. Analysis The nodal spacing is given to be x = 0.02 m. Then the number of nodes becomes 1. i m. i m. i m

Transcription

1 aper Nuerca Meds n Hea nducn - - A uranu pae na a a unfr eperaure s subjeced nsuan n ne sde and cnvecn n e er. e ransen fne dfference fruan f s prbe s be baned, and e nda eperaures afer n and under sead cndns are be deerned. Assupns Hea ransfer s ne-densna snce e pae s are reave s cness. era cnducv s cnsan. Radan ea ransfer s nebe. Prperes e cnducv and dffusv are ven be = W/ and. / s. Anass e nda spacn s ven be =.. en e nuber f ndes beces / L M =./.+ =. s prbe nvves unnwn nda eperaures, and us we need ave equans. Nde s n nsuaed bundar, and us we can rea as an nerr ne b usn e rrr ae cncep. Ndes,, and are nerr ndes, and us fr e we can use e enera epc fne dfference rean epressed as e fne dfference equan fr nde n e r surface subjeced cnvecn s baned b appn an ener baance n e af vue eeen abu nde and an e drecn f a ea ransfers be wards e nde under cnsderan: cnvecn: Nde Nde nerr: nerr: Nde Nde nerr: : Nde nsuaed r were, W/, W/, W/.,, and. /s. e upper f e e sep s deerned fr e sab crera a requres a prar ceffcens be reaer an r equa zer. e ceffcen f s saer n s case, and us e sab crera fr s prbe can be epressed as / / snce /. Subsun e ven quanes, e au awabe e e sep beces. s ]. / W/.. W/ /s[.. erefre, an e sep ess an. s can be used sve s prbe. Fr cnvenence, e us cse e e sep be = s. en e es Furer nuber beces, Insuaed

2 aper Nuerca Meds n Hea nducn. / s s.. Subsun s vaue f and er ven quanes, e nda eperaures afer / = e seps n are deerned be Afer n: =., =., =., =., and =. b e e needed fr ransen peran be esabsed s deerned b ncreasn e nuber f e seps un e nda eperaures n ner cane. In s case sead peran s esabsed n ---- n, and e nda eperaures under sead cndns are deerned be =, =, =, =, and = Dscussn e sead sun can be ceced ndependen b bann e sead fne dfference fruan, and svn e resun equans suaneus. -

3 aper Nuerca Meds n Hea nducn - "!PROBLEM -" "GIVEN" L=. "[]" = "[W/-]" apa=.e- "[^/s]" _= "[]" _d=e "[W/^]" _nfn= "[]" = "[W/^-]" DELA=. "[]" "e= [s], paraeer be vared" "ANALYSIS" M=L/DELA+ "Nuber f ndes" DELA= "[s]" au=apa*dela/dela^ "e ecnque s sre e eperaures n e paraerc abe and recver e as d eperaures usn e varabe ROW. e frs rw cnans e na vaues s Sve abe us ben a rw. Use e DUPLIAE saeen reduce e nuber f equans a need be ped. un cnans e e, cun e vaue f [], cun, e vaue f [], ec., and cun e Rw." e=abevauerw-,#e+dela Dupcae =, _d[]=abevauerw-,#[] end "Usn e epc fne dfference apprac, e s equans fr e s unnwn eperaures are deerned be" []=au*_d[]+_d[]+-*au*_d[]+au*_d*dela^/ "Nde, nsuaed" []=au*_d[]+_d[]+-*au*_d[]+au*_d*dela^/ "Nde " []=au*_d[]+_d[]+-*au*_d[]+au*_d*dela^/ "Nde " []=au*_d[]+_d[]+-*au*_d[]+au*_d*dela^/ "Nde " []=-*au- *au**dela/*_d[]+*au*_d[]+*au**dela/*_nfn+au*_d*de LA^/ "Nde, cnvecn" -

4 aper Nuerca Meds n Hea nducn e [s] [] [] [] [] [] Rw r ef [] ef r [] e [s] -

5 aper Nuerca Meds n Hea nducn - e passve sar ean f a use ru a rbe wa s suded. e eperaure dsrbun n e wa n nervas and e aun f ea ransfer durn e frs and secnd das are be deerned. Assupns Hea ransfer s ne-densna snce e epsed surface f e wa are reave s cness. era cnducv s cnsan. e ea ransfer ceffcens are cnsan. Prperes e wa prperes are ven be =. W/,. /s, and.. e ur varan f n averae aben eperaure and sar ea fu ncden n a verca surface s ven be e f da a-a a-p p-p p-p p-p p-a a-a a-a Aben eperaure, Sar nsan W/ rbe wa Hea an n n Sun s ras Gazn Hea ss u u n n u u Anass e nda spacn s ven be =., en e nuber f ndes beces M L / =./.+ =. s prbe nvves unnwn nda eperaures, and us we need ave equans. Ndes,,,, and are nerr ndes, and us fr e we can use e enera epc fne dfference rean epressed as e fne dfference equan fr bundar ndes and are baned b appn an ener baance n e af vue eeens and an e drecn f a ea ransfers be wards e nde under cnsderan: Nde : r n A n + A A n + n n -

6 aper Nuerca Meds n Hea nducn Nde : Nde : Nde : Nde : Nde : Nde u A u Aq sar + A A r u u + u q sar were L =., =. W/.,. / s, u and. u =. W/., n =, n =. W/., and =.. q sar are as ven n e abe, Ne we need deerne e upper f e e sep fr e sab crera snce we are usn e epc ed. s requres e denfcan f e saes prar ceffcen n e sse. We nw a e bundar ndes are re resrcve an e nerr ndes, and us we eane e fruans f e bundar ndes and n. e saes and us e s resrcve prar ceffcen n s case s e ceffcen f n e fruan f nde snce n > u, and us n u erefre, e sab crera fr s prbe can be epressed as n / n / n snce /. Subsun e ven quanes, e au awabe e e sep beces.. s /s[. W/.. /. W/. ] erefre, an e sep ess an s can be used sve s prbe. Fr cnvenence, e us cse e e sep be = s = n. en e es Furer nuber beces. /ss.. Ina a a r =, e eperaure f e wa s sad var near beween a nde and a nde. Nn a ere are nda spacn f equa en, e eperaure cane beween w nebrn ndes s - F/ =.. erefre, e na nda eperaures are,.,.,,.,., Subsun e ven and cacuaed quanes, e nda eperaures afer,,,,,,, and are cacuaed and presened n e fwn abe and car. -

7 aper Nuerca Meds n Hea nducn e e Nda eperaures, sep, a p p a a p p a a e rae f ea ransfer fr e rbe wa e nerr f e use durn eac e sep s deerned fr Newn s aw f cn usn e averae eperaure a e nner surface f e wa nde as Q Q A A[ / ] rube wa rube wa n n n n erefre, e aun f ea ransfer durn e frs e sep = r durn e frs n perd s Q rubewa n A[ / n ].W/.. [. / F].. Bu e neave sn ndcaes a ea s ransferred e rbe wa fr e ar n e use wc represens a ea ss. en e a ea ransfer durn a specfed e perd s deerned b addn e ea ransfer auns fr eac e sep as I Q Q A[ / ] rube wa rube wa n n I were I s e a nuber f e nervas n e specfed e perd. In s case I = fr, fr, ec. Fwn e apprac descrbed abve usn a cpuer, e aun f ea ransfer beween e rbe wa and e nerr f e use s deerned be Q rbe wa = - J afer Q rbe wa = J afer Q rbe wa = J afer Q rbe wa =, J afer Dscussn Ne a e nerr eperaure f e rbe wa drps n ear rnn urs, bu en rses as e sar ener absrbed b e eerr surface dffuses ru e wa. e eerr surface eperaure f e rbe wa rses fr. n jus because f e sar ener absrbed, bu en drps. b ne rnn as a resu f ea ss a n. erefre, a be wrwe cver e uer surface a n nze e ea sses. As e use ses J ru e rbe wa e s dae as a resu f e w sarup eperaure, bu devers abu, J f ea e use e secnd da. I can be swn a e rbe wa w dever even re ea e use durn e rd da snce w sar e da a a er averae eperaure. -

8 aper Nuerca Meds n Hea nducn eperaure [] e [ur] -

9 aper Nuerca Meds n Hea nducn - - Hea cnducn ru a n L-saped sd bar w specfed bundar cndns s cnsdered. e eperaure a e p crner nde # f e bd afer,, and n s be deerned w e ransen epc fne dfference ed. Assupns Hea ransfer ru e bd s ven be ransen and w-densna. era cnducv s cnsan. Hea eneran s unfr. Prperes e cnducv and dffusv are ven be = W/ and. / s. Anass e nda spacn s ven be ===.. e epc fne dfference equans are deerned n e bass f e ener baance fr e ransen case epressed as Q G V A sdes eeen eeen e quanes q R,,, and d n cane w e, and us we d n need use e superscrp fr e. As, e ener baance epressns can be spfed usn e defnns f era dffusv / and e densness es Furer nuber / were. We ne a a ndes are bundar ndes ecep nde a s an nerr nde. erefre, we w ave re n ener baances ban e fne dfference equans. Usn ener baances, e fne dfference equans fr eac f e ndes are baned as fws: Nde : q L Nde : Nde : I can be rearraned as Nde : q L Nde nerr: Nde : Nde : Nde : were, W/, W/ L q =., = W/, = W/, and =. q L, Insuaed

10 aper Nuerca Meds n Hea nducn e upper f e e sep s deerned fr e sab crera a requres e ceffcen f n e epressn e prar ceffcen be reaer an r equa zer fr a ndes. e saes prar ceffcen n e equans abve s e ceffcen f n e epressn snce s epsed s cnvecn per un vue s can be verfed, and us e sab crera fr s prbe can be epressed as snce deerned be / / /.. Subsun e ven quanes, e au awabe vaue f e e sep s..s /s[ W/.. / W/. ] erefre, an e sep ess an. s can be used sve s prbe. Fr cnvenence, we cse e e sep be = s. en e es Furer nuber beces. /ss. fr = s. Usn e specfed na cndn as e sun a e = fr =, sweepn ru e equans abve w ve e sun a nervas f s. Usn a cpuer, e sun a e upper crner nde nde s deerned be,, and a,, and n, respecve. I can be swn a e sead sae sun a nde s. -

11 aper Nuerca Meds n Hea nducn - "!PROBLEM -" "GIVEN" _= "[]" = "[W/-]" apa=.e- "[^/s]" _d=e "[W/^]" _b= "[]" _nfn= "[]" = "[W/^-]" q_d_l= "[W/^]" DELA=. "[]" DELA=. "[]" "e= [s], paraeer be vared" "ANALYSIS" =DELA DELA= "[s]" au=apa*dela/^ R=/apa "R=r*" "e ecnque s sre e eperaures n e paraerc abe and recver e as d eperaures usn e varabe ROW. e frs rw cnans e na vaues s Sve abe us ben a rw. Use e DUPLIAE saeen reduce e nuber f equans a need be ped. un cnans e e, cun e vaue f [], cun, e vaue f [], ec., and cun e Rw." e=abevaue'abe ',Rw-,#e+DELA Dupcae =, _d[]=abevaue'abe ',Rw-,#[] end "Usn e epc fne dfference apprac, e e equans fr e e unnwn eperaures are deerned be" q_d_l*/+*/*_nfn-_d[]+*/*_d[]-_d[]/+*/*_d[]- _d[]/+_d*^/=r*^/*[]-_d[]/dela "Nde " **_nfn-_d[]+*/*_d[]-_d[]/+*/*_d[]-_d[]/+**_d[]- _d[]/+_d*^/=r*^/*[]-_d[]/dela "Nde " **_nfn-_d[]+*/*_d[]-_d[]/+*/*_d[]- _d[]/+_d*^/=r*^/*[]-_d[]/dela "Nde " q_d_l*+*/*_d[]-_d[]/+*/*_b-_d[]/+**_d[]- _d[]/+_d*^/=r*^/*[]-_d[]/dela "Nde " []=-*au*_d[]+au*_d[]+_d[]+_d[]+_b+_d*^/ "Nde " **_nfn-_d[]+*/*_d[]-_d[]/+**_d[]-_d[]/+**_b- _d[]/+*/*_d[]-_d[]/+_d*/*^=r*/*^*[]-_d[]/dela "Nde " **_nfn-_d[]+*/*_d[]-_d[]/+*/*_d[]-_d[]/+**_b- _d[]/+_d*^/=r*^/*[]-_d[]/dela "Nde " */*_nfn-_d[]+*/*_d[]-_d[]/+*/*_b- _d[]/+_d*^/=r*^/*[]-_d[]/dela "Nde " -

12 aper Nuerca Meds n Hea nducn e [] [] [] [] [] [] [] [] Rw [s] [] e [s] -

13 aper Nuerca Meds n Hea nducn - A n sd bar s subjeced ransen w-densna ea ransfer. e cenerne eperaure f e bar afer n and afer sead cndns are esabsed are be deerned. Assupns Hea ransfer ru e bd s ven be ransen and w-densna. Hea s eneraed unfr n e bd. e ea ransfer ceffcen as ncudes e radan effecs. Prperes e cnducv and dffusv are ven be = W/ and / s. Anass e nda spacn s ven be ===.. e epc fne dfference equans are deerned n e bass f e ener baance fr e ransen case epressed as Q G V eeen eeen A sdes e quanes,, and d n cane w e, and us we d n need use e superscrp fr e. e enera epc fne dfference fr f an nerr nde fr ransen wdensna ea cnducn s epressed as nde ef p r b nde nde ere s ser abu e verca, rzna, and dana nes passn ru e cener. erefre, and, and,, and are e n unnwn nda eperaures, and us we need n equans deerne e unque. As, we can repace e ser nes b nsuan and uze e rrr-ae cncep wen wrn e fne dfference equans fr e nerr ndes. e fne dfference equans fr bundar ndes are baned b appn an ener baance n e vue eeens and an e drecn f a ea ransfers be wards e nde under cnsderan:,,,, Nde : Nde : Nde nerr: were W/, =., and = W/, = W/, and =. e upper f e e sep s deerned fr e sab crera a requres e ceffcen f n e epressn e prar ceffcen be reaer an r equa zer fr a ndes. e saes prar ceffcen n e equans abve s e ceffcen f n e epressn snce s epsed s cnvecn per un vue s can be verfed, and us e sab crera fr s prbe can be epressed as / / snce /. Subsun e ven quanes, e au awabe vaue f e e sep s deerned be. s /s[ W/.. / W/. ] -

14 aper Nuerca Meds n Hea nducn erefre, an e sep ess an s can be used sve s prbe. Fr cnvenence, we cse e e sep be = s. en e es Furer nuber beces /ss. fr = s. Usn e specfed na cndn as e sun a e = fr =, sweepn ru e equans abve w ve e sun a nervas f n. Usn a cpuer, e sun a e cener nde nde s deerned be.,.,.,.,.,.,., and. a,,,,,,, and n, respecve. nnun n s anner, s bserved a sead cndns are reaced n e edu afer abu urs fr wc e eperaure a e cener nde s. -

15 aper Nuerca Meds n Hea nducn -E A pan wndw ass na a a unfr eperaure s subjeced cnvecn n b sdes. e ransen fne dfference fruan f s prbe s be baned, and s be deerned w n w ae fr e f n e wndws cear up.e., fr e nner surface eperaure f e wndw ass reac F. Assupns Hea ransfer s ne-densna snce e wndw s are reave s cness. era cnducv s cnsan. Radan ea ransfer s nebe. Prperes e cnducv and dffusv are ven be =. Bu/.f F and. f /s. Anass e nda spacn s ven be =. n. en e nuber f ndes beces M L / =./.+ =. s prbe nvves unnwn nda eperaures, and us we need ave equans. Ndes and are nerr ndes, and us fr e we can use e enera epc fne dfference rean epressed as snce ere s n ea eneran. e fne dfference equan fr ndes and n e surfaces subjeced cnvecn s baned b appn an ener baance n e af vue eeen abu e nde, and an e drecn f a ea ransfers be wards e nde under cnsderan: Nde cnvecn: r Nde nerr: Nde nerr: Nde cnvecn: r were =./ f, =. Bu/.f F, =. Bu/.f F, =+*/F n secnds, =. Bu/.f F, and =F. e upper f e e sep s deerned fr e sab crera a requres a prar ceffcens be reaer an r equa zer. e ceffcen f s saer n s case, and us e sab crera fr s prbe can be epressed as / / snce /. Subsun e ven quanes, e au awabe e sep beces../f. s f /s[. Bu/.f. F./ /.Bu/.f. F] erefre, an e sep ess an. s can be used sve s prbe. Fr cnvenence, e us cse e e sep be = s. en e es Furer nuber beces. f / s s.. / f Subsun s vaue f and er ven quanes, e e needed fr e nner surface eperaure f e wndw ass reac F avd fn s deerned be never. s s because sead cndns are reaced n abu n, and e nner surface eperaure a a e s deerned be.f. erefre, e wndw w w be fed a a es. F Wndw ass -

16 aper Nuerca Meds n Hea nducn - - e fran f f n e ass surfaces f a car s be prevened b aacn eecrc ressance eaers e nner surfaces. e eperaure dsrbun ruu e ass n afer e srp eaers are urned n and as wen sead cndns are reaced are be deerned usn e epc ed. Assupns Hea ransfer ru e ass s ven be ransen and w-densna. era cnducv s cnsan. ere s ea eneran n a e nner surface, wc w be reaed as prescrbed ea fu. Prperes e cnducv and dffusv are ven be =. W/ and. /s. Anass e nda spacn s ven be =. c and = c. e epc fne dfference equans are deerned n e bass f e ener baance fr e ransen case epressed as Q G V A sdes eeen eeen We cnsder n ndes because f ser. Ne a we d n ave a square es n s case, and us we w ave re n ener baances ban e fne dfference equans. Usn ener baances, e fne dfference equans fr eac f e ndes are baned as fws: Nde : Nde : Nde : Nde : Nde : Nde : Nde : W Nde : Nde : Heaer W/ era ser ne. c c Ouer surface Gass Inner surface era ser ne

17 aper Nuerca Meds n Hea nducn - were =. W/., /. /s, = = - = W/., = W/., =., and =.. e upper f e e sep s deerned fr e sab crera a requres e ceffcen f n e epressn e prar ceffcen be reaer an r equa zer fr a ndes. e saes prar ceffcen n e equans abve s e ceffcen f n e epressn snce s epsed s cnvecn per un vue s can be verfed. e equan fr nde can be rearraned as erefre, e sab crera fr s prbe can be epressed as Subsun e ven quanes, e au awabe vaue f e e sep s deerned be r, s..... W/ W/ /. s erefre, an e sep ess an. s can be used sve s prbe. Fr cnvenence, we cse e e sep be = s. en e eperaure dsrbun ruu e ass n afer e srp eaers are urned n and wen sead cndns are reaced are deerned be fr e EES suns ds n: = -., = -., = -., = -., = -., = -., =., =., =. Sead-sae: = -., = -., = -., = -., = -., = -., =., =., =. Dscussn Sead peran cndns are reaced n abu n.

18 aper Nuerca Meds n Hea nducn - - e fran f f n e ass surfaces f a car s be prevened b aacn eecrc ressance eaers e nner surfaces. e eperaure dsrbun ruu e ass n afer e srp eaers are urned n and as wen sead cndns are reaced are be deerned usn e pc ed w a e sep f = n. Assupns Hea ransfer ru e ass s ven be ransen and w-densna. era cnducv s cnsan. ere s ea eneran n a e nner surface, wc w be reaed as prescrbed ea fu. Prperes e cnducv and dffusv are ven be =. W/ and. /s. Anass e nda spacn s ven be =. c and = c. e pc fne dfference equans are deerned n e bass f e ener baance fr e ransen case epressed as Q G V A sdes eeen + eeen We cnsder n ndes because f ser. Ne a we d n ave a square es n s case, and us we w ave re n ener baances ban e fne dfference equans. Usn ener baances, e fne dfference equans fr eac f e ndes are baned as fws: Nde : Nde : Nde : N: Nde : N: Nde : W Nde : Nde : Heaer W/ era ser ne. c c Ouer surface Gass Inner surface era ser ne

19 aper Nuerca Meds n Hea nducn were =. W/., /. /s, = = - = W/., = W/., =., and =.. an e sep be = n, e eperaure dsrbun ruu e ass n afer e srp eaers are urned n and wen sead cndns are reaced are deerned be fr e EES suns ds n: = -., = -., = -., = -., = -., = -., =., =., =. Sead-sae: = -., = -., = -., = -., = -., = -., =., =., =. Dscussn Sead peran cndns are reaced n abu n. -

20 aper Nuerca Meds n Hea nducn - e rf f a use na a a unfr eperaure s subjeced cnvecn and radan n b sdes. e eperaures f e nner and uer surfaces f e rf a a n e rnn as we as e averae rae f ea ransfer ru e rf durn a n are be deerned. Assupns Hea ransfer s ne-densna. era prperes, ea ransfer ceffcens, and e ndr and udr eperaures are cnsan. Radan ea ransfer s snfcan. Prperes e cnducv and dffusv are ven be =. W/. and. / s. e essv f b surfaces f e cncree rf s.. Anass e nda spacn s ven be =.. en e nuber f ndes beces M L / =./.+ = s. s prbe nvves unnwn nda eperaures, and us we need ave equans. Ndes,,, and are nvecn ncree Radan nerr ndes, and us fr e we can use e enera epc, rf fne dfference rean epressed as e fne dfference equans fr ndes and subjeced cnvecn and radan are baned fr an ener baance b an e drecn f a ea ransfers be wards e nde under cnsderan: Nde cnvecn: Nde nerr: Nde nerr: Nde nerr: Nde nerr: Nde cnvecn: wa s were =. W/., /. /s, =, wa = K, =, s = K, = W/., = W/., =., and = n. As, e es Furer nuber s. / s s.. Subsun s vaue f and er ven quanes, e nner and uer surface eperaures f e rf afer / = e seps are deerned be =. and = -.. b e averae eperaure f e nner surface f e rf can be aen AM., ave. en e averae rae f ea ss ru e rf a n beces Q A A ave s W/,W, ave s wa -.. Radan. - W/ K nvecn, [K. K ] -

21 aper Nuerca Meds n Hea nducn - A refrerar wse was are cnsruced f -c c ureane nsuan afuncns, and sps runnn fr. e eperaure nsde e refrerar a e end f s perd s be deerned. Assupns Hea ransfer s ne-densna snce e was are are reave er cness. era prperes, ea ransfer ceffcens, and e udr eperaure are cnsan. Radan ea ransfer s nebe. e eperaure f e cnens f e refrerar, ncudn e ar nsde, rses unfr durn s perd. e ca asperc pressure s a. e space ccuped b fd and e crner effecs are nebe. Hea ransfer ru e b surface f e refrerar s nebe. Prperes e cnducv and dffusv are ven be =. W/. and. / s. e averae specfc ea f Refrerar fd es s ven be. J/.. e specfc ea and wa dens f ar a a and are p =. J/. and =. / abe A-. Anass e nda spacn s ven be =.. en e nuber f ndes beces M L / =./.+ =. s prbe nvves unnwn nda eperaures, and us we need ave equans. Ndes and are nerr ndes, and us fr e we can use e enera epc fne dfference rean epressed as e fne dfference equans fr ndes and subjeced cnvecn and radan are baned fr an ener baance b an e drecn f a ea ransfers be wards e nde under cnsderan: Nde cnvecn: Nde nerr: Nde nerr: Nde cnvecn: were =. W/., /. /s, = = na, =, = W/., = W/., =., and = n. As, e es Furer nuber s. /s s.. e vue f e refrerar cav and e ass f ar nsde are V ar V. /.. Ener baance fr e ar space f e refrerar can be epressed as Nde refr.ar : r were A A A ar ar fd fd Subsun, eperaures f e refreraed space afer = e seps s deerned be n = =.. -

22 aper Nuerca Meds n Hea nducn - "!PROBLEM -" "GIVEN" _ns=. "[]" =. "[W/-]" apa=.e- "[^/s]" _= "[]" _= "[W/^-]" _= "[W/^-]" _nfn= "[]" _fd= "[]" _fd= "[J/-]" DELA=. "[]" DELA= "[s]" "e=* [s], paraeer be vared" "PROPERIES" r_ar=densar, =_, P=. _ar=par, =_*nverj/-, J/- "ANALYSIS" M=_ns/DELA+ "Nuber f ndes" au=apa*dela/dela^ R=/apa "R=r*" "e ecnque s sre e eperaures n e paraerc abe and recver e as d eperaures usn e varabe ROW. e frs rw cnans e na vaues s Sve abe us ben a rw. Use e DUPLIAE saeen reduce e nuber f equans a need be ped. un cnans e e, cun e vaue f [], cun, e vaue f [], ec., and cun e Rw." e=abevaue'abe ',Rw-,#e+DELA Dupcae =, _d[]=abevaue'abe ',Rw-,#[] end "Usn e epc fne dfference apprac, e s equans fr e s unnwn eperaures are deerned be" _*_nfn-_d[]+*_d[]-_d[]/dela=r*dela/*[]- _d[]/dela "Nde, cnvecn" []=au*_d[]+_d[]+-*au*_d[] "Nde " []=au*_d[]+_d[]+-*au*_d[] "Nde " _*_d[]-_d[]+*_d[]-_d[]/dela=r*dela/*[]- _d[]/dela "Nde, cnvecn" _*A_*_d[]-_d[]=_ar*_ar*[]-_d[]/DELA+_fd*_fd*[]- _d[]/dela "Nde, refr. ar" A_=*.-.*.-.+*.-.* *.-. _ar=r_ar*v_ar V_ar=.-.*.-.*.-. -

23 aper Nuerca Meds n Hea nducn e [s] [] [] [] [] [] Rw [].. e [s] -