ%2! /-! #&$! $22$%#/4$! #$1.$0,#;0$! %&,'*$! (2! #&$! 2);/3! ,-! /#! 2)(?-! #&0(;*&! #&$! %()3! &$,#! $>%&,'*$0<! ,'3! EL! /-! #&$! 1,--! (2! 2);/3! #&,#! 2)(?-! #&0(;*&!#&$!"56!?&$'!/#!/-!3$1,*'$#/O$39!G2!#&$!0$*$'$0,#(0!&,-!,!4$0+! &/*&!';1:$0!(2!#&$01,)!#0,'-2$0!;'/#-!7]=a8<!#&$!#$1.$0,#;0$!(2!#&$!2);/3! $>/#/'*! #&$! "56! ?/))! %)(-$)+! 1,#%&! #&$! #$1.$0,#;0$! (2! #&$! -()/3! 0$20/*$0,'#! ,#! #&$! %()3! $'39! G'! ,33/#/('<! /2! #&$! #&$01,)! 1,--! (2! #&$!.

(29) 18. Chapter 2. 0$20/*$0,'#!/-!1;%&!*0$,#$0!#&,'!#&$!#&$01,)!%,.,%/#+!(2!#&$!#(#,)!2);/3!2);>! #&0(;*&! #&$! 0$*$'$0,#(0<! #&$! #$1.$0,#;0$! (2! #&$! -()/3! ?/))! '(#! %&,'*$! 1;%&9! =&$! 0,#/(! (2! #&$! 2);/3! #&$01,)! %,.,%/#+! #(! #&$! 0$*$'$0,#(0! #&$01,)! 1,--!/-!%,))$3!#&$!;#/)/O,#/('!,'3!/-!3$2/'$3!,-<! ! ௠೑ ௖೛ ! !!!!!!!!!ߔ ൌ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9FF8! !. ெ௖್. ?&$0$(0!/-!#&$!1,--!(2!0$20/*$0,'#!/'!#&$!0$*$'$0,#(0!,'3!X8!/-!#&$!&$,#! %,.,%/#+!(2!#&$!0$20/*$0,'#!#,C$'!,#!,!0$2$0$'%$!.(/'#!7(2#$'!,#!%XMGNAH("\^89! G'! #&$! )/1/#! (2! 4$0+! -1,))! ;#/)/O,#/('! ,'3! ),0*$! ]=a<! ,'3! ,--;1/'*! .,0,-/#/%!&$,#!)$,C-!,0$!/'-/*'/2/%,'#<!#&$!#$1.$0,#;0$!%&,'*$!(2!#&$!2);/3! ,-! /#! ,:-(0:-! &$,#! #&0(;*&! #&$! %()3! &$,#! $>%&,'*$0! /-! $@;,)! #(! #&$! 1,*'$#(%,)(0/%!$22$%#!(2!#&$!0$20/*$0,'#!,#!#&$!%()3!$'3!(2!#&$!0$*$'$0,#(0<! ǻ%L(\(ǻ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ொሶሺ௫ሻ ܵሶሺ‫ݔ‬ሻ ൌ ൌ ܿ‫!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!ݐݏ݊݋‬7Q9FQ8! ்ሺ௫ሻ. ! ?&$0$! S ! ,'3! Q ! ,0$! #&$! $'#0(.+! ,'3! &$,#! 2)(?! 0,#$! ,'3! T ! /-! #&$! ,:-();#$! #$1.$0,#;0$<! ,))! ,#! #&$! -,1$! ,>/,)! )(%,#/('! O_! E;0#&$01(0$<! #&$! :(;'3,0+!%('3/#/('-!,#!#&$!&(#!,'3!%()3!$'3!,0$X! ! !!!ܳሶ௖ ൌ ݉ሶ௙ ܿ௣ οܶ௔ௗ೎ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9FS8! ! !!!!ܳሶ௛ ൌ ݉ሶ௙ ܿ௣ οܶ௔ௗ೓ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9FT8! ! =&;-<!-;:-#/#;#/'*!7Q9FS8!,'3!7Q9FT8!/'#(!7Q9FQ8!?$!(:#,/'! !.

(30) 5,*'$#/%!6$20/*$0,#/('!=&$(0+! ο்ೌ೏೎. !!!!!!!!!. ்೎. ൌ. ο்ೌ೏೓ ்೓. 19. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9FU8!. ! !A,-#)+<! /2! ?$! %('-/3$0! #&$! #$1.$0,#;0$! (2! #&$! &(#! $'3! #&$! 0$2$0$'%$! #$1.$0,#;0$<!#&$!,:(4$!$>.0$--/('!-;**$-#-!#&,#!#&$!1,*'$#(%,)(0/%!$22$%#! 1;-#!-%,)$!?/#&!#$1.$0,#;0$!,%%(03/'*!#(!#&$!2())(?/'*!0$),#/('X! ! ௜ௗ௘௔௟ ሺܶሻ !!!οܶ௔ௗ ൌܶ. ο்ೝ೐೑ ்ೝ೐೑. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9FV8!. ௜ௗ௘௔௟ ?&$0$!!!οܶ௔ௗ /-!#&$!/3$,)!5JH!,#!#$1.$0,#;0$!%(<! 'Tref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e$%#/('!#$1.$0,#;0$<!;'3$0)+/'*!#&$!%(1.)$>/#+!(2!#&$!/'#$0,%#/('!(2!#&$! #$1.$0,#;0$! .0(2/)$! ?/#&! #&$! )(%,)! 5JH9! P;%&! /'#$03$.$'3$'%+! -;**$-#-! ,'(#&$0! .(--/:)$! /--;$! ?/#&! 1;)#/W1,#$0/,)! 0$*$'$0,#(0-X! /'/#/,)! %('3/#/('! -$'-/#/4/#+9! "--;1/'*! #&,#! ,'! "56! -#,0#-! (.$0,#/'*! ?/#&! ,! ;'/2(01!.

(31) 20. Chapter 2. #$1.$0,#;0$! (2! %( \( %"<! /#! ?/))! $4$'#;,))+! 0$,%&! ,! .-$;3(! -#$,3+! -#,#$! #$1.$0,#;0$! 3/-#0/:;#/('9! "#! #&$! :$*/''/'*! (2! #&$! .0(%$--<! %(()/'*! /-! ,)1(-#!$'#/0$)+!.$02(01$3!:+!#&$!&(#!$'3!),+$0<!?&/%&!/-!,)0$,3+!?/#&/'!/#-! 5JH! (.$0,#/'*! #$1.$0,#;0$! 0,'*$! 7,--;1/'*! #&,#! #&$! 1,#$0/,)-! &,4$! -/*'/2/%,'#)+! 3/22$0$'#! J;0/$! #$1.$0,#;0$-89! "-! ,! #$1.$0,#;0$! *0,3/$'#! -#,0#-! #(! 3$4$)(.<! #&$! (#&$0! ),+$0-! :$*/'! %('#0/:;#/'*! #(! #&$! (4$0,))! 0$20/*$0,#/('! .0(%$--<! ;'#/)! ,! -#$,3+! -#,#$! #$1.$0,#;0$! .0(2/)$! /-! $-#,:)/-&$39! =&$! ),0*$0! #&$! 2/',)! #$1.$0,#;0$! -.,'<! #&$! 2;0#&$0! ,?,+! #&$! %()3!$'3!/-!20(1!/#-!5JH!(.$0,#/'*!0,'*$!,#!#&$!:$*/''/'*!(2!#&$!.0(%$--9! =&;-<! /#! /-! .(--/:)$! #&,#! ?&$'! -#,0#/'*! 20(1! ,! #$1.$0,#;0$! .0(2/)$!%ZO[( \( %"<!#&$0$!/-!'(#!$'(;*&!%(()/'*!.(?$0!#(!30/4$!#&$!"56!#(!#&$!$>.$%#$3! (.$0,#/'*! 0$*/1$9! G#! %(;)3! #&$'! :$! '$%$--,0+! #(! .0$W%(()! #&$! %()3! $'3! #(! f.0/1$g! #&$! 0$*$'$0,#(09! G'! #&/-! %,-$! #&$! "56! %(;)3! &,4$! #?(! (0! 1(0$! (.$0,#/'*!0$*/1$-!3$.$'3/'*!('!#&$!/'/#/,)!%('3/#/('-9!! Y(4$0'/'*! $@;,#/('-! 2(0! ,'! "56! -+-#$1! &,4$! :$$'! 3$4$)(.$3! #&0(;*&(;#! #&$! +$,0-! ?/#&! #&$! (:e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`\X! ! !! !ߩ௙ ܿ௣ ‫ܣ‬௙. డ்೑ డ௧. ൌ െ݉ሶ௙ ܿ௣. డ்೑ డ௫. ൅. డ. డ௫. ቀ݇௙ ‫ܣ‬௙. డ்೑ డ௫. డ௣ ௠ሶ. ቁ ൅ ݄ܲ௪ ൫ܶ௦ െ ܶ௙ ൯ ൅ ฬడ௫ ఘ ฬ!!!!!!!! ೑. ! !!!!!!7Q9F_8!! ?&$0$! ȡL! /-! #&$! 3$'-/#+<! #L! /-! #&$! ,0$,! (2! 2);/3! 2)(?<! DL! /-! #&$! #&$01,)! %('3;%#/4/#+<!C!/-!#&$!%('4$%#/('!&$,#!#0,'-2$0!%($22/%/$'#<!$R!/-!#&$!?$##$3! .$0/1$#$0<! (0! %0(--W-$%#/(',)! %('#,%#! ,0$,! :$#?$$'! #&$! 2);/3! ,'3! #&$! 0$*$'$0,#(0! 1,#0/><! ,'3! F! /-! #&$! 2);/3! .0$--;0$9! "))! .,0,1$#$0-! ?/#&! #&$! -;:-%0/.#! L! 0$2$0! #(! #&$! 2);/39! =&$! 4/-%(;-! )(--$-! ,0$! ,! 2;'%#/('! (2! #&$! డ௣ .0$--;0$!30(.! <!?&/%&!-#0('*)+!3$.$'3-!('!#&$!(.$0,#/'*!20$@;$'%+!,'3! డ௫ -+-#$1! .0$--;0$9! D0$--;0$! 30(.! -$#-! ,! 1,e(0! )/1/#,#/('! ('! "56! $22/%/$'%+<! #&;-<! 1;%&! ?(0C! /-! 2(%;-$3! ('! /#-! 1/'/1/O,#/('! #&0(;*&! #&$!.

(32) 5,*'$#/%!6$20/*$0,#/('!=&$(0+!. 21. %&(/%$!(2!&$,#!#0,'-2$0!2);/3<!0$*$'$0,#(0!1,#0/>!1/%0(-%,)$!-#0;%#;0$<!,'3! "56!,-.$%#!0,#/(9! P/1/),0)+!#&$!$'$0*+!:,),'%$!2(0!#&$!-()/3!1,#0/>!%,'!:$!$>.0$--$3!,-! /#!2())(?-![F`\X! !!!!!!!!!!!!!! డ்ೞ డ௨ೞ డ௠ డ ߩ௦ ‫ܣ‬௦ ቀ െ ‫ ܤ‬ቁ ൌ ቀ݇௦ ‫ܣ‬௦ ቁ ൅ ݄ܲ௪ ൫ܶ௙ െ ܶ௦ ൯!!!!!!!!7Q9F`8! డ௫ డ௧ డ௧ డ௫ ! ?&$0$! #&$! 1,*'$#/%! ?(0C! #$01! &,-! :$$'! *0(;.$3! ('! #&$! )$2#! -/3$! (2! #&$! $>.0$--/('! ?/#&! #&$! /'#$0',)! $'$0*+! #$019! B(#&! #&$! 2);/3! ,'3! 1,#0/>! $>.0$--/('-! ,--;1$! ;'/2(01! .0(.$0#/$-! /'! #&$! 0,3/,)! 3/0$%#/('! ,'3! ,3/,:,#/%! %+)/'30/%,)! ?,))-9! G'! H@;,#/('! 7Q9F`8! #&$! 3/--/.,#/('! #$01-! ,0$! '(#! .0$-$'#<! &(?$4$0! #&$0$! /-! ,'! ,33/#/(',)! 1,*'$#/%! ?(0C! #$019! =&$! H@;,#/('!7Q9F_8!%,'!:$!$>.0$--$3!,-![F`\X! !!!!!!!!! ݇. డ்೑ డ௧ ‫כ‬. ൌ െߔ. డ்೑ డ௫ ‫כ‬. ൅. డ. ൬. ఝ డ்ೞ. డ௫ ‫ כ‬௉௘೑ డ௫ ‫כ‬. ൰ ൅ ܷܰܶߔሺܶ௦ െ ܶ௙ ሻ!!!!!!!!!!!!7Q9F^8!. !. ?&$0$!#&$!2())(?/'*!!'('W3/1$'-/(',)!.,0,1$#$0-!&,4$!:$$'!/'#0(3;%$3X! ! !!!!!!!ߔ ൌ. ௠ሶ೑ ௖೛ ఛ ெೞ ௖ಳ. !!!!ܷܰܶ ൌ ݇ൌ. ௛஺ೢ. ௠ሶ೑ ௖೛. ெ೑ ௖೛ ெೞ ௖ಳ. !!!!!ܲ݁௙ ൌ. !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9QZ8! ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9QF8!. ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9QQ8!. ௠ሶ௖೑ ௅. ௞೐೑೑ ஺೑. ! !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9QS8!. ! !!!!!!‫ ݐ‬ൌ Ǣ‫ ݔ‬ൌ !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!7Q9QT8! ் ௅ ! ?&$0$!#R!/-!#&$!?$##$3!,0$,<!0L!#&$!1,--!(2!#&$!*,-!?/#&/'!#&$!0$*$'$0,#(0<! 5!)$'*#&!(2!#&$!0$*$'$0,#(0<!,'3!DALL!/-!#&$!%('3;%#/4/#+!(2!#&$!0$*$'$0,#(0! ,'3!2);/3<!#,C/'*!/'#(!,%%(;'#!3/-.$0-/('!$22$%#-9! ‫כ‬. ௧. ‫כ‬. ௫.

(33) !. Chapter 3 Thermal Regenerators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e$%#$3!#(!#&$!&(#!-.,%$![F^\9!! =&$!2/0-#!#$%&'/%,)!,..)/%,#/('!#&,#!1,3$!;-$!(2!0$*$'$0,#(0-!1/*&#!:$! #&$! P#/0)/'*! $'*/'$9! G'! ,! #?(! %+)/'3$0! #+.$! P#/0)/'*! $'*/'$! #&$! #?(! %+)/'3$0-!,0$!%(''$%#$3!;-/'*!,!0$*$'$0,#(09!=&$!0$*$'$0,#(0!.$0/(3/%,))+! -#(0$-!#&$!$'$0*+!#&,#!/-!3/-.),%$3!20(1!$/#&$0!#&$!&(#!(0!#&$!%()3!%+)/'3$09! I/#&(;#! #&$! 0$*$'$0,#(0! #&$! -#(0$3! ,1(;'#! (2! #&$01,)! $'$0*+! ?(;)3! :$! /00$4$0-/:)+!0$e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

(34) =&$01,)!6$*$'$0,#(0-!. 23. 3.1 Thermohydraulic Optimization of Regenerators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d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

(35) 24. Chapter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assive Regenerator Testing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d'%$! #$-#! 3,#,! &,-! :$$'! %())$%#$3<! #&$! 3,#,! /-! ,',)+O$3! ,'3! ;-$2;)! /'2(01,#/('! )/C$! ];--$)#! ';1:$0! /-! $>#0,%#$39! =&$! .),;-/:/)/#+! (2! #&$! 0$-;)#-! /-! 4,)/3,#$3! ?/#&! /'3$.$'3$'#! -/1;),#/('-! ,'3b(0! %(1.,0/'*! #(! $>/-#/'*! %(00$),#/('-c! (;#%(1$-9! "2#$0! -(1$! /#$0,#/('-! #&$! *$(1$#0+! %,'! :$! %(1.,0$3! #(! .0$4/(;-)+! #$-#$3! -#0;%#;0$-9! G'! #&/-! ?,+<! .0$2$00$3! *$(1$#0/$-! %,'! :$! 2,:0/%,#$3! ;-/'*! ,%#/4$! 1,*'$#/%! 1,#$0/,)-! ,'3! #&;-!.

(36) =&$01,)!6$*$'$0,#(0-!. 25. ,))(?-!2(0!#$-#/'*!/'!"566!.0(#(#+.$-9!M(?$4$0<!/#!1;-#!:$!.(/'#$3!(;#! #&,#! ,! ?$))! .$02(01/'*! .,--/4$! *$(1$#0+! 1/*&#! :$! /'2$,-/:)$! 2(0! ,%#/4$! 1,*'$#/%! ;-$<! :$%,;-$! /#! $'&,'%$-! 1,*'$#/%! )(--$-<! )/C$! -#0('*! 3$1,*'$#/O/'*!$22$%#-!(0!$33+!%;00$'#!3/--/.,#/('9! ! 3.3 Previous Work and Literature Review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

(37) 26. Chapter 3. ';1:$08<!#&$01,)!3/-.$0-/('!,'3!#&$01,)!#(0#;(-/#+9!G'!,33/#/('<!$22$%#/4$! #&$01,)! %('3;%#/4/#/$-! ,..$,0! /'! #&$! :,),'%$! $@;,#/('-! 20(1! 4();1$! ,4$0,*/'*9! G'! #&$(0+<! ,))! #&$-$! k'$?k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d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`\! %,1$! ;.! ?/#&! ,! '$?! ];--$)#! ';1:$0! %(00$),#/('! 2(0! .,%C$3! :$3! (2! -.&$0$-! ?/#&! 3/,1$#$0! (2! T119! M$! /'4$-#/*,#$3! #&$! &$,#! #0,'-2$0! ;-/'*! ?,#$0! ,'3! ?,#$0W*)+%()! 1/>#;0$-! ,-! &$,#!#0,'-2$0!1$3/;19!=&$!0$*$'$0,#(0!3/1$'-/('-!,0$!4$0+!-/1/),0!#(!#&$! .0$-$'#! ?(0C9! M$! 2(;'3! #&,#! &/-! '$?! %(00$),#/('! -/*'/2/%,'#)+! ;'3$0! .0$3/%#-!#&$!I,C,(!%(00$),#/('!73$0/4$3!2(0!*,-$(;-!&$,#!#0,'-2$0!2);/3-89! M$! ,)-(! 2(;'3! ,! ),0*$! $>.$0/1$'#,)! ;'%$0#,/'#+! (2! #&$! ];--$)#! ';1:$0! ?&/%&! /-! ,1.)/2/$3! :+! #&$! #$1.$0,#;0$! 3$.$'3$'%$! (2! 6$+'()3-! ,'3! D0,'3#)! ';1:$09! M/-! %(00$),#/('! #;0'$3! (;#! #(! :$! %)(-$! #(! #&$! ('$! .0$-$'#$3!:+!5,%/,-W5,%&/'!$#!,)![Q^\!?&(!/'4$-#/*,#$3!];--$)#!';1:$0! 2(0!)/@;/3!&$,#!#0,'-2$0!2);/3-!(')+9! G#! 1;-#! :$! .(/'#$3! (;#! #&,#! ,))! #&$! ?(0C! 0$4/$?$3! #(! #&/-! .(/'#! %(00$-.('3-!#(!#&$!-(!%,))$3!f-/'*)$W:)(?f!#$%&'/@;$9!G'!#&/-!#$%&'/@;$!#&$! 0$*$'$0,#(0! /-! 2);/3/O$3! ,#! ,! %('-#,'#! 2)(?! 0,#$9! "#! #&$! :$*/''/'*! (2! #&$! $>.$0/1$'#! #&$! 0$*$'$0,#(0! /-! -;:e$%#$3! #(! ,! @;,-/W-#$.! %&,'*$! /'! #$1.$0,#;0$9!P/1;)#,'$(;-)+<!#&$!#$1.$0,#;0$!/-!0$%(03$3!3(?'-#0$,1!(2! #&$! 0$*$'$0,#(09! =&$! #$1.$0,#;0$! 0$-/3;,)! (2! 1(3$)! ,'3! $>.$0/1$'#! 3(?'-#0$,1!(2!#&$!0$*$'$0,#(0!/-! 1/'/1/O$3!:+!,'!,..0(.0/,#$!%&(/%$!(2! #&$!&$,#!#0,'-2$0!%($22/%/$'#!3$#$01/'$3!:+!,!)$,-#!-@;,0$!$-#/1,#(09!=&/-! 1$#&(3!(')+!,..0(>/1,#$-!#&$!&$,#!#0,'-2$0!/'!0$*$'$0,#(0-!-/'%$!#&$!2)(?! /'!#&$01,)!0$*$'$0,#(0!(.$0,#/('!/-!(-%/)),#/'*9!.

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