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1 Rheter tte f ehlgy R Shlr Wrk hee he/de lle 2995 ret perfre f prllelflw rflw ret trfer type het exhger wth tep tepere hge the pty e fl tre Br D. le Fllw th l wrk t: Reee t le, Br D., "ret perfre f prllelflw rflw ret trfer type het exhger wth tep tepere hge the pty e fl tre" (995). he. Rheter tte f ehlgy. Aee fr h he brght t y fr free pe e by the he/de lle t R Shlr Wrk. t h bee epte fr l hee by thrze tr f R Shlr Wrk. Fr re fr, plee tt hlrwrk@.e.

2 ret Perfre fprllelflw r Flw Dret rfer ype Het xhger wth Step epere hge the M pty Rte Fl Stre by Br D. le A the btte prl flfllet fthe reqreet fr the egree f Mter fsee Mehl geerg Apprve By: Prfer Sh G. Klkr (he Avr) Prfer Blwt V. Krlekr Prfer Al H. Nye Prfer hrle W. He (Depet He) DPARMN F MHANAL NGNRNG LLG F NGNRNG RHSR NSU F HNLGY DMBR 995

3 R w Abt Prllel rflw wth bth fl xe, ret trfer type het exhger re ele lzg therl etwrk g f e retr. A erlly vlble ftwre pkge, heret, llte the tret tlet tepere fr teytte el tre t e hge (tep pt) let tepere f the fl tre. Bth el re vlte gt lyl l prve ltere. Sl re verfe t wth x peret e fferee f 4 % f lyl l fr prllelflw, % f lyl l fr rflw het exhger. ble re geee whh prve ew ele tret tlet tepere effevee vle fr prllel rflw wth bth fl xe, het exhger. he prllelflw tepere repe re preete grphl fr fr the pef preter: NU eql t.5,.,.; eql t.2,.6,.; eql t.5,., 2.; eql t.,.,.; t eql t.25,., 4.. he rflw tepere repe re preete grphl fr fr the e preter lte bve exept NU eql t.. D regrg the ele preter' effet the tret repe f the het exhger prve. he tret perfre tble prve qk referee fr tret tlet tepere l reqre fr prl trl het exhger ly.

4 Akwleget wh t expre y eret thk ppre t Dr. Sh Klkr. H refl ge, pp, kwlege e ple f th wrk pble. Al, eeply gefl t y wfe, J, fr her pp, pee, ergeet thrght th pre.

5 Per Grte, Br D. le, hereby grt per t the Wlle Merl Lbrry f the Rheter tte f ehlgy t repre y the etle "ret Perfre f PrllelFlw rflw Dret rfer ype Het xhger wth Step epere hge the M pty Rte Fl Stre" whle r p. Ay repr wll t be fr erl e r prft. Deeber 4, 995 Br D. le

6 ble f tet Lt f ble Lt f Fgre v Neltre v tr 2 herel Bkgr Ltere Revew 7. PrllelFlw Het xhger 7.2 rflw Het xhger 4 Appl f herl Netwrk Slver 2 4. PrllelFlw Het xhger rflw Het xhger 2 5 Vl f herl Netwrk Slver Ary 7 5. PrllelFlw Het xhger rflw Het xhger 42 6 Relt PrllelFlw Het xhger rflw Het xhger 62 7 D f Relt 66 l 7 9 Referee 72

7 Appee 75 A. Prl Appl f ret epere ffevee ble B. Sple Spreheet fr Prllel rflw epere ffevee ll. xel Spreheet Frl D. Dele Preter q xpe t Prl er. Prere fr Prllel rflw Dt Geer

8 Lt f ble ble Pge. Avlble Sl fr PrllelFlw fgr 7.2 Avlble Sl fr rflw fgr 4. Dele Vle Ulze fr pl pr fr 2 rflw Het xhger 4.2 pl Nber f Seget Aly fr rflw Het xhger Bth Fl Uxe/Sgle P 5. ret Perfre Vl fr PrllelFlw Het 7 xhger 5.2 ret Perfre Vl fr rflw Het xhger Dele Preter Ue th Aly fr Dret 54 rfer PrllelFlw Het xhger 6.2 ret epere ffevee Vle fr NU =.5, 55 Wll pte R =., PrllelFlw Het xhger 6. ret epere ffevee Vle fr NU =., 56 Wll pte R =., PrllelFlw Het xhger 6.4 ret epere ffevee Vle fr NU =., 57 Wll pte R =., PrllelFlw Het xhger 6.5 ret epere ffevee Vle fr NU =.5, 5 Wll pte R., PrllelFlw Het xhger = 6.6 ret epere ffevee Vle fr NU =., 59 Wll pte R., PrllelFlw Het xhger = 6.7 ret epere ffevee Vle fr NU =., 6 Wll pte R =., PrllelFlw Het xhger 6. ret epere ffevee Vle fr NU =.5,.,., 6 Wll pte R =, PrllelFlw Het xhger

9 ble Pge 6.9 Dele Preter Ue th Aly fr Dret 62 rfer rflw Het xhger 6. ret epere ffevee Vle fr NU =., 6 Wll pte R =., rflw Het xhger 6. ret epere ffevee Vle fr NU =., 64 Wll pte R =., rflw Het xhger 6.2 ret epere ffevee Vle fr NU =. 65 Wll pte R =, PrllelFlw Het xhger v

10 SteyStte ypl SteyStte Lt f Fgre Fgre Pge. Step pt 2.2 Freqey pt. ple pt 4.4 Dret rfer PrllelFlw Het xhger r Se 5.5 Dret rfer rflw Het xhger 6 Sgle P, Bth Fl Uxe.6 perg Befre After Step 7 hge Ht Fl let epere PrllelFlw.7 tlet epere Dtrb fr rflw Het xhger. perg Befre After Step 9 hge Ht Fl let epere rflw 2. PrllelFlw Het xhger reetl trl Vle 2 4. Dret rfer PrllelFlw Het xhger r Se 2 ( Seget Mel She Dgr) 4.2 Dret rfer PrllelFlw Het xhger herl Netwrk 2 Mel, N Wll herl Rete ( Seget Mel) 4. Dret rfer PrllelFlw Het xhger r Se 24 (2 Seget Mel She Dgr) 4.4 Dret rfer PrllelFlw Het xhger herl Netwrk 24 Mel, N Wll herl Rete (2 Seget Mel) 4.5 trl Vle fr Fl Flw Rete Derv Dret rfer rflw Het xhger, Bth Fl 2 Uxe (4x4 Seget Mel)

11 Fgre Pge 4.7 Dret rfer rflw Het xhger herl Netwrk 29 Mel, Sgle P/Bth Fl Uxe (x Seget Mel) 4. Dret rfer rflw Het xhger herl Netwrk Mel, Sgle P/Bth Fl Uxe (6x6 Seget Mel) 4.9 Dret rfer rflw Het xhger herl Netwrk Mel, Sgle P/Bth Fl Uxe (x Seget Mel) 4. pl Nber f Seget fr NU = pl Nber f Seget fr NU = pl Nber f Seget fr NU = heret Ver Re (95) Vl, PrllelFlw Be (995) pr f heret l t l by 4 Myer et l. (967), PrllelFlw Be (995) pr f heret l t l by 4 Rzk (956), PrllelFlw 5.7 heret Ver he (992) Vl, rflw heret Ver Spg (97) Vl, rflw heret Ver Re (9) Vl, rflw 4 v

12 2 r Neltre A het trfer re, p pef het t tt prere, J/(kg K) fl het pty e, Wp r rhp, J/( K) w w fl tre het pte, Mp, J/K ele het pty e, /x wll het pte, (Mp)w, J/K ele wll het pte, (Mp)w/(Mp) eergy per t e, J/ r Wtt h ve het trfer effet, W/(2 K) hgt heght, k therl vty, W/( K) L M NU q R () (t) () thk t t t t het exhger legth, flw e fthe fl tre, kg/ f fl r wll terl the het exhger, kg ele ber f het trfer t, UAJ\ het trfer e, J/ r Wtt ele therl rete r, (ha),^^]^),,,!,, tepere, K r Stey tte tlet tepere befre tret pt h bee pple, K r tlet tepere t e t, K r New tey tte tlet tep, fter tret pt h bee pple, K r thke, e, trg wth zer t begg f the tep hge, ele e, t/t5 well e, the e reqre fr fl prle t p thrgh the het exhger, ele well e, t^/tx t well e f fl, t x well e f x fl, U verll het trfer effet, W/( K) V V wth W fl velty, / vletr flwe, / het exhger wth, flw e fthe fl tre, kg/ X ele te, x/l x p the het exhger lg the flw re, v

13 Greek Letter r f effey ele teytte effevee 6f p ele tepere effevee, =[(t)()]/[()()] ety, kg/ Sbrpt t the begg f the tret hge l, fl wth teppe hge t let tepere, 2,b fl wth hge (teppe) t let tepere, f teppe fl fte e fter the tep hge pe, ew tey fl let teppe fl tte t x w tlet het pty e fl x het pty e fl het exhger wll Sperrpt ele qty v

14 tr he tet f th the t evelp vlte plfe therl etwrk el fr bth prllel rflw ret trfer type het exhger. he prve ey t e tret perfre effevee tble whh ver we rge f ele het exhger eg preter. Kwlege regrg the tret perfre f het exhger pt fr pre egeer het exhger eg egeer. Pre egeer re terete tret repe t ree yle e betwee prt hge, ree tp e, fr pre trl. h kwlege t the het exhger eg egeer whe lyzg terl tree, pzg the het exhger geetry, reg the t t ftre ew het exhger. hree type f tret tepere pt ext. hey re the tep pt, freqey pt,. the ple pt. Fgre hw tep pt whh e hge let tepere r flw e t ew, tt vle.

15 Fgre.: Step pt. S Q _. D. H e

16 he freqey pt, hw fgre.2, perlly vryg hge let tepere r flw e.

17 Fgre. hw ple pt whh hge let tepere r flw e f fte plte, bt ftel r. A tret trbe te wth het exhger the tep pt t the het exhger let. herefre the preet wrk wll f prvg tret tlet tepere l whh r e t tep pt t the let f bth prllel rflw ret trfer type het exhger. A het exhger eve whh trfer terl therl eergy betwee tw r re fl t fferet tepere. he type f exhger elete fr th the re ly lze ftrg tre. he elete exhger re prllel r flw glep, ret trfer type het exhger. Prllelflw refer t bth fl flwg

18 the e re thrgh the het exhger. rflw e the tw fl re flwg perpelr t eh ther. Sglep te the fl r pth ly e wth the het exhger. Flly, ret trfer type e the tw fl re epe by th wll thrgh whh het trfer r. here re vg p the het exhger. Bth fl flw ltely wth xg betwee the tw fl. Fgre.4 hw typl prllelflw glep, ret trfer type het exhger. Fgre.4: Dret rfer Prllelflw Het xhger r Se Het xhger Fl M^M^^e^^ Seprg Wll Fl b

19 A typl rflw glep, ret trfer type het exhger hw fgre.5. Fgre.5: Dret rfer rflw Het xhger SgleP, Bth Fl Uxe Het xhger AAA Seprg Wll N Fl terl Pr \l \l \l A Fl b Fr rflw het exhger, vl fl tre re ere ether xe r xe. he rflw het exhger el th the fr bth fl xe. ht e the terl pr prevet fl re trvere t the flw re fr eh vl fl tre.

20 fr ypl tey tte perg befre fter hge tep the ht fl let tepere re hw fgre.6 prllelflw het exhger. Fgre.6: Steytte perg befre fter tep hge ht fl let tepere PrllelFlw l teytte perg Steytte perg fter tep pt pt tep hge Repe Repe 2 l Fl let tlet Flw Legth

21 he typl let tlet tepere trb fr rflw het exhger hw fgre.7. Fgre.7: ypl tlet erpere Dtrb fr rflw Het xhger t, W H V l, _J wwq J Ll,t t,ut

22 fr ypl tey tte perg befre fter tep hge the ht fl let tepere re hw fgre. rflw het exhger. Fgre.: Steytte perg befre fter tep hge ht fl let tepere rflw l teytte perg Steytte perg fter tep pt epere pt tep hge Ht Fl Ht Fl let Repe 2 Repe l Fl l Fl let She t ppret fr fgre.6 tht there wll be tw t fl tlet tepere fr the prllelflw het exhger. he rflw het exhger wll hve vryg tlet tepere fr eh fl epeg p the l he r the flw re. he typl tehqe fr hlg th vre t verge eh fl tlet tepere t prve tw t e tlet tepere.

23 ble he tret lyze erbe fllw. A het exhger yte lly t tey tte ely tre t tret the fr f tep pt. A tep pt e hge ether the let tepere r flwe f e f the fl t ew, tt vle. he tret ly beg wth the tep pt e e the yte rehe the ew tey tte t. he prllel rflw het exhger erbe bve were ele g therl etwrk hee. A therl etwrk pre f e retr ete b t repreet the het exhger fl therl rete. Speflly, e repreet the fl eprg wll, retr repreet the fl flw pte veve rete. he etwrk w lyze g fte fferee l tehqe erlly vlble therl etwrk lver, heret rhx. he b gverg eq fr prllel rflw het exhger erbe by Shh (9), were ree t ele preter typl fr het exhger eg. he ele preter lze le NU,, R,, t, t. were geee whh prve ele tret tlet tepere effevee vle (, 2 ) fr prllel rflw het exhger verg we rge f ele pt preter. he vl fl tepere effevee, e,, 2 re l tht te het exhger perfre. he tepere effevee vle rge fr t. Zer the l teytte ele tepere, the teytte ele tepere fter the tep pt h bee pple. he tble geee prve qk referee fr tret tlet tepere l.

24 he 2 herel Bkgr he prpe f th e t tte the p, hw the gverg fferel eq erbg the tret behvr f het exhger, tte the l bry, lt the ele preter lze t erbe prllel rflw het exhger, gve feel fr the plexe te wth lyl l fr tret het exhger perfre. he fllwg elz preete by Shh (9) re lze ervg the gverg fferel eq.. tepere f bth fl the wll re f f e p (e e fr prllelflw het exhger, tw e fr rflw het exhger). 2. Het trfer betwee the exhger the rrg eglgble. here re therl eergy re wth the exhger.. he flw e f bth fl, lthgh y be fferet, t vry wth e. he fl re frly trbte lg the flw pge. 4. he velty tepere f eh fl t the let re fr ver the flw r e re tt wth e exept fr the pe tep hge. 5. he veve het trfer effet eh e, the therl prpere f bth fl the wll re tt, epeet f tepere, e p. 6. Lgtl het wth the fl wll well the trvere wth the fl eglete.

25 7. he het trfer rfe re eh fl e frly trbte.. ther the wll therl rete flg rete re eglgble r they re lpe wth veve therl rete ht l e. 9. he therl pte f the het exhger hell ere eglgble relve t tht f the het trfer rfe. A eergy ble, lzg eq 2., pple t reetl trl vle fr the P P = P '' ''t ^tre (2.) ht fl, l fl, eprg wll hw fgre 2. relt the fllwg plfe Fgre 2.: Prllelflw Het xhger reetl trl Vle Ht Fl Het xhger h,, h, ^^km^^ Seprg Wll l Fl x x fferel eq lr t teflw fferel eq plfe by Shh (9): 2

26 Ht Ht fl fferel eq: h^f + hz ^ + (ha)h(hw) = (2.2) l fl fferel eq: ^f + z + (ha)(w)=, (2.) Wll fferel eq: w^(lha)h(hw) + = (lha)(w) (2.4) where w Mwp = w = Wll het pte (2.5) h = Mhp h = Ht fl hetpte (2.6) = Mp = l fl hetpte (2.7) h = hp, h fl het pty e (2.) = p = l fl het pty e (2.9) ther ter re efe the eltre. he l fr the fl wll re bte fr the teytte tepere befre the tep pt. he bry re the let tepere hge f the teppe fl t t' ew vle the tt let tepere f the teppe fl. t ppret fr the fferel eq tht the epeet fl wll tepere re f f eleve epeet vrble preter: h = f[x,\,,h,,(ha)h,(lha),flwarrgeet,t,w,h,] (2.)

27 r R = g[x,h,,h,,(r ha)h,(rha),flwarrgeet,t,w,h,] (2.b) wh[x,\,;,h,,(lha)h,(lha),flwarrgeet,t,w,h,] (2.) Dele preter hve bee frlte fr the fferel eq t prve teytte tret ele grp fr ee eprg the preter fr ether ly. Sele w l be typl vrble te wth het exhger eg. he ele preter re efe fllw: : = ^ = ele tepere repe (2.) ()() X: X ele flw legth = vrble (2.2) = JL; UA NU: NU = = ber f trfer t (2.) : = x = pty e r (2.4) :, lh (rha)(x = = _ x _ therl rete r (2.5) (^ha)^ w ==^ = wll pte r (2.6) t : t =5L well e r (2.7) l,x t : t = t, = ele e vrble (2.) 4

28 h he ele preter ree the epeet vrble fr eleve t eve. = f[x\nu,,t\r\;,t;] (2.9) = g[x\nu,,t,r,;,t;] (2.9b) teret ly the tret tlet tepere repe f eh fl fher plfe the ly by elg X whh eql r t ether e f the het exhger. L (95) prpe ther eg fr the epeet ele vrble whh lze th wrk t ree f betwee. te f g, they prpe t e ele tepere effevee vrble efe by eq e (t)() (22). 2(t)2() 6f'2 "2()2() (22) Sbrpt f, f, 2 refer t the teppe teppe fl, repevely. All tepere eq re tlet tepere. ] (t) the tlet tepere fr the teppe fl t y pefe e t rg the tret repe t tep pt. x () the tey tte tlet tepere fr the teppe fl befre the tret pt h bee pple t the het exhger.! () the ew tey tte tlet tepere fr the teppe fl fter the 5

29 t R tret pt h bee pple. Sbrpt 2 erbe bve refer t the teppe teppe fl, repevely. Flly, the epeet ele preter re ree t the x preter hw eq b. f f [NU,,,, ;, t ] (2.22) ef]2=g[nu,,t,r,;,t;] (2.22b) ret ly f rflw het exhger re fflt pre t prllelflw het exhger bee the tepere f f e tw p vrble (x z). Ftely, ll f the ele preter erve fr prllelflw het exhger re pplble fr rflw het exhger. Fher re f the ele preter typlly perfre fr reg the plexty f the lyl l fr pef e f teret. hee fher re lt the blty t prve tret l fr we rge f ele preter. he erl l tehqe eplye th the prve fr tret perfre l whh ver we rge f ele preter. 6

30 Ltere Revew w preheve ltere revew regrg the tret perfre f het exhger ext. Ltere w revewe p t 9 by Shh (9). Be Klkr (995) revewe ltere p t 995. t w te by Be Klkr (995) tht everl plex lyl l re preete fflt t lze f.. PARALLLFLW Sl fr prllelflw fgr re rze ble.. ble.: Avlble Sl fr prllelflw fgr Retr Sl Meth Referee Dwell e f fl re eql r bth fl Alyl Re (95) re ge herl pte f the re e t be eglgble pre t the therl pte f the teppe fl. Alyl L (96) Bth fl t be ge. Alyl Gvze(97) Re (95) preet lyl l lzg fr ele preter 9,, R, NU. Severl grphl l re preete fr pef ele grp. Bth fl re rete t eql vele r bth fl re ge. h lyl tehqe reqre the tegr f Beel f. he therl pte f the re e eglgble pre t the therl pte fthe teppe fl. 7

31 L (96) preet lyl l tehqe whh vl fr lq t lq lq t g het exhger where the teppe fl the lq. he fl vele be fferet. he tehqe lze the Lple trfr reqre the tegr f Beel f. Gvze (97) preet l where bth fl re ge, the therl pe f the tw fl re eglgble relve t the therl pty f the het exhger re, t vl fr y type f pt tepere hge (l, expel, tep f, et.)..2 RSSFLW ble.2 rze the vlble ltere l tehqe fr rflw het exhger. ble.2: Avlble Sl fr rflw fgr Retr Sl Meth Referee e fl xe, ther xe Fte Dfferee Dberre (959) Alyl Myer etl. (967) xe fl teppe w lrge Bth fl xe Fte Dfferee Yht etl. (97) Bth fl ge Alyl Re (9) Bth fl xe Bth fl ge Bth fl xe Bth fl ge Bth fl xe Delt pt ly Bth fl xe Delt pt ly Bth fl xe Bth fl ge Alyl Gvze (96) Alyl Alyl Spg, Spg(97) Spg, Spg(9) Alyl he, he (99) Alyl he, he (992) Bth fl xe Bth fl xe Alyl Spg, Spg (992)

32 Dberre (959) preete the f pper t bt the tret perfre f gt g rflw het exhger wth bth fl xe. He lze fte fferee tehqe. Sl were t verfe wth y ther re. Myer et l. (967) etere the tret behvr f gtg rflw het exhger wth the teppe, ht fl xe. Repe t th tep hge w f lzg plex lyl pprh whh vlve the tegr f Beel f. All l were f fr the e where the wll pte w w ere lrge. Grphl l re preete hwg 9 % repe e fr the e tlet tepere. Yht et l. (97) llte the tret tlet tepere repe wth ether fl xe lt regrg the wll pte ze fr tep hge let tepere lzg fte fferee tehqe. ffet f the gverg preter t, / ^,, R, NU, were llte grphlly by vryg eh preter wth the ther vle fxe t be ty. Re (9) pple Lple trfr tehqe t gtg rflw het exhger. Grphl l were preete fr glep exhger wth ether g xe. A t tep ree w pple t the etre tepere f ether g. xt e tepere l re gve grphl fr fr the fllwg rge f ele preter: NU (), (.6.67), R (.52.). Gvze (96) prve lyl l fr gtg, lrge wll pte, glep rflw het exhger wth bth fl xe. Sl re preete grphlly fr rbtrry e vryg l let tepere. 9

33 pble fr the fl t be ge r lq, fte wll het pty t be lze. Relt re vl fr rbtrry e vryg l let tepere. he he (99, 992) plfe the pleet f the Spg Spg (97, 9) wrk by prpg trght frwr fr pter e tehqe tht eree pter e. he he (99) lyze gtg rflw het exhger wth ether g xe prve grphl tpt. Spg Spg (992) prpe ext lyl l fr tep hge the let tepere f the ht fl. Bth fl re xe ge r lq. Fte wll pte lze. he ltere revew hw l ext fr the tret tlet tepere repe f het exhger t tep pt the let e f the het exhger gve pef retr. All f the prllelflw l re lyl. w f the rflw l lze fte fferee tehqe whle the reg eght lze lyl l tehqe. he fte fferee tehqe re t e the lyl l, hwever fte fferee l ver wer rge f epeet preter. All f the vlble l re rete t rrw rge f ele preter. hee retr ke t fflt t prve referee tble whh ver we rge f het exhger eg r pre. 2

34 Appl f herl Netwrk Slver 4 h ly el wth prllelflw rflw rettrfer type het exhger. hee het exhger t f tw epeet flwg fl epe by fxe, very th terl r wll. he eterg fl re t fferet tepere relg het trfer fr the hgher tepere fl t the lwer tepere fl. Fl flw e re tt. he prllelflw het exhger fl eter the exhger the e e, flw the e re, ext the exhger the ppte e fr where they etere. he fl flw perpelr t eh ther the rflw het exhger. h ppl t f bth fl the het exhger lly t teytte. Steytte te the exhger fl tepere t hge wth e. he pty e fl tre tepere ttely ree t ew, tt vle. h let tep tepere hge e the ere yte t hge tepere ver e l t rehe ew teytte. he repe f teret t the pre egeer the tret tlet tepere repe f eh fl t th tep pt hge. herl etwrk el were evelpe t repreet prllel rflw het exhger. Ne repreet the fl r wll reg the het exhger, retr re lze t repreet het trfer rete. hee el were etp heret erlly vlble therl etwrk ftwre pkge whh w lze t llte the tret tlet tepere repe fr th ppl. Sl were bte fr the fllwg ele preter: NU,, R, w, t, t. 2

35 4. PARALLLFLW HA XHANGRS Splfe 2 eget rettrfer prllelflw het exhger re re hw Fgre 4. 4., repevely. h plfe el lze e (t) t yblze the fl eprg wll the het exhger. h e repreet pef vle f fl r wll reg repreete by the "bxe" reg rrg eh e. Bth fl eter the exhger the e e, flw prllel t eh ther, ext the e bt ppte e fr the let. qvlet therl etwrk eretr el re geee fr the plfe re hw retly belw eh re fgre , repevely. 22

36 Fl Fl Fl Fl Fl Fgre 4.: Dret rfer Prllelflw Het xhger r Se ( Seget Mel She Dgr) Fl (Steppe Fl) r 2 ', ', 4 J 5! 6! 7!! 9 ', :;:. Wll 2 ] ; 4 5 \ 6 \ 7 ] 9 \ 2! ! 25 26! 27! 2! 29 2 Fl b (Uteppe Fl) Ne: 2 e b e Wll e Fgre 4.2: Dret rfer PrllelFlw Het xhger herl Netwrk Mel N Wll herl Rete ( Seget Mel) Fl (Steppe Fl) "" " ^ '" "yfl^v^^ '; Fl b (Uteppe Fl) ' 2 \l 24 V 25 VV 2Q6 VJ ^ V^ 2 V 29 ^V Retr: ^ 2 Fl Flw pte /p 2 b Flw pte /p veve Rete /ha 4 b veve Rete /ha 2

37 "' ' Fl Fl Fl Fl Fl Fl Fgre 4.: Dret rfer PrllelFlw Het xhger r Se (2 Seget Mel She Dgr) Fl (Steppe Fl) [ f , 9 2 "^ Wll \ \9 2 ^ l , 2 \ Fl b (Uteppe Fl) J Ne: e 2 b e Wll e Fgre 4.4: Dret rfer PrllelFlw Het xhger r Se herl Netwrk Mel N Wll herl Rete (2 Seget herl Netwrk Mel) FlJ (Steppe Fl) ; 2 r, A/ (.9 V..2.'? \_ 2 :,' 2 Fl b (Uteppe Fl) 22 "" JJ 2 V, 24 JJ 25 JJ 26 JJ 27 J7 2 JJ /29 22 ^ / 29 Retr: Flw pte /p 2 b Flw pte /p veve Rete /ha 4 b veve Rete /ha 24

38 Het trfer rete re e t the plfe el. Fl e re epe by fl flw retr (l/[ flw e e pef het]), veve rete betwee the fl e wll e. Fl flw retr eerge fr eergy ble hw fgre 4.5 the erv belw: Fgre 4.5: trl Vle fr Fl Flw Rete Derv Ne# \ trl Vle Fl Flw Dre 2 F F +F = F^ L/ ""t ^geee tre (4.) where geee = => q+ + rhp(+2+) = v (2+2) Ax (4.2) where rhp ("+ 2+ ) repreete lf+?+) R (4.) where R = = Fl Flw pte (Kelv/Wtt) (4.4) 4 + (2+) + > (2) = R vp ^ (4.5) 25

39 he teppe fl repreete by e bere the e hre, the teppe fl by e bere the tw hre, the wll by e bere the three hre. he tlet tepere e fr the teppe fl bere e, the teppe fl bere 2. h llw fr qk reg rg elg, l fr ee f exp t lrger eget el. A eget el te the het exhger h bee ve t pef reg the re f fl flw. he 2 eget el te v t 2 reg. ree eget el typlly le t re e tlet tepere ll ple wth ree pter r e. herl wll rete perpelr t the fl flw re w exle fr th el bee f the tyle het exhger beg lyze. he eprg wll betwee the tw fl extreely th. herefre wll therl rete perpelr t the flw re ere eglgble. herl rete the eprg wll the flw re ere fte bee the eprg wll extreely th. he relve het the flw re eglgble relve t the het trfer perpelr t the flw re. he pl e tep ber f eget reqre fr tg ry ze pter r e w etere by Be (995). hee vle lte the errr t le th peret. Fr NU 2, eget el w reqre. Fr 2 NU, 2 eget el w ffet. A etep pt reqre fr heret f hlf the well e f the ftet flwg fl w etere ffet fr ll e by Be (995). h tehqe el the prllelflw het exhger lzg e retr whh re lve by heret therl etwrk lver. heret lve teytte tret het trfer prble. he het trfer yte repreete therl etwrk g the fllwg eletrl lgy: 26

40 Het flw e, Q => rret, epere fferee, A => Vltge, V herl rete, R => letrl rete, R. A bkwrfferee hee eplye t prve lly tble lver fr teytte tret prble. he ter lly tble e the l re tble fr ll pe e tervl. heret hle vrble therl vty, vrble ve het trfer effet, r fl tre. t h eyte terve ww frt e. he b eq eplye re erbe rper De Wtt (pge ). vl fl tepere effevee vle ], e2 were geee lzg ele preter etp preheet t geee retr e vle t be e by heret. heret lze the retr t l fl let tepere t llte the l teytte tepere trb f the het exhger. h teytte t the trferre t the preheet fr e the e t tble. he e t tble t e vle l tey tte tepere fr fr eh e the el. he e tble trferre t heret. heret lze bth the retr e tble t t llte the tret tlet tepere repe f bth fl t tep pt hge fr the fl. he tret tlet tepere repe w trferre t the preheet S, were llte fr pprpe t vle. Vle ft were elete t le the fll rge fr t fr the we rge f pt ele preter. 27

41 4.2 RSSFLW HA XHANGRS A plfe 4x4 eget gle p rettrfer rflw het exhger hw Fgre 4.6. Fgre 4.6: Dret rfer rflw Het xhger Bth Fl Uxe (4x4 Seget Mel) Legth Heght Fl tt % Wll hke Heght Fl b Wth Fl Fl Ne Fl b Ne Fl b he tw fl re xe, epe by wll, flw perpelr t eh ther. h e repreet pef vle f fl r wll reg. qvlet therl etwrk e 2

42 Fl Fl Fl retr el re hw fr x, 6 x 6, x eget el fgre 4.7, , repevely. Fgre 4.7: Dret rfer rflw Het xhger herl Netwrk Mel Sgle P/Bth Fl Uxe (x Seget Mel) Fl (Steppe Fl) \ Fl b (Uteppe Fl) Flw pte /p 2 b Flw pte /p veve Rete /ha 4 Fl b veve Rete /ha 29

43 Fl Fl Fl Fgre 4.: Dret rfer rflw Het xhger herl Netwrk Mel Sgle P/Bth Fl Uxe (6x6 Seget Mel) Fl (Steppe Fl) \ Fl b (Uteppe Fl) Flw pte /p 2 Fl b Flw pte /p veve Rete /ha 4 b veve Rete /ha

44 Fl Fl Fl Fl Fgre 4.9: Dret rfer rflw Het xhger herl Netwrk Mel Sgle P/Bth Fl Uxe ( x Seget Mel) Fl (Steppe Fl) \ Fl b (Uteppe Fl) Flw pte /p 2 b Flw pte /p veve Rete /ha 4 b veve Rete /ha hee eqvlet therletwrk el re geee fr eqvlet plfe three el el lr t the e hw fgre 4.6. Fl e re epe by fl flw retr (l/[ flw e e pef het]), veve rete betwee the fl e wll e. h vl fl tre e ete ly t' flw re. h ke eh fl xe. Fr x eget el, t reqre 9 e fr fl, 9 e fr fl b, 9 e fr the wll (egleg wll rete), 6 e fr the tlet tepere f fl b. h gve ttl f e reqre fr x eget el. A eget prllelflw el reqre ly e. A 6 x 6 eget el reqre 2 e ver 2 fr 6 eget prllelflw el. A x eget el

45 2. reqre 2 e ver 2 fr eget prllel flw el. he rret heret ftwre pkge lze fr th ly lte t e el whh ret the ttl ber f eget t 7 x 7 reqrg 9 e. herl wll rete w exle fr th el. he pl ber f eget reqre fr tg ry zg pter r e w etere by prg tey tte heret r t tl therel tlet tepere vle llte by the effeveenu eth. pr w perfre fr the ele preter rge lte tble 4.: ble 4.: Dele Vle Ulze fr pl pr fr rflw Het xhger NU R ble 4.2 hw the peret ev fr tl fr the rge f preter lte bve l the ttl r e fr eh e. 2

46 r~ l' : ' M, r ' " ^~ ' _ ' S : _) Mll" ' D _l lr. = S. " t> r t X r t X r 9 r X t X, t! Rl 5 > r t ^ "S! t Q M Sft b ' r ft r p p 2 S l J! r l g! r ; r~ t r r p r r > r g r r p r r r p? r r r :. r _J.! S l r e 5 t r p p. S S S! 5? r r t S Ml S? e r M r 5 p r p p p t r w r t r r r t S r t r b r r r > l r t r t r p f ff r ( _= X LU _ B 5 ( JZ "> 5 M e. X 2 X l ] > ;f 5? > M r r r r p M p (X t 6 w t r t p r p ft g p N Q\ w> ^ t^lt^'r >. r p r r^: r^ p' r ^!p.^ r ' t r^ > r t r r r SSS r W '^lrf. '^.r ^] M l rpr lwlf S r plr!>.l MW v V rlv r t r r r r M p t r t > 5 r 5 M Jr M S \D D p ll NN r~ r h JN ll w r Jt h r r ^MJ > t^! p w r r r r > rf. f; N SJ5 5 5 p p ) r p ff. ^ A p t r t r l M ff. t tf 5 r. r r r p r r r r e l 2 p l^ l l l l^ V t r r ll t t r? S rf l r r r. M l r r!_ r^ ft" 6"! S: : >ll 5S 5 N S t >. > r =?2 w "g.=!l S _ ;. f X t f 2 6 :_ z L X e & l N D p p : : (..!!!:M!:l! [^ '2 ts ' l p p!! l \ >: :gl ;,5 p! : ] :! \ rm / p ^! S S: p!! :..,, ;,!! : : : : Pl ^, : l ;! : p ; J! ' M ;!S ;! r "! :! : ;! S t 5 ' S 'M! "; tn. J ; 6; ; ' ].; ll! :

47 pter r e ree ywhere fr 2 t 4 e the ttl e fr the x ver the 6x6 eget el. he x eget el tk fr t 22 e lger pre t the 6 x 6 el. tl pter r e w lger NU ree fr eh eget el. Fr NU =.5, peret ev fr therel le th 2 % fr the x, 6 x 6, x eget el hw Fgre 4.. w =, =.2., R =.5 2., t =. 2 _ f ^ f.4 > ) L_ l.2 JZ \. ^ >.2 Fgre 4.: pl Nber f Seget fr NU =.5 Fr NU =., peret ev fr therel le th % fr the 6x6, x eget el, le th 2.2% fr the x eget el hw fgre 4.. 4

48 w =, =.2., R =.5 2., t =. 2.5 Fgre 4. : pl Nber f Seget fr NU =. Fr NU = 2., peret ev fr therel le th.4 % fr the x eget el, le th 6. % fr the 6x6 eget el, le th 4.% fr the x eget el hw fgre

49 w =, =.2 2., R =.5 2., t =. re xseget 6x6 Seget x Seget re > Q Fgre 4.2: pl Nber f Seget fr NU = 2. herefre, the 6x6 eget el reee fr NU. t heve ry wth % ze pter r e. Fr NU 2. the x eget el reee t heve ry wth.4%. Fllwg prev ree fr Be (995) regrg the etep, etep f hlf the well e f the ftet flwg fl w etere ffet fr ll e. h tehqe el the rflw het exhger lzg e retr whh re lve by heret. he e eth erbe fr prllelflw het exhger pple t rflw het exhger. vl fl tepere effevee vle, were geee lzg ele preter fr NU =. lzg the 6 x 6 eget el. 6

50 Vl f herl Netwrk Slver Ary heret relt fr tret perfre f prllelflw rflw het exhger were eh vlte gt three epe pper f the ltere revew. h pper lve fr the tret l lzg lyl tehqe. heret tret relt were pre t ltere relt by llg the peret e fferee gve by eq 5.. % Me Dfferee = Averge fferee betwee l ver the e x tl hge fl tlet tepere fr e t= t t= (5.) 5. PARALLLFLW heret relt fr tret perfre f prllelflw het exhger were vlte fr three epe e hw ble 5.. ble 5.: ret Perfre Vl fr PrllelFlw Het xhger Athr Appl Sl Meth pr Fgre # Steppe Fl % Me Dfferee Uteppe Fl % Me Dfferee Re (95) Re (95) Myer et l. (967) Rzk (956) PrllelFlw =. Alyl PrllelFlw Alyl =. Step =,^ Fl = Alyl 5.. hge.4 tl. Step x Fl hge Alyl

51 . = e by Myer (967), Rzk (956) were vlte by Be (995). Myer (967) Rzk (956) ele the x = fl hvg well e f zer. Be (995) ele the x = fl heret hvg tt tepere, flw. herefre, the heret vl fr = re flw re epeet fr the fl relve t the x fl. h ke the vl pplble t bth prllelflw teflw het exhger. Peret e fferee betwee heret l ver eh e rge fr.2.65% (Re, 95),.4 % (Myer et l., 967),..74 % (Rzk, 956). pr t Re (95) Myer et l. (967) y vry re th tl fr heret e t reblty errr f the grphl repreet gve eh pper. Be (995) llte retly fr Rzk' (956) lyl expre the Rzk (956) pr. Fgre 92 pre the tret perfre gve by heret ver eh lyl l. h e ele w fr fferet, pef, NU, R, w vle.

52 _. =., NU =.5, R =., w = 5 t S. D) Q Steppe Fl ^ _^_?Re, Fl Re, Fl b heret, Fl k heret, Fl b + Q Uteppe Fl " e (Se) Fgre 5.: heret Ver Re (95) Vl =., NU =., R =., w = 5. t 75 7 Steppe Fl Q ( 5 5 Q Uteppe Fl? Re, Fl Re, Fl b heret, Fl ^heret, Fl b e (Se) Fg re 5.2: heret Ver Re (95) Vl 9

53 r~ _. Steppe ^^^ ^ ^ =, NU =.596, R =.29, w = , w 6 _. Bl 56 Q 5 \ _. 4. t 46 Fl?Myer 967 heret 4 6 () e (Se) F gre 5.: Be (995) pr f heret l t l by Myer et l. (967) =, NU =.7, R =.79, w = t 4 l 4 Steppe Fl 9 4 _. Ql Q. 7? Myer 967 heret e (Se) Fgre 5.4: Be (995) pr f heret l t l by Myer et l. (967) 4

54 Uteppe =, NU =.95, R = 2.99, w =.59? 2 _ 22 ( 2 Uteppe Fl ^ l Q ? heret Rzk F:gre 5.5: Be (995) e (Se) pr f heret l t l by Rzk (956) =, NU =.55, R =., w =.7 9 t 6. 4 Q 29 Fl _. 24 re. G 9? Rzk heret e (Se) Fgre 5.6: Be (995) pr f heret l t l by Rzk (956) 4

55 5.2 RSSFLW heret relt fr tret perfre f rflw het exhger were vlte gt three lyl l hw ble 5.2. ble 5.2: ret Perfre Vl fr rflw Het xhger Athr Appl Sl pr Steppe Fl Uteppe Fl Meth Fgre # % Me Dfferee % Me Dfferee he, rflw Alyl he Bth fl 5. (992) ge Bth fl xe Spg, rflw Alyl Spg Bth fl 5. (97) ge Bth xe fl Re rflw Alyl (9) Bth fl 5.6 ge Bth fl 5. xe NU: : ~ R:

56 .57 he 6x6 eget therl etwrk el w lze fr ll pr hw ble 5.2. h w he be the ry pter r e er fr NU =. e. rflw het exhger vl rge fr % (he, he/992),.64 % (Spg, Spg/97), % = (Re/9) fr NU.. Fr NU 2., Spg, Spg (97) ver heret hwe % e fferee rge fr 5.97 t 6. %. Fgre pre the tret perfre gve by heret ver eh lyl l. 4

57 ' ' =., NU =., R=., w= 5 ( 2 r Ql D Steppe Fl ^r ^ 2 L /?he, Fl heret, Fl ( e (Se) Fgre 5.7: heret Ver he (992) Vl =., NU =., R=., w= t. t Q? 2 75 Uteppe Fl? Q.?he, Fl b > heret, Fl b e (Se) Fgre 5.: heret Ver he (992) Vl 44

58 l =., NU=.5, R=., w= flr Ql 2 > Q? 4 t l_ Q. Q> y^ Steppe Fl?Spg, Fl heret, Fl e (Se) Fgre 5.9: heret Ver Spg (97) Vl =., NU=.5, R=., w=?spg, Fl b heret, Fl b ) e (Se) Fgre 5.: heret Ver Spg (97) Vl 45

59 _. ' ==., NU =., R=., w= 5! t 2 ) Q > > Steppe Fl y^ yr Spg, Fl fll yy "heret, Fl 75 ) e (Se) Fg re 5.: heret Ver Spg (97) Vl ==., NU =., R=., w= t _ l Q _ t _. Q. fl) ?Spg, Fl b heret, Fl b Fg re 5.2: e (Se) heret Ver Spg (97) Vl 46

60 7 =., NU=2., R=., w= 65 2 t Q ) 6 Steppe Fl 2 Q. 55 Spg, Fl heret, Fl e (Se) Fgre 5.: heret Ver Spg (97) Vl =., NU=2., R=., w= (A ) t Q l 9 5 Uteppe Fl _. > (Q. Spg, Fl b ) H 75 heret, Fl b US H e (Se) Fgre 5.4: heret Ver Spg (97) Vl 47

61 '..? =., NU =., R=., w= 5 t 2 t Q Steppe Fl > 2 Q. H 75?Re, Fl heret, Fl e (Se) Fgre 5.5: heret Ver Re (9) Vl 75 =., NU =., R=., w= t 2 t t Q 7 Uteppe Fl 65 Q. )?Re, Fl b heret, Fl b e (Se) Fgre 5.6: heret Ver Re (9) Vl 4

62 y y/ _ ' ^^^ '""" 95 =.67, NU =., R=., w= t! Steppe Fl 9 f ) " / ^^ Q ^ D 5 _ ^r > y ( ^r. ^r ) S " ) H Re, Fl heret, Fl e (Se) Fgre 5,7: heret Ver Re (9) Vl =.67, NU =., R=., w= _ fl> Q 95 Uteppe Fl 9 re _ Q. ) 5 Re, Fl b heret, Fl b e (Se) Fgre 5.: heret Ver Re (9) Vl 49

63 _. _. Steppe ' 9 =.25, NU =., R=., w= 5 Fl?. _L '^^? re _. 75 ^^ ^^ ^y r?re, Fl heret, Fl 7 ) e (Se) Fg re 5.9: heret Ver Re (9) Vl 5 =.25, NU =., R=., w= t ) l_ ) Q 75 Uteppe Fl re Q. > 7?Re, Fl b heret, Fl b e (Se) Fgre 5.2: heret Ver Re (9) Vl 5

64 ^^ ". ^.^? =.6, NU =., R=., w= > 75 f Steppe Fl " V 7 l + ^^ 2 65 D ] Re, Fl heret, Fl, e (Se) Fgre 5.2: heret Ver Re (9) Vl 5 =.5, NU =., R=.5, w= Steppe Fl t.. > 5 J fl) " > _. ; re L. 95 fl) S'' Re, Fl " heret, Fl > 9 l 5 h H e (Se) Fgre 5.22: heret Ver Re (9) Vl 5

65 ' =.2, NU =., R=.5, w= 5, Steppe Fl _. re Q. A> / y X Re, Fl y heret, Fl 7 ) e (Se) Fg re 5.2: heret Ver Re (9) Vl 75 =.5, NU =., R=2., w= t _ ) Q 7 Steppe Fl re _. > 2. Re, Fl heret, Fl e (Se) Fgre 5.24: heret Ver Re (9) Vl 52

66 ^^ ' =., NU =., R=2., w= ^ t. ) Q _. 2 > Q., 75 7 Steppe Fl ^ Re, Fl!! heret, Fl "!! e (Se) F gre 5.25: heret Ver Re (9) Vl =., NU =., R=2., w= 7\ t ) Q 2 ) Q Steppe Fl Re, Fl heret, Fl e (Se) Fgre 5.26: heret Ver Re (9) Vl 5

67 6 Relt 6. PARALLLFLW HA XHANGRS ret perfre effevee tble were geee fr tep pt hge t the fl fr the rge f ele preter lte tble 6.. ble 6.: Dele Preter Ue th Aly fr Dret rfer Prllel Flw Het xhger Dele Preter Vle Preter NU R ret tepere effevee vle f 2 ) geee fr prllelflw het exhger re hw ble

68 ' J,^' "" " '^ ^. ^~ " M N fl t V ^> q L. e e w x t _? e _ 6 fs bs ts V r^ t t v, R r v v v # r l r t t^ v v V v v v S e fl v V v v V R v v v V v v l v v R R r l v V V 7v g g r V l l. v ( v v l U) P g t v V w VV S VV ts v v V p t. v v h v v v v f v ptf v l t V M V t v t t v p V v v r v v v v v r~ _, v r^ _, t ^. t l v f> V, ^ r V,, tr, S # S v v v.,. M ^ > V v ts t \ Wv (S v v v v ^ S N r ts. t U " H Z th r V V > e (^ r fs t Ml _ fl ( fl fs v r~ f7v v v v v f V _. J v v r> D M B D # t V,?; v V l v v S S V, # H v v v v l _> f e > S, w r, t. D > _ S S v V v v v v v v f? v._ v t > v v v > v l v v g V t^ v w. v v v v v _ e _ e t H # V l Wv v ^, v. r> ts (S, U S _ flt v l 6 t v S t^ w w v v v v _J t, pr) _: q V Vl t t ^ v ^ fl ^ v V v S V t v v VV t e Z e H V t. ^ ^. _ (N v t r t (S t l" r V t^ r^ B # t V t v,^" VV Wl V V. w. V t t v v VV 7 55

69 _ M e J= x W S S p e_s t t 2 t t fl V v \ V v N v V v tn V M v fl VV V V V ( J? V v v v S t v t (S V r^ v v r^ v v v w v v V r v v v v v v bs _J v t> fs S v V fl v v t V fl V v v v V v V t f t w (N r^ 7\ w r~. v v v t N t fs S f r^ v? r 7v (N V v v v V v v v V v ^ v V w> V t ^. V v! r S ^,^ v v v v r tt V v v v v V t. e e D S _ fl S ^r fl fl ^ V r W) V l> v v v v v V V ~~ v v v v v ( S,,. _ v r fl V v v v r fl V f v v v ( e e_ (N S r \ V v? fv v v v v v v v t V r^ D v v v v v v ( fs l S e D. e U e r> _ S v? N V v v v v fl 7v v v v f7v "? M v ^ v v v # (S ) v v v v v f VV r~ v v v v v v ^p V r^ v v v v v v V M v v M v, fl fs v v V v v v v V V v v v v v H " >. v fv v 7\ t~ (7v N N! f t fl v t v v v fl V v v v v v v t ^ V v v v v v D v; _ H v r~ v v fl v v v v v v ( Q f r r r t> r V t V r ^> ^t N? t v v fl V V v V V v v v v v v (S t S BS BS? v fl r^ ^> H v r v (^ N v M fl v r~ v v 7v t S e. _ H 4 B "5 e. v V f7v ^ N f v PS V r^ v v. v r t M _ B B D B BS v fl t h S V fl = w. v > V V t v fl v v V v v 7v r _ t > r V v v fl V t> v v v v V D e fl t S v fl ^ ^ fl rr V " "f N S v t t~~ " V v v v " v v V N r V V v fv v v S V v v v v. fv v ( f v e H,, r> v r fl tr v V r r fl V V v V ll fl V tn t t fl fl f ' S f fl fl _) 56

70 > fl" M JS W > e r S SR fl v w. v N V l fl v v v v V v v v v fv fv r V p V v v v v v v v t r S V V V v fl v 6 6.! SR t V v v v v v V _^ w v/> P ^J v v v v v v v v L V r w v v t v v v v S v v v v v v v v N V 7v fv v v v v (7V ~>, _ fl fl V fl v _ S S p fv v v (7v v fl V V V v v 7v (7v p v V V v 2 e fl p r V _^ f v V V V t v v v v v v v v r V v v v v l v v v S ty! S v rv fv fv (7v v v v v v v v v v v v v v v v e e e S U " Bt f t H.2 r fl V V V v v t v v V v V fl v v v v v v v v v (S r t S S v _ fl v v V v fl v v v v v v v V tn VV v t> v v v v v v ' ' V v v v v v v V fl v v v v v v v v v v v w V, v fv tr> r> v fv r v v r r v p v v v (N t v v fl v. r r (N V (N v r v fl v p p f r V v v v fl V fl v v v v H f D S _ VD V _ r> 4 r t V r^ v v v N V v v v v v v v v v v v v v v t SS e w U v H +_ e "S e e H S + r V S v (N v v tn fl v v v v v v v v t (N r _ \ v. p P # S._ w (N r (N r r v V t v v v V v v fl v. v v v v v ( S flv> p v v v v> ^H r VV w V V v v p v v v v v v v v v r, ^H r t _^ t # S S # S flr V v V p v v v v fl v v v v v v V V v fl v tn v flt t v t e fl f fl r v v v v v v v v v v v v fl v v v v v ( t 6 v r t v fl v v v V v p^ V l V r^ fl v V V V v,_ fl ^H r f t fl fl? w p v v v v v v v VV V p v v f> v v v v v v ( rō p fl v v r v V v v v v v v v v V v v v v S v v r V t V f v f v v v v r v v t v v fl v v fl v v _ e H ^, (N v v fl N t t fl " v v r^ v N f V t. flr flt V " ~ r S r fl fl fl t v fl 57

71 _> t tn v V V v fl v v V V P^ v V p v v v v v v S v v v r v V r VV. V fl v P^ v v v V v v v v v v v v, _ r v V V r^ PS v rrv v v v v?v Jl v v Dv r ( D, r (N v p V w v v f V (v v v t e r r. x +_ e v X 6 _,? v V V v v P; fl w v tn V v v V V v \ r v v v v v v v v v r V v v V V fl v v V v v v v V v V S e v V v P v v V p p v v V v v t V v v v v v 6 fl v r e V v v v v p v f. ^ v v v p r V Vf> p St v v r V v r^ r w V v v fl v fn V V V V v v v v V V v v v N v P v t e L. e V w tn r v P v V tn V r P^ v V v fl v v v v v P^ v v v v v V v (N v fn r (N V p^ v r V v 7V t 6 r v v p~ v V v v v p V v v v fl V v v v v v v S? v r v v fl v V flp v v fl v V v v _ e _! v r S? t r v v v r r v v V v V v v v v p~ v v. v v v fl v v v v v v v v v V v v V V v v v v v ' ' t S (N fl v v v v P v v V V p v V v v e U " St vf e lh : H fl 6 V S t tn rf v v p~ tn r v P V v V V V v P fl v :P f V v v v v V v P^ v v v w v fl v v v v v v v V v v v v p^ v v v v v S p fl V fl v V r v e V v v N V p^ v t P P v V v p ( v w fl v V v v r 7v V v v p fl V v v V (S V P v S_ v r V v v v v v v t t V V v r p r r V r P e v v V v P^ v v S v fv p~ v V v> N t S fl V p~ v v v fl v v V v r^ v v v v v v V v v v e > tn V r ^ e v v v v r v fl V v v v ( v v v > S t v r S v e V v v fv f fl P v v v v v v > X v v Dv (v v v 6 fl v r v (7v => v 7v 7v ~ v v v v v v v v v v v v v v v V e_ H _ B 4) e _. H e H V W t fl (7v v v v v 7v V, V V v v v v V v V r t w P v ^ v v v v v v V fl N v N V v V f V r~ r v v v tn v v v v v v > ^ 7v 7v 7v => 7v 7v v v v v W) V v v. v V V ^ z> :f S K V V == V v v V V r> S h 5

72 fl" ^ > fl" fl" S f v r t) S fl V V v p^ v fl" v> v v r fl v v v v v p v v v v v v v fl; v v v v v v v v v t, '! e B e S x _ r e D S flf v v f fl" S tn V v > Wl fl t^ V fl V p v v? v P v fl v r_ v v v v v v fl V v p v v v v v v t t r. f V V V V v fl v ^ V v f fl r P^ r v p^ r tn V M; flv v v v v v v v S fl r t V v v v v v v v t t _ v V P^ V p r^ p p^ v ^ fl" v p r r r v P v f t^ p^ v e V p X fl V v v v v v fn v P^ v v v v v t _^ t S V v V v V p w w v r # V f v fl p t v N fl (^ flv v r r r V V v v v v v v fl fl; V P^ v v v v v v fl V v P t ( e. f r r~ P~ tn v t> r~ P^ v fn r v v fl r t S fl P^ p^ V fl V r^ r^ f tn V v V r~ v v v v fl V v p v v v v v V t w S r fl fl v fl f V r V V flr~ fl V fl V p v V r V v v fl V v v v v v v fl V v r~ v v v v v f V v t t P_ e e 7 _ v p^ t fl V v v v p v v fl V v V v V f v V v G. v fl V p~ v v v v v v V p v v v v v t fn ( S S V V tn > V V v tn e w v v v v v v v t^ v v v v v p v p v ;v v v > (v v v vt v_ P^ v v v v v v v ; t t r v f r v v v v fl v f> S fl r S V? v v p~ v p fl V v v V v flv P^ v v v v v v v lh v v D t D! S V. " v S _ v r v v V f f V r^ fl vl V V fl v r ( v V V V v V V flv p v v fl " v p v v v v v v f V V t^ v v v v v v v t t l H Z " > p H f S V v p^ r f,, P V _ v v ^. _ v p _ v P~ v v r fn w v v v r t^ V v v v f t p v v v v v v fl; V) v r fl P! S fl fl fn ^ v ^ (N v v v V v p v v v v v > fl V v v v v v f V V v r v v v v v t t v f p~ r v f. r V flr w ft v flfl \ ^ v p^ r v v v v V fn w _ P v v v ^r v v v V v v v v r V p v v v v v v v t t ' r U _ B > "_ U v V V P; V v w v v v V v v! S v v v fl v v v v r~ v v w v v v v e r v r v v v v _ V fl v (N r N v v v v S p v! _ v & v v v tn v> v v v v v v S t N t ^ B H r f) v fl f fl v v fn fl f. v P f V V v v v v v N r P^ P^ p~ V V v p v fl; v r v v p V r V v v e H l _> e H V V " S S V f r v v v v fl f r r V v fl r V v v v fn f t r flv r v r r r r ^t V V v fl p r flv (N v fl v V v v p v v r v r v v r r v v fltn 59

73 f v V V flfl P v v _^ _^ S VD P p w r v v v V V v (N v v v v v v tn V v v v v v v V v v v v v V v v fl; t t fn ^ 6 P v v v S p~ flf v v v v V fl v v v r V p v v v v p fl V v v v v v (N v v v v v P; " " S V f V r P S ^ fl v ^ r v v P~ f ^ p tn V p P f V V _ f v p v v v v t v v v w kp S v (N r r v V v v fl V V v fl v f v p V v v v v v r V v t t p t t S e J r 6 P P r v P V fl v V fl V r p f r V p 2 V v v ~ N V p f V r~ v v v tn v v P v v v v ( fl" V : r~ V V P t fl V f v fl v N V V V ' P fl v v fl fl v V t v v v r p v v v v J V v P^ v v? v V r p V V f fn p r v (N p v r fl v r p~ P p v v v v f v v v v v v v v r V VD P t S v tn f v r fl fl p r t p r V fl V v r t v f fl v fl v p f v V v v fl r v fl v v v r t V v p_ r v v v t t > e PL, V v r fl P f w V (N v t p V V p f r v fl V P r v v P V 2 f flv p v v v tn V v P v v v v t S v f fl S tn v tn r p r r V f v r t v p^ fn V p v p tn (N t v fl V t> r V p P v v v fl V p v v v t t e _ r U e p v _ V V f V V v tn fl v (N VD p v v V v p v V V > v v v v r V p v v v v v r v p v t r _ fn v v fl v v V t v V v fl V p~ fl P fl v r v v V V p v V f V v v v v v v (N v P v v v v v v t t. e " St t H Z " > p V f fl v P v f fl ^ v v V v _^ v V f v tn r v f V p v V V p V P v v v fl v v v v v p V f Jr tn t S p f Q v > S S fl P P fl v v p S v V v p v p v v v tn V p v v v f VD V v v v v t t v V r V V v r t fl V v v v v v p t v v v v r V v v v v (v v v p v v v v v v v (N t f (J S U H _ v r t v p~ v fl V v v V V p v v v v v v v v V fl p p~ fl t r v t VD v V p v v v V v v v e _. H > \6 4) e H V V S ^ tn v r v fl; tn f tj ^ ^ V p p v r tn (v f v v v v v r! l V ^ v v v tn _ 6

74 ' ^. fl t fl ^. S bl ^ Z t w V _ t r^ fl P e v t 5 fl V ^ V (> t tz> r S ^ t _ ^ v v v v v> t p fl t). v t v fl S, fl v w (> v ^! eg. U l, p 6 l ^ v t fs v. V ^ V p B B S ^ l) v v ' p' r>v v w t w% vfl p p #, ^ r t^ v > v v S e S D ^ PS _ v vtl r V. ^ ^ rr,, S v v v t> r S v (S S t p~ fl t r ^ " S Q l_l (^ Wl S V r~ 'f > B S S M r> rl ^. V. ^ ^ fl J >. v V r^ > ' _5 S V fl V) f, f, t ^ w P H Z V) p H f ft t V V t_> ~> U S D " p p H H " ' w f S S V, l bl z,. fl fl rr, M fl V (S V f ^ t v \. > v v B B S S fl ^. ^ fv ' t ^ S \tr. t t ; S... V f, fs > v (S VJ f, p' v l _ v S t v v v v.._ p. r S. v v v v v v v v S _ t (S r^ ^ " v v l v f,. t t~> ft r _ U % v fl w t^ S t t r^ p V B S > v t^ V t t v r^ v t tl) S._ r^ t^ v v v S t. _ t fl l ^. _ ^. ^ V w v. v > > (S fl V p v v ^ S _ " M p v v v V t fs p v ^ ^ e H 7 _ t t t V v v t r fl V V p t v v> v v V t. ^ fl V V p v 2 V 6

75 6.2 RSSFLW HA XHANGRS ret perfre effevee tble were geee fr tep pt hge t the fhr fr the rge f ele preter lte tble 6.9. ble 6.9: Dele Preter Ue th Aly fr Dret rfer rflw Het xhger Dele Preter Vle Preter NU R ret tepere effevee vle f e2 ) geee fr rflw het exhger re hw ble

76 _, t" A" A t v A V v P^ v v v e V v V bl ] D S S S fl r~ V v v v fl v t V v V V v t V V t V r v v (v v V fl V v v _ t V t p V V v v fl V V P v v v fl" A A _ M e x r 6 D S r v v v V r r t V fl P^ v r p V vd v fl fl V v t v fl" v V V t VD v r v V VD v t v p V. p~ p p^ p~ r V A v r fl V fl VD v t v p V (S v V p v v t v V) VD v V v v r^ r VD M v v v vd U r S S fl r ( V t fl V v P v v S v V v (N P~ e v P V v v V V v tn V (v v v A V v v V r v 5 r V p (v v v (7v (v v v v t v S fl V V A fl p~ t V v fl V VD V v v v 5 (v fl S p V V A v v v fl flt V v V t S v r V p~ V V A p~ A v v V fl t> v v (V v v v r " V v (v v v v v V v t v V l v v VD v fl t v e v v e v 6 t vd p V v r^ _? V V v P~ v v v v v v V P^ V (v v v t V S _. V r^ p S v N r v _ V P v v v v v v e A v r^ v v v v t e r^ V V v r v ^ _ e _ " eg, e U " P H f e > v > ' S tn ^ V VD v r^ A v v S t V v v v v V v v V v r v v v v v v t 6 V v v V v r V VD v v (v V v " " "" ' ;t^ v fl" fl w V r> P~ (v V ^ ^ U ; t t "" S A V r^ v v v v v v V v v v v v v v v _ V VD t l D " D! # U? U v v v v fl V P v v v v v t A V p v v v v =>! V A" fl N _ v v v v P A r^ p v t (S V v v v t A v r~ v V v v v b!h V r^ v v v v v v (S A V r^ v v fl V v p v v v v v D S p v _ r^ N N fl > P v v v v v v v r^ v v v v V (N e V D r t^ v v V v! tn r? V P P v vd V r^ D V 7v V v v v v v? ', V V v p v v v v tn fl ^ V V V p VD fl v v v v v v : l v _ e t..! r v v v _ A V V V flv P v v v t V p V v v v v v t v _ N v e v, A _ v vd v v _: e H e H r, t =>! D D S Q S? v v U U r v vd A v fl v P v v (7 v v v _ v v v v v vd t v t V v p~ v V V v V V v v v v p~ v v v p e A t VD p~ v v v! v! V V V V V t t r V A tn v V t t v v ^ fl V t t S A A" fl t fl r N S fl l r 6

77 A" A A" A flrn VD tr A" A" A" A A A" A v r v D v U S V p v v v v v VD V _ vd P! t!r A" e M S X e (N ^ (J 5 v p V (N fn t v t _. vd v V VD v p~ v p VD VD vd fl v r v fl p^ P~ V vd v v v A, V p~ V v v v v v v tn p v t S _ fl P S t V VD v p v VD (N V v V tn P~ v P^ v v ; v v A" v_ P v v v V v v v t S A A V fl V v v r r fn v e V v V v v t vd V fl V VD v v v v v v p M v v v A V p~ V V p v v tn t _ t _ tl DeS V v ^ V p p p v V A A e V V V fl w P VD VD V fl A v r v fl V VD P v v v v v t V V p 5v v v v v v U v_> fl V V r (N e e A p v v e V v V 2 VD VD t V v fl P e V t V VD p A V V p v v v v v A V p v v v v v (N p v V t S S? A VD t _ V tn V r v p V V (N V p^ V P v A v v (N v p~ V v v v v (N V v v v v v S V v r~ t J B ' 6 V V v vd fl A e t v V VD v fl SD v v r vd p V v v P V VD P~ A p v V v v v v A; V v v V v V v v v t r f S _ p r V A P (N V V p~ v v r P v v v v v _ V P p v p V l e fn tn V f v v v V p v v v v v e e P H f p f ^H P H f vd U 6 e: V S vd A" fn V A" v N fl A V (S v v e P^ p A p fl fl (N v p A" V P v v v v v v tn A VD p v v v v v t v t S? fl t V V V V V v V v fl" v v V P v ^ v v v v V fl v P v v (v V A" V P v P v v v v v v A" V P v v v V v v t t V P e fl v fn t V P V v r V vd v t V (N p A V P V V v v v v v v V v v v v v v P f A" t t S V VD V P V fl" rn v V w t A V V t t fl vd v v VD v tn P v w v A" V P A" V v p v v v v v V v V v v v t B tn _ V (N p~ v t~~ A v fl v vd v A v e v V V p v v v v V v v v v v v v v v v p~ V p ^ t r p v e' e v p v v v v _ S VD (N v r v N v v v VD v v _ e l ) Q. H B JJ B e S v V VD P V _ p V (N fl V p v A A V V r~~ fl tn V V p V V v v v v v r V v v v v v v A v tn _ t vd t t vd VD p~ VD 6 p r (N V p r fl; V t v D fn V v P v v v v v V p fl P (N V P V fl fl A" P V P V v v p t fl V vd p r V v v v v v A A; v p^ v p v v v V v v v t v v v A" v v v V v P S fl V t (N v D V V fn p^ v v v v t v e H V 4 V flv (N A" vd (N A V V p (N A V fl v fn fn fn (N 64

78 , A" A" A" A" A A A" A" 4 e W e v fl (N t VD tn t P (N S v P w fl V > v v v v v v P fn V v t r S V S fl V S V v v (N v v P v v v v v v t fn v fl p V r v > v fl V v r V V P v v v v v v t 6 v P v vd v P (N vd V t p^ A" v P v v v v v v v v v t U V r V fl p v tn v p V V> p v V v p v v v v v v v S _ A" p v p A" t v v A" fn tn V p v v _ A V P v v v v v t ) B e 4 e e U " tn t v e vd A r v A" A" P fl v V v v v v v v p fl V v t S [ S p v r V v vd v v P p V v v v p v v v flv. A fn V p~ fl w v t V v v v v v v v ^ t A _ 6 S v f (N P v v v ^H p V V P V v v v v v V _ H f D V V V V V A p A v (S_ p V v v v v v v t S tn v (N v P A" V v tn p V V p v v v v V t r D r fl V V v v v v A v v v v v v v P v t "_? 6 P V t P t v v v vd v p v v L. _ e ) & H _ B _2 "5 B e H r ^ D U S V? r v v w v v P v tn V v v p v v v v v v v V V v V p v v f V t v v v v v t P v V V V v A A v V p p V v v r^ v v v v v fl t 6 v V v P tn (N v v fl V P~ v v v 4 t e e H vd A V (N v tn p r vd v v V W v v p v fl fl V p v r tn 65

79 7 D f Relt he ber f trfer t (NU) ebly ffet the rge fr ^, = ^, =. he t rge eree the NU vle ree fr gve 'w. t tke le e t heve tey tte fr hgher NU vle. NU the relt f the b preter hw eq 7.. NU = (^p). (ha) + (ha) (7.) Fr NU t ree, the flwe, pef het f the pty e fl, r bth t eree. h trlte t lwer fl vele r lwer fl pef het. verely, the ve effet r rfe re t ree. he r fthe wll therl pte t the fl pte efe by ^,. he rge ree ^ ree. t wll tke lger t reh teytte wth ree wll e by ether hgher ety wll terl, thker wll betwee the fl, hgher pef het terl, r b f ll three preter. q 7.2 hw the prl preter ffeg w. 66

80 >. (Mp (pavpl (pphgt(wth)l) _ (ppal). PwlL(wth)thkwllpwll. (y2) verely, ree ^ l be e by le ee fl, lwer pef het fl, r rrwer fl pge. ^, e f the re pt preter the tret perfre f het exhger. he effet f t, R,, NU re epeet the vle f ^,. A ree, the e reqre t heve the ew tey tte tepere effevee vle ree fr the fl, ll ther preter hel tt. A reg vle pper t hve gft effet the e fr the x fl. he rge fr the tble geee re fr.2 t. whh te the lwer pty e fl het pty e reg t pprh the hgher pty e fl het pty. q 7. hw the preter te wth. _ = (p(hgt) wthvp )_ = ^ (pl = x ( (pavj (p(hgt)wthvp) x reg the flwe f the fl wll ree, whh ree the e t reh tey tte tepere. reg the heght f the fl pge, r the velty f the fl re tw wy t heve lrger. A ree pge heght ree the t f fl t be hete r le. A ree velty, ree the well e, whh wll ree the het p r l w e f the fl. he x fl t gftly hge ver the rge f vle e t t t beg the teppe fl, hvg ether hgher pef 67

81 (hlwth) _^ het, fl velty, fl pge heght, r ety relve t the teppe fl. he preter trlte t hgher flwe r pef het p l =. A reg R le t reg tepere effevee vle fr gve t\ ll ther preter hel tt. h te the tey tte beg heve fter R ree. q 7.4 hw the preter fr R.. (ha) (hlwth). (ha) v ' v. ' (74) A ree h fr the hgher pty e fl le t ree R, whh te the het trfer r veve het trfer effet f the x fl hgher reqrg le e t heve the ew tey tte tepere effevee vle fr bth fl. he preter t ffete the tepere effevee vle fr w. eql t.. t h eglgble effet fr w eql t. Fr thk wll, t rehe pt where the well e f the fl h l effet the tepere effevee vle. q 7.5 hw the preter te wth t. + t, v J J. q^ v / "t>x"fl^ "flwth(hgt)^ V.' f~ \ he lwer pty e fl pprhe the ew tey tte tepere effevee vle fter th the hgher pty e fl wth ll ther preter hel tt. he tepere effevee vle exhbt expete expel rel wth e. 6

82 he perfre tble geee pblhe the relt e re very efl fr eterg tret tlet tepere fr eh fl ver e fr prllel rflw het exhger. he ele preter ver the we rge f pef gverg preter fr prllelflw het exhger lte ble 6.. he ple tble geee fr rflw re l very efl, yet lte rge. h tehqe be ely fe fr ther geetre, r, wll therl pte. Ftre er wl be t llte the tepere effevee vle fr tep pt t the x fl, etere hee geee tble fr elg rflw het exhger wth bth r e fl xe, plete the rflw effevee tble fr teppe ; fl vlte th the. 69

83 l h the preet ew tehqe fr lvg the tret tlet tepere repe fr prllelflw rflw het exhger lzg heret therl etwrk lver. t l preet ew rge f preter vegte. heret l re verfe t wth x peret e fferee f 4 % f lyl l fr prllelflw, % f lyl l fr rflw het exhger. Prllel rflw het exhger re ele lzg tw fl epe by wll. he fl wll reg re repreete by e. Retr epe the fl wll e repreet veve fl flw rete. Ne lkg ret etere the het exhger fgr t be ether prllel r rflw. he rflw el fr glep, bth fl xe rflw het exhger. tlet tepere llte fr rflw re e tlet tepere. Fr ry ze pter r e, the prllelflw het exhger w ve t eget fr NU 2, 2 eget fr 2 NU. he rflw het exhger w ve t 6x6 eget fr NU., x eget fr NU 2. A etep fhlfthe well e f the hghet velty fl w ffet fr ll e. ret tlet tepere effevee f 2 ) vle were geee fr tep hge t the fl fr prllelflw rettrfer type het exhger. hee vle were geee fr ew, wer rge f ele preter whh le NU,, R,, t, t. ret e tlet tepere effevee (! 2 ) vle were geee fr tep hge t the fl fr gle p, bth fl xe rflw 7

84 rettrfer type het exhger. New tble were geee fr NU =. the fllwg rge f ele preter whh le, R, ^,, t, t. he tret perfre tble geee th the re very efl fr eterg tret tlet tepere fr eh fl fr prllel rflw het exhger. Appl f the ew tble geee reqre ll f ele preter lte the tble pef fr e' ppl. he tret tlet tepere llte fr the tble effevee vle fr the pef e r e f teret. 7

85 9 Referee Be, D.J., 995, "ret Repe f Het xhger," Mter' the, R Depet f Mehl geerg, My, 995. Be, D.J., Klkr, S.G., 995, "ret Repe f Het xhger Preete t the Se ASMSHM feree Mglre,, Deeber 2, 995. he, H., he, K., 992, "ret Repe f rflw Het xhger wth Fte Wll pte," r f ASM, Jrl f Het rfer, Vl. 4, Agt, 992, pp he, H., he, K., 99, "Sple Meth fr ret Repe f GtG r Flw Het xhger wth Nether G Mxe," terl Jrl f Het M rfer, Vl. 4, N., Nveber, 99, pp , R.M., L, A.L., 95, "he ret Repe f wfl terflw Het xhge he Grbe Regeer," r f ASM, Vl., N.5, pp le, B.D., Klkr, S.G., 995, "ret Perfre f PrllelFlw Het xhger wth Step epere hge M pty Rte Fl Stre," Preete t the 2 rpe herlsee 4th U Nl Het rfer feree, Re, My 29, 996. Gvze, D.D., 97, "Alyl Sl f ret Repe f GtG Prllel terflw Het xhger," r f ASM, Jrl f Het rfer, Vl. 9, N. 4, pp Gvze, D.D., 96, "Alyl Sl f ret Repe f GtG rflw Het xhger wth Bth Fl Uxe," r f ASM, Jrl f Het rfer, Vl., Nveber, 96, pp rper, F.P., DeWtt, D.P., 95, Fetl f Het M rfer, 2, Jh Wley & S, New Yrk. Klkr, S.G., Be, D.J., le, B.D., 995, "ret Perfre f terflw Het xhger wth Step epere hge M pty Rte Fl Stre," Preete t the Preeg f the Syp herl See geerg hr f hellr hgl e t the Uvey f lfr, Berkeley, Nveber 4,

86 Ky, W.M., L, A.L., 964, pt Het xhger, Se, MGrwHll, New Yrk. L,.H., 96, "xt ret Sl f Prllelrret rfer Pree r f ASM, Jrl f Het rfer, Vl., N. 2, pp L, A.L., Spell, D.F., MGw, J.G., 964, "he ret Repe f G rbe Plt Het xhgeral Sl fr Regeer f the PerFlw Dretrfer ype," r f ASM, Jrl fgeerg fr Pwer, Vl. 6, pp L, A.L., Br, F.R., Mthell, J.W., 959, "he ret Repe f G rbeplt Het xhgerregeer, terler, Preler, Dg r f ASM, Jrl fgeerg fr Pwer, Vl, tber, pp Myer, G.., Mthell, J.W., Le,.F., 97, "he ret Repe f Het xhger Hvg fte pte Rte Fl," r f ASM, Jrl f Het rfer, Vl. 92, Sere, N. 2, pp Myer, G.., Mthell, J.W., Nr, R.F., 967, "he ret Repe f rflw Het xhger, vpr, eer," r f ASM, Jrl f Het rfer, Vl. 9, N., pp. 75. Rzk, J.W., 956, "herl Lg Flwg preble Fl Syte tg Het ptr," r fasm, Vl. 7, tber, pp.474. Re, F.., 95, "ret Repe f PrllelFlw Het xhger," Jrl f Het rfer, Vl. 7, pp Re, F.., 9, "ret Repe f GtG rflw Het xhger Wth Nether G Mxe," r f ASM, Jrl f Het rfer, Vl. 5, N., pp Shh, R.K., 9, Het xhger herlhyrl Fetl Deg, "lf f Het xhger," ete by Kk, S., Bergle, A.., Myger, F., Hephere rp., Whgt. Shh, R.K., 9, Het xhger herlhyrl Fetl Deg, xhger," "he ret Repe f Het ete by Kk, S., Bergle, A.., Myger, F., Hephere rp., Whgt. Spg, G., Spg, M., 9, "ret epere Fel rflw Het xhger wth Fte Wll pte," r f ASM, Jrl f Het rfer, Vl., Febrry, 9, pp

87 Spg, G., Spg, M., 97, "wdel ret Sl fr rflw Het xhger wth Nether G Mxe," r f ASM, Jrl f Het rfer, Vl. 9, My, 97, pp HRMNrHX, herl Netwrk Slver, 995, erl ftwre evelpe by HRMN Lt., Rheter, NY. Yht, H., z, R., Ygh, S., "Aly f the Dy her f rflw Het xhger wth Bth Fl Uxe," Blle f the JSM, Vl. 2, N. 5, Mrh,

88 Appee 75

89 Appex A Prl Appl f ret epere ffevee ble: Deg Preter Reqre fr Applyg repe t tep pt hge f fl: tble t etere tret tlet tepere Het xhger De: L Legth wth Wth hgt hgtx thkw,, Heght f pge fr fl Heght f pge fr x fl hke f exhger wll eprg bth fl Mterl fr: Seprg Wll: Pwll Dety f terl p,wll Spef het t tt prere kwll herl vty Fl: V Vletr flw e P Dety p. Spef het t tt prere veve het trfer effet

90 ,().t) let tepere befre tep hge let tepere fter tep hge x Fl: Vx Px Vletr flw e Dety p>x Spef het t tt prere hx,x(),x() veve het trfer effet let tepere befre tep hge let tepere fter tep hge Hw t e ble: Detere ele preter NU,, R, + = w, t, t fr eg fr lte bve. F effevee vle ver t fr tret tble fr ele preter llte tep. llte teytte tlet tepere fr bth fl befre fter the tep pt g the effeveenu eth (rper et l. 95), kwg NU. 4. Fr pef e, llte t t f the pprpe effevee vle fr eh fl.

91 5. llte tret tlet tepere repe by rerrgg effevee eq (Fl => fl, Fl 2 => x fl): /,> = yt) = [t{) rm()]+ ru().= 2{t)2{) ' 2()2{) l,2 ( = [ () 7^ (>)] + 7^ ()

92 pe Prble Ue f ble: GVN: PrllelFlw Sgle P Het xhger (lg l) wth hw Fgre Fgre : Dret rfer Prllelflw Het xhger Ar Steppe Fl r() = 7 _,.(+) = 4 Flwe = 4.9 / h = 5 W/2 Het xhger (lg l) r,tlet (t) Al Seprg Wll Wter Uteppe Fl () = 2 h2 (+) = 2 Flwe =.72 / h = 56 W/2 L H2,tlet (t) NAL NDNS: BUNDARY NDNS: r() = 7 h2() = 2 _(+)=4 h2(+) = 2 L DMNSNS: Legth =.6 eter Wth =.6 eter Heght f r pge = 2. eter Heght fwter pge =.2 eter Seprg wll thke =. eter FND: tlet epere f Ar Wter t e = 9.4 e, e = 47.4 e fter tep pt hge. V.QANS: Refer t Sl.

93 tt ASSUMPNS:. fl prpere 2. Neglgble r effet. Neglgble het l t rrg 4. N therl eergy re wth l 5. Wll therl rete eglgble SLUN: Deg Preter Reqre fr Applyg repe t tep fl: ' pt hge f tble t etere tret tlet tepere Het xhger De: L Legth =.6 eter wth Wth =.6 eter hgt Heght f pge fr fl 2. = hgtx Heght f pge fr x fl =. 2 thkw hke f exhger wll eprg bth fl =. eter Mterl fr: Seprg Wll pwl p w k^ Al: Dety f terl = 272 kg/ Spef het t tt prere = 9 J/kg 24 W/ herl vty = Fl Ar: V p h " () () Vletr flwe = 4.9 / =.225 kg/ Dety Spef het t tt prere = J/kg veve het trfer effet = 5 W/ let tepere befre tep hge = 7 let tepere fter tep hge = 4 Fl 'x Wter:, V Vletr flwe=.72 / x Dety= px v'p,x 997. kg/ Spef het t tt prere = 4 J/kg r 2 h veve het trfer effet =56 W/

94 Detere R _,x(),x() let tepere befre tep hge = 2 let tepere fter tep hge = 2. ele preter NU,, R, w, t fr eg fr lte bve. NU. V'w = =.2 =.5 t = F effevee vle ver t fr tret tble fr ele preter llte tep.. llte teytte tlet tepere fr bth fl befre fter the tep pt g the effeveenu eth (rper et l. 95), kwg NU. PrllelFlw Frl: lxp(n(l + )) =.52 [+] SteyStte tlet epere: :,t \t) ^ ^t) [l \t) M.x wj x : t x(tj = l ) + L l,w l,x\t/j Befre Step pt: : t= 4. x: t= 25.2

95 W)] After Step pt: : t = 7.2 L ^x: lt Fr pef e, llte t t f the pprpe effevee vle fr eh fl. A t = 9.4 e => t = 4 => ef =.4 =.6 A t = 47.4 e => = 2 => =.97 = llte tret tlet tepere repe by rerrgg effevee eq: f/= ^((^(() =>W = ^W) ~ + V() vrx fy w(t)r w\ =w b 2[Ut 2()2(J )] + w() A t = 9.4 e: Ar: t(9.4) = 5.6 Wter: t (9.4) = 2.7 A t = 47.4 e: Ar: t(47.4) = Wter: t (47.4) =.4

96 Appex B Sple Spreheet fr Prllelflw rflw epere ffevee ll: PrllelFlw:. eget el 2. 2 eget el rflw:. x eget el 2. 6x6 eget el. x eget el

97 _= Q ^ = : _= _ f. " _ "'^? g ' ' M [! r ' >. ;! ; M \ l ' H Z t t ' " ^r!". & f ' p f,%! S! vl 9 p P^B x: X t^^=r! Q: ^^ > r? 5 S2 =: S eg. e S : p f=^s ^ S Q D "V J v J : t _! f. f [ SrS 5 D t? t l _ N == V e ) K M 2 D X S 4 ; ; : 5 V V ^ > r t V V V V V V (V V V V V t \ U) t V h v. r.r K D G t h> J l f. t h g g g g g 5 g g ~! " f P H l ; H A ; 55 e J 5. 5 : ^ 5 S J U.. Z : l t 9 e 6 e H "e? V t N N l 4 V l v l l J Z S t &B t ^ = e 5. > e ' el 2 e r "5 2. > 7 "5! ^ S z z _. V l rō vt! l J t V M V l l l l l l > l

98 M". P U l > _ t f f S f t t D t. J Z " S t_ e_ e J z e 5 P l & ) r S t. _L td _2 2 e e. g l V V 4 V r. l f v V e > e 2 e J z t S ^ > e ^, V t t? M"? ) l t t.!_ l SJ l r V f r B 5 f V V,^. ". v 5 er t'.t^, V

99 DAA GNRAN PARALLLFLW SGMN MDL terpl Frl: N: Fl Fl (Steppe Fl), Fl b Fl 2 (Uteppe Fl) Vle fr ble: ff (Fl ) ff(fl b) t terpl frl re hghlghte => 4 S)t_ yv w. :t_r^>f w e! (Se) Ne # Fl Ne# Fl b Vle fr ble: epere epere ff (Fl ) ff(fl b) t (Degree F) (Degree F) ! 2. f...sm^f S.6S2Q gtg5w2565z wtwfws5.p9s ;6249?4H562>

100 DAA GNRAN PARALLLFLW SGMN MDL :92942 w/ H fl l M97M6&'&7M& VS^MMMS,?e.959Hf59l ! re lP9S_pJ(l]992&52_]

101 ; _= ' tr' " ' =!, :.. r! l ll r~ k (D V ev P Z >. >r LL. e ". J f LU??S v e? (? 5 5 N P^, 5 f 2 ^r f^?"^: X ~:_ : : t :_ ^y>= '! ; ' ' l! l rrl ] [ :! \!: 5 ' :!! S J '! LU ' S,. l ;! : > N _ h! & LL " ; e "!.rf.7 2! X r.! ; " J ; J rv J= J? ^ > U) U) f.. l r. >! X 5 D / _ fg! r. r : e? U ; S "5> "D ] z LL 5 J r > S. ^. )? S r Q f 5 ft M Z 5. "& 5 k z " > B S l! e?s fe >!?: t^ ff 2r S" " J & p 2, rf X J. H^ X e G 5 "5 M > e = > e " S. 5 >> S Q > r l=s J H _ Z z 5 r _ ~ v r > > ^ ^ ~ B 5 xz 2 r^ > V V V ^ "5 "5 _ 2 ^! 2 S > _^ " H z z 2 S.

102 ' ' ~ r!!! (. ; ^ t t > > e > >! t t > t l t ) t > t vl l ) > J f r^ ^ t r. ) ^ S. > r^ r^ r^ e r^ e ; ~ vt e! J.: >\. ^lre;e. t >! w J e e t e e e r > 5 > ^, t 5 > Bl. 5 v ).2 &. r t Q Q. t t V e D e X

103 _ ' ' " ' : '! ' ;..! :. l l ; : ; : t.. ;! : : M ; J! tz Z! : S MM; z > S l H S S l ' S t " " e e N >.!! ;! ; ll > ;! ; : ) ^ r > M r S. _L > r r l. r Q e N M >. J e 2. l= e z e > l ^ r eb r V v > V l S td D td t : k pr 'e ; ^JMJe!! ' ; : : J. ^ e e r f V X 5 f: e ^ " r l U) e > td l l D w > V t 'e! l V f ( e t' e

104 S + r V r S UL r r Q. N

105 DAA GNRAN PARALLLFLW 2 SGMN MDL terpl Frl: te: Fl Fl (Steppe Fl), Fl b Fl 2 (Uteppe Fl) t Vle fr ble: ff (Fl ) ff(flkj b) terp frl re hghlghte => 4 _DS e (Se) Ne # Fl Ne# Fl b Vle fr ble: epere epere ff (Fl ) ff(fl b) (Degree F) (Degree F)! t ! ! ^fe&b r9fflzq77j wwmft wzwewkb7b5b , P2Z2ZM5ZSS6St wm 2: g SDSS5_2X45l ; ^S252lB&P

106 DAA GNRAN PARALLLFLW 2 SGMN MDL ,^SM_l w ^ &g&tsl

107 . _5 '! J _D ^ f! St w tr t. N F e! z> z ; f t t N r. h S ^~ " ( S!. LU ; "e S 5 J ^".g SP? e X Pg^ % S % S ; U. Pf JZ : Q. ; e! Q > D! M J l t > "t "D f Z LU S " t 2 g ^ ll N J (^ >>? ^ X,! X > J B t ) l t t l t > > t t t l t t t t t.?y t t t t l D t D D D D X 2 M fer f g g g g g g g g g p; W? t S? r e X + _ 5 LL W S M r h Q! zr_ S ^ W %W J= U f D M Q. M e D_ > D (J t S. H 5 S b LL UU e z Q ~ " ~ U 2 Z J > Q. e 2 L D z rō e z. &P e > M K M " JZ.& >; Q g e > e e? l M " M > M t 9 z Q S!

108 . P t e t e > J z l!! D Z > e t t l t S U t S r X rf r 2. ) M fl r. Q e A >. 5 e _ e. z D t f"~ 5 5 t 5 e r > S t r t R t e e l l td S S r l

109 = _ ' l>w. _ ^., LL S r! % V r, t f S LL 5 t A ll p S l V P p? ".? l r X? Q 5 l. _ ft. r l r t e D. "r t $ L 2 f f V 5 V N > V g S r v r l g r v g g g r > N N g r r r r r g J, r r r N g S r r > r B N g N r r N r N g r N g r r r t _ X DJ X LL J> D K g z " > e Z "5 > z S xz z. J M S UL e 9 e J= r J 'SS 5 5 " ) "5 U "B. r & J? l "S S l _ 7. z K b 2_ ^ l z> Q y N ) z B z. e ^ r M V S r t r t r S v v V r r f. t l ' L

110 ( > S! X L J, t Q

111 r [! p r $ r r r r r r g r r r Ml r r r g r g r r r r r g g r r g r r r r r r > ( g S r r p r r g r r r r r S e Kt r r r r> S J " z 2 > e S N t A g r N t ( t N D ) t t X t!_ LL (fl JS fl ( L? r Wl R r Ml 5 g r r r r r t r Nt Nt r r N >> % r e r 4f z ^

112 ' ' ~!! F ; ' ; ;!! ll! 6 5 5! l p l g g g g g g g g g g S g g g g S g S t"! J l' t e J X ' 2 S! L J, g & r V r ; v _ tr, r r Wl r 5 Wl w w; v K D r f. v v Wl r ^ w v 5 Wl _ r ' t K g t t N. r l M 5 V w Pl g J r v tr. ^ 4 V S 2 v r r f v 5 l M> f [ [J

113 ll! WlllJWl Wll p p > "!l' gg: l D ) ( X J t _. (fl fl r w Q UN(

114 _S A 2 > ~ "" ^ ^ 't fl l_ ) Q ) 5 ) ^ " S" ) ^ 5 S r^ 9 V r ' r^ > ^ 5 L r^ r 2 "5 SH 2 LL e 9 LL 5 L Bl " US ^H' ^ 5 LU P) g ' z$ gbs _. H,_, ) ^~ ~ r ^ H r H r r~ 'S S. g >r) ^ 2 ^ (^ K^ff f r^ _ 2 >> > PH^ f^h f ^S ~ ^ f ^. K L f ^ ^ LL leg t B ~ r b LL f^ W$M L ) Kf > ^^ ^"^ P l rj h~ # " t pp t: p H(Q r > 5 LU BS! ^r 5 L ) r > t> L S ~ l L f^ r L ^f r^ p L ~ v e v ^ vr A ~ r^ t LL.. LL h t V M" ^ "Jt D " A? ( t ) J? t~ L L L _ D. r r _= t J Q.!_ '5._? L t b t ^ t V Q l! L r S r 2 LL.22 z ^ 2 r r J LU r "" x~ ^ r ^ r t 2 5 r t > > Q. 2 _. L _. r L e D Q l S. H ) t ^ X LL L r LL t 2 L 4 z H L ^r Q. P _ H Z

115 t ^ ^ l J" " S ~ _ ~ _ '",_ ^_ M l MM RN g_ th RU e bfl P! r> r er J2 W r W e W&t Br U>lr A ^ r f ( U L Bt ^^ L l M_S Pl L LV r HSl l^ lw h L g ff'l Mr B M r L 5 t Sf fl r t % > Mr!N S 6 h. r l_ J^H ^^ ^~ W SKg q W Ht B,;" w w tl t> f t^l^ (Q B r H r r rr r r Hr r B B^ S ^ ~ r MN S r h~ psh D L l ' r> "US r JSf Pl" Hw t ftj llll L KStll fw > S" KB > B r W ^^ f S v w S> r p N v J ll S h p v Hw S > r 9 5y ^~ r U H B w g 5 { r SJt t p ^ &?. L w r PSt t ) f Bf r BK ] r r p r t SM r rl l lf^ v l B Be l S. ^_S r 6 r r r Kglr r ^^^ r r t r pl t tf ^ L D ^r f r~ r ^ W r r r r r^ V~ r r r^ r t r L U) r r t r f ^ t t tt > f r r^ L t r r^ r^ f t t r ;r r ^ ^ ^r t t r^ ^ l_ ) Q D) X LL l_,. ' h~ r t r^ r^! r^ U) ; t r^ ll r t r L r^. r^ r r h f^ h~ t r L t ~! L f~ ^ ^r r r t w q v le t L K ^ K K >: tt U) f ^r r t r r r^ l w _ r^ r r r r^ L U) t, r^ r r^ L r r r h r h~ 'S r t r tt t ^r t ~ t r U) ~ t w U t l ^ r^ ^ r r v ^ t ^r L U) L U) w w L U) h h~ r r L

116 ^J" v ~ L r ^ r t r r^ w r~ r r ^r w.l ' t v 'S ~ ~ v S pb H h p tt St r ^ h.^ SM w H > fh W w ps " tplw h pl r HH pl r e r r Hgr r H r H lll Jl t r^ y? w ^ H te w ^ fl t r^ t fs^lf w x r fw " w w US S H ep P ""'Bk U) t ; r r^ t t D l r^ f^ r t t t' t. r^ U) t t w S r ^ r w ) x t LL w w w w 5 Q

117 D z = _, _ J J " J ; ' LL S > 6 V. ( D L v 5 f > t "_f Pl : A LL 5 X r D $?M^ "5 LL F! J! l J L. Dl D X D U > l M e D = K $ LL X!! Q S t Q t g 5 L D " J Dl P P "S l S 2 ^ g N 5 Q_ ; L l l e g' e e e e e l l t t > e t t ) t e > t e t t l t l t t t > l t t t t t t > t t l t t t > t t t t! J M L Q. t 4> p 5 e. Z S w Q_ S w > L "2 5 S N M > S LL e e t t t t t t t tle t t S r ^ X e 5 LL e> ( _ k Q J e M K 5 9 A Z _ f. Z e > e Q. A "5 e > z > e ) X z w M f S l l e JZ Ml D J = X LU "D G=. l _l ^ D z fm r. J Z V) _ r f D ^ l t l> l 5 > l t t 2 v t v V t t

118 M"! [ t! ; t > t ) l t t > t l l td l l t l l l l l l J l l l l l > > l l l l t l t t t t t t t t U) t t t t e t t t t e t e > e t t t t t e e 2 t t e t t t t t t t t t t t e t t t t t.t l ' t, l ' t t t e t t t! t t t t t t : V 5 ^ l fl e l t t f l t t. Dl l t t S S 5 fll pr fl l w l V t l> ^ R ^ l X > e l 5 l t ^ ^ ^ R $ l t '

119 : N" fl" fl"! ; ;, L_. l ll'll ; ; :.!! ; : > 6 l l l t l > l l l l S t. 6 r P. r ^ l r e. ; t e l ' t td l l l l t; l l 5> l t l l l tn l f tn > >!! ^ rō l S S Rl > td N \t t t ll l' t D l J l l l l ' N'l N" ' rō ld t t t e

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