Problems on transformer main dimensions and windings

Transcription

1 Probles_Trn_winding Probles on rnsforer in diensions nd windings. Deerine he in diensions of he core nd window for 500 ka, /400, 50Hz, Single phse core ype, oil iersed, self cooled rnsforer. Assue: Flux densiy. T, Curren densiy.75 A/, Window spce fcor 0., ol / urn 6.8, ype of core: Crucifor, heigh of he window ies window widh. Also clcule he nuber of urns nd cross-secionl re of he conducors used for he priry nd secondry windings. Since vol / urn E 4.44 φ f, Min or Muul flux φ f 4.44 x Wb φ Ne iron re of he leg or lib A i B Since for crucifor core A i 0.56d, dieer of he circuscribing circle d A i widh of he lrges sping 0.85d 0.85 x widh of he rnsforer 0.9 widh of he slles sping b0.5d 0.5 x Heigh of he yoke H y (.0 o.5) (sy) 0.9 ka. f δ A i B A w K w x x 50 x.75 x 0 6 x 0.06 x. x A w x 0. x 0 - Are of he window A w Since H w W w, A w H w W w W w Therefore, widh of he window W w 0.5 nd heigh of he window H w x Deils of he core Leg nd yoke secion (wih he ssupion Yoke is lso of crucifor ype) All diensions re in c Overll lengh of he rnsforer W w + d Overll heigh of he rnsforer H w + H y or x Widh or deph of he rnsforer 0.9 Nuber of priry urns T 9 E 6.8

2 Probles_Trn_winding Nuber of secondry urns T Priry curren I ka x 0 E x A Cross-secionl re of he priry winding conducor Secondry curren I ka x x A Cross-secionl re of he secondry winding conducor I δ I δ Deerine he in diensions of he lib core (i.e., phse, leg core ype rnsforer), he nuber of urns nd cross-secionl re of he conducors of 50 ka, 000/ 00, sr / del, phse, 50 Hz rnsforer. Assue: ol / urn, xiu flux densiy.5 T. Ne cross-secion of core 0.6 d, window spce fcor 0.7, window proporion :, curren densiy 50 A/c, ON cooled (ens oil iersed, self cooled or nurl cooled ) rnsforer hving ±.5% nd ± 5% pping on high volge winding E 0.05 Wb 4.44 f 4.44 x 50 φ A i B.5 φ Since A i 0.6 d, d A i Since A i 0.6 d corresponds o sepped core, 0.9d 0.9 x Widh or deph of he rnsforer 0.4 H y (.0 o.5).0 (sy) 0.4 ka. f δ A i B A w K w x x 50 x 50 x 0 4 x 0.04 x.5 x A w x 0.7 x 0 - A w 0.06 Hw Since window proporion is :, Hw W w nd A w W w W 0.06 w Therefore W w nd Hw x Deils of he core.4 Leg nd Yoke secion All diensions re in c Overll lengh of he rnsforer W w + d + x 4. x x c

3 Probles_Trn_winding Overll heigh of he rnsforer H w + H y or 4 + x c Widh or deph of he rnsforer.4 c [ wih +.5% pping, he secondry volge will be.05 ies he red secondry volge. To chieve his wih fixed nuber of secondry urns T, he volge / urn us be incresed or he nuber of priry urns conneced cross he supply us be reduced.] 00 Nuber of secondry urns T 00 E 000 / Nuber of priry urns for red volge T 577 E Nuber of priry urns for +.5% pping T x E required E wih pping 000 / 00 x x / for.5% pping 00 x x / for + 5% pping 00 x.05 x / for 5% pping 00 x 0.95 x Obviously priry winding will hve ppings 608 h urn, 59 nd urn, 577 h urn, 56 rd urn nd 550 h urn. ka x 0 50 x 0 priry curren / ph I x 000 / 8.4 A ph Cross-secionl re of he priry winding conducor I / δ 8.4 / c Secondry curren / ph I ka x 0 ph 50 x 0 x A Cross-secionl re of he secondry winding conducor I / δ 5.5 / c. Deerine he in diensions of he core, nuber of urns nd cross-secionl re of conducors of priry nd secondry of 5 ka, / 460, 50Hz, Single phse core ype disribuion rnsforer. Mxiu flux densiy in he core is.t, curren densiy 50 A/ c, Assue: crucifor core llowing 8% for he insulion beween linions. Yoke crosssecion s 5% greer hn h of he core. Window heigh ies window widh, Ne cross-secion of copper in he window is 0. ies he ne cross-secion of iron in he core, window spce fcor 0.. Drw ne skech o suible scle. [Noe: ) for crucifor core wih 0% insulion or K i 0.9, A i 0.56d. Wih 8% insulion or K i 0.9, A i 0.56d 0.9 x 0.57 d 0.9 ) Since he yoke cross-secionl re is differen fro he leg or core re, yoke cn considered o be recngulr in secion. Yoke re A y H y x K i ] A cu A w K w 0. A i. () ka. f δ A i B A w K w x 0-5. x 50 x 50 x 0 4 x A i x. x 0. A i x 0 - A i 5. x 50 x 50 x 0 x. x 0. x

4 Probles_Trn_winding 4 Since wih 8% insulion, A i 0.56 d x 0.9 / d, d Since he expression for he widh of he lrges sping is independen of he vlue of scking fcor, 0.85 d 0.85 x Widh or deph of he rnsforer 0. Since he yoke is recngulr in secion A y H y x K i.5 A i.5 Ai.5 x 0.04 Therefore H y 0. Ki 0.9 x Ai 0. x 0.04 Fro equion, A w 0.0 K 0. Since H w W w, A w H w W w W w 0.0 Therefore W w 0.0 w 0. nd H 0. x 0. w Deils of core Leg secion All diensions re in c T where E 4.44φ f 4.44 Ai Bf 4.44 x 0.04 x E T T 4 E 0.7 I I ka x 0 ka x 0 5 x 0 5 x A, 7.7 A, I δ I δ c.087 c 4.Deerine he in diensions of he core nd he nuber of urns in he priry nd secondry windings of phse, 50 Hz, /( ) in seps of ½ %, del / sr rnsforer. The vol / urn 8 nd he xiu flux densiies in he lib nd yoke re.5 T nd. T respecively. Assue four sepped core. Window diensions 50 c x c.

5 Probles_Trn_winding 5 E 8 φ 0.06 Wb 4.44 f 4.44 x 50 φ A i B.5 Since for 4 sepped core A i 0.6d, d 0.9 d 0.9 x Widh or deph of he rnsforer 0.9 φ A y B. y Since he yoke re is differen fro he leg re, yoke cn be considered o be of recngulr secion. Therefore A y 0.0 H y 0.9, wih he ssupion h K i 0.9 Ki 0.9 x 0.9 Since he window diensions re given, Lengh of he rnsforer W w + d + x 0. + x Overll heigh of he rnsforer H w + H y x Widh or deph of he rnsforer / T (for xiu volge of 440) 8 T for xiu secondry volge of 440 x T x / T for iniu secondry volge of 400 x / Since volge is o be vried ½ %, fro (400 o 440), he pings re o be provided o ge he following volges 400,.05 x ,.05 x ,.075 x nd.0 x Generlly he h winding is due o nuber of coils conneced in series. ou of he ny coils of he h winding, one coil cn be de o hve urns wih pping fciliy every 0 urns o provide volge vriion of ½ % on he secondry side 5.For he preliinry design of 00kA, 50Hz, 000/00, phse, del / sr, core ype disribuion rnsforer, deerine he diensions of he core nd window, nuber of urns nd cross-secionl re of HT nd LT windings. Assue : Mxiu vlue of flux densiy.t, curren densiy.5 A/ window spce fco 0..Use crucifor core cross-secion for which iron re A i 0.56d nd he xiu lii hickness is 0.85d, where d is he dieer of he circuscribing circle vol / urn 0.6 ka, overll widh overll heigh. [NOTE: since overll widh overll heigh ie., (W w + d + ) (H w + H y or ). his condiion when subsiued in A w H w W w leds o qudric equion. By solving he se he vlues of H w W w cn be obined.] 6. Deerine he in diensions nd winding deils for 5 ka, 000/400, 50Hz, Single phse shell ype rnsforer wih he following d. ol / urn., flux densiy.0 T, curren densiy. A/, window spce fcor 0.. Drw diensioned skech of he gneic circui. Soluion: b( o ) 7.5

6 Probles_Trn_winding 6 E. φ 0.05 Wb 4.44 f 4.44 x 50 Since φ is esblished in he Cenrl leg φ Cross-secionl re of he cenrl leg A i B.0 If recngulr secion core is ssued hen A i x K i b x K i x ( o ) If he widh of he rnsforer b is ssued o be.5 ies nd K i 0.9, hen he widh of he Ai 0.05 cenrl leg 0.5 (.5) K.5 x 0.9 i Widh or deph of he rnsforer b.5 x.5 x Heigh of he yoke H y 0.5 / ka. f δ A i B A w K w x 0-5. x 50 x. x 0 6 x 0.05 x.0 x A w x 0. x 0 - A w 0.0 [Since he window proporion or vlue for H w / W w is no given, i hs o be ssued] Since H w /W w lies beween.5 nd.5, le i be.0 Therefore A w H w W w W w 0.0 W w nd Hw x Winding deils: T 78 T 6 E. E. I ka x 0 5 x A, I δ ka x 0 5 x 0 I.5 I.5 A, δ. Clcule he core nd window re nd ke n esie of he copper nd iron required for 5 ka, 000 / 400, 50 Hz single phse shell ype rnsforer fro he following d. Flux densiy. T, curren densiy. A/, vol / urn., window spce fcor 0., specific grviy of copper nd iron re 8.9 nd 7.8 respecively. The core is recngulr nd he spings re ll 7 c wide. [Noe: A shell ype rnsforer cn be regrded s wo single phse core ype rnsforers plced one beside he oher.] E. φ φ 0.05 Wb, A i f 4.44 x 50 B. ka. f δ A i B A w K w x 0-5. x 50 x. x 0 6 x x. x A w x 0. x 0 - A w 0.0

7 Probles_Trn_winding 7 Single phse shell ype Trnsforer Upper yoke reoved Skech showing he diensions of L & H windings ogeher A 7 P Q 7 S R Shell ype rnsforer due o wo single phse core ype rnsforers. If he whole window is ssued o be filled wih boh L & H windings, hen he heigh of he winding is H w nd widh of he L & H windings ogeher is W w. Weigh of copper olue of copper x densiy of copper Are of copper in he winding rrngeen x en lengh of copper in he windings x densiy of copper A w K w x lengh wxyzw x densiy of copper Men lengh wxyzw (wx + xy) [ ( + W w ) + (b + W w )] Since he spings re ll 7 c wide, 7c & 4 c Ai b 0.6 K 0.9 x 0.4 i 7 7 Since H w / W w lies beween.5 nd.5, le i be.0 Therefore A w H w W w W w 0.0.

8 Probles_Trn_winding 8 Thus W w nd Hw x 0 0. wxyzw [ (4 + 0) + (6 + 0)] 40 c Widh of copper 0.0 x 0 4 x 0. x 40 x 8.9 x kg Weigh of iron x volue of he porion A x densiy of iron A x i x Men core lengh PQRSP x densiy of iron x x 0 4 x [ (0+7) + (0 + 7)] x 7.8 x 0-79 kg 7. Deerine he in diensions of 50kA, phse, 50Hz, Sr/del, 000 / 00 core ype disribuion rnsforer. Assue disnce beween core cenres is wice he widh of he core. For phse core ype disribuion rnsforer E 0.45 ka E 8.4 φ φ 0.08 Wb, A i 4.44 f 4.44 x 50 B Since he flux densiy B in he lib lies beween (. &.4) T, le i be. T Therefore A i. 0.0 If sepped core is used hen A i 0.6 d. Therefore d 0.9d 0.9 x Widh or deph of he rnsforer 0. H y (.0 o.5) 0. ka. f δ A B A w K w x If nurl cooling is considered (upo 5000 ka, nurl cooling cn be used), hen curren densiy lies beween.0 nd. A/. Le i be.5 A/. 0 0 K w Kvhv x 50 x.5 x 0 6 x 0.0 x. x A w x 0.4 x 0 - A w 0.09 Aw 0.09 Since W w + d, W w x nd H w Ww 0.9 Overll lengh of he rnsforer W w + d x Overll heigh of he rnsforer H w + H y x Widh or deph of he rnsforer Probles on No lod curren. Clcule he no lod curren nd power fcor of 00/0, 50Hz, single phse core ype rnsforer wih he following d. Men lengh of he gneic ph 00 c, gross re of iron core 50 c, specific iron loss 50 Hz nd. T. W / kg pere urns / c for rnsforer seel.t 6.. The effec of join is equivlen o

9 Probles_Trn_winding 9 Soluion: n ir gp of.0 in he gneic circui. Densiy of iron 7.5 grs / cc. Iron fcor 0.9 No-lod curren I 0 I + I c Core loss Core loss coponen of he no lod curren I c Core loss loss / kg x volue of he core x densiy of iron loss / kg x ne iron re x en lengh of he core or gneic ph x densiy of iron. x 0.9 x 50 x 00 x 7.5 x W Therefore I c 0.98 A 00 AT Mgneising curren I + iron lg B T AT iron AT/c x en lengh of he gneic ph in c 6. x T where E 4.44 φ f E 00 T x x 0 I x A i B f 4.44 (K i A g ) B f 4.44 x 0.9 x 50 x 0-4 x. x x..98 A I A Ic 0.98 No-lod power fcor cos φ 0 0. I Clcule he no-lod curren of 0/0, ka, 50Hz, Single phse rnsforer wih he following d unifor cross-secionl re of he core 5 c, effecive gneic core lengh 0.4, core weigh 8 kg, xiu flux densiy. T, gneizing force 00 AT/, specific core loss.0 W/kg I 0 I c I + I c Coreloss loss / kg x weigh of core in kg x A 0 ATfor iron lg B ATfor iron I T T s here is no d bou he effec of joins or l g is ssued o be zero AT for iron AT / x Effecive gneic core lengh 00 x

10 Probles_Trn_winding 0 T where E 4.44 φ f E 4.44 A i B f 4.44 (K i A g ) B f 4.44 x 0.9 x 5 x 0-4 x. x 50 if K i T I I 0 80 x A A. A 00 ka, /400, del / sr, 50Hz, phse core ype rnsforer hs he following d. Nuber of urns/ph on H winding 80, ne iron re of ech lib nd yoke 60 nd 97 c, Men lengh of he flux ph in ech lib nd yoke 55 c nd 86.9 c. For he rnsforer seel Flux densiy in esl AT/ Coreloss / kg Deerine he no lod curren 86.9 c 60 c 55 c Soluion: I 0 I c Coreloss / ph ph I + I c loss in legs + loss in yokes Coreloss / ph Loss in legs x loss in one leg x loss / kg in leg x volue of he leg i.e, (A i x en lengh of he flux Ph in leg) x densiy of iron B φ A i where φ 4.44 f T Core nd Yoke deils 4.44 x 50 x c 0.06 Wb

11 Probles_Trn_winding 0.06 B.8 T x 0 A.8 T, loss / kg in he leg.7 s obined fro he loss/kg grph drwn o scle. Loss in legs x.7 x 60 x 55 x 7.55 x W wih he ssupion h densiy of iron is 7.5 grs / cc Loss in yokes x loss in one yoke x loss/kg in yoke x volue of he yoke i.e, (A y x en lengh of he flux ph in he yoke) x densiy of iron AT/.8T Loss/kg AT/ 00 Loss/kg φ B y 0.06.T - 4 A y 97 x 0 A.T, loss/kg in yoke.9 Loss in yokes x.9 x 97 x 86.9 x 7.55 x W Coreloss / ph 58.7W 58.7 I c 0.08A (ATfor iron lg B) / ph ATfor iron / ph I s here is no d bou l g T T ATs for legs + ATs for yokes AT for iron / ph x AT/ for leg x en legnh of he flux ph in he leg + x AT/ x en lengh of he flux ph in he yoke A B.8T, AT/ for he leg 00 nd A B y.t, AT/ for he yoke 00 s obined fro he gneizion curve drwn o scle. x 00 x x 00 x Therefore AT for iron / ph I 0.76A x 80 I A 4. A, 50Hz single phse rnsforer hs core of shee seel. The ne iron cross secionl re is.6 x 0 -, he en lengh is. nd here re four lp joins. Ech lp join kes ¼ ies s uch recive f s is required per eer of core. If he xiu flux densiy s for yoke

12 Probles_Trn_winding.T, find he cive nd recive coponens of he no lod curren. Assue n pliude fcor of.5 nd f /, specific loss.76 W/kg, specific grviy of ples 7.5 Coreloss Acive coponen of no lod curren I c Coreloss specific core loss x volue of core x densiy.76 x.6 x 0 - x. x 7.5 x W 665. I c 0.A AT Recive coponen of he no-lod curren I Mxiu vlue pliude fcor.5 rs vlue AT iron x AT for 4 lp joins l g B 4 x x 4 iron l.5 T T φ f 4.44 A B f 4.44 x.6 x 0 x. x 50 i g B s pek, cres or I x A 5. A single phse 400, 50Hz, rnsforer is buil fro spings hving relive perebiliy of 000. The lengh of he flux ph.5, A i.5 x 0 -, T 800. Esie he no lod curren. Iron loss he working flux densiy is.6 W/kg. Iron weighs 7.8 x 0 kg/, iron fcor 0.9 [Hin: B µ µ AT H x flux ph lengh 0 r H, iron Probles on Lekge recnce. Clcule he percenge recnce of 5 ka, 000/440, sr-del, 50Hz rnsforer wih cylindricl coils of equl lengh, given he following. Heigh of he coils 5c, hickness of L 4c, hickness of H c, en dieer of boh priry nd secondry ogeher 5 c, insulion beween H & L 0.5c, vol / urn, rnsforer is of core ype I Xp Percenge recnce ε x x 00 ka x 0 5 x 0 I 0.8A x 000/ X p π f T p L µ 0 L c bp bs / T p T 76 E L Men lengh of urn of boh priry nd secondry ogeher π x en dieer of boh priry nd secondry ogeher π x c X p π x 50 x (76) x 4π x x Ω x. ε x x /

13 Probles_Trn_winding. Deerine he equivlen recnce of rnsforer referred o he priry fro he following d. Lengh of he n urn of priry nd secondry 0 c nd 00 c nuber of priry nd secondry urns 500 nd 0. Rdil widh of boh windings.5 c, widh of duc beween wo windings.4 c, heigh of coils 60 c. b L p bs X p f Tp 0 Lc π µ + + L Men lengh of urn of boh priry nd secondry ogeher π x (. +.0) /.46 π x 50 x 500 x 4π x x Ω 0.6 OR X p x p + x ' s x p + x s (T p / T s ) L b p p xp f Tp 0 Lc π µ + π x 50 x 500 x 4π x x +.0Ω 0.6 Ls bs x s π f Ts µ 0 + Lc π x 50 x 0 x 4π x x x 0 Ω 0.6 X p x x 5.55Ω 0.Clcule he percenge regulion full lod 0.8pf lg for 00 ka, /440, del-sr, phse,50hz, core ype rnsforer hving cylindricl coils of equl lengh wih he following d. Heigh of coils 4.7 c, hickness of H coil.6 c, hickness of L coil.5 c, insulion beween L & H coils.4 c, Men dieer of he coils 7 c, vol/urns 7.9, full lod copper loss.75 Kw I R p Cosφ + I XpSinφ Percenge regulion x 00 ka x 0 00 x 0 I 5.5A x Since full lod copper loss I R.75 x 0 p, R p 5.45 Ω x (5.5) b L p bs X p f Tp 0 Lc π µ + + T p T 86 E 7.9 L Men lengh of urn of boh priry & secondry ogeher π x c

14 Probles_Trn_winding 4 X p π x 50 x (86) x 4π x x Ω x 5.45 x x.77 x 0.6 Percenge regulion x A 750 ka, /45, 50Hz, phse, del sr, core ype rnsforer hs he following d. Widh of L winding c, widh of H winding.5 c, widh of duc nd insulion beween L & H.0 c, heigh of windings 40 c, lengh of en urn 50 c, vol / urn 0. Esie he lekge recnce of he rnsforer. Also esie he per uni regulion 0.8 pf lg, if xiu efficiency of he rnsforer is 98% nd occurs 85 % of full lod. b L p bs X p f Tp 0 Lc π µ + + T p T 660 E 0 X p π x 50 x (660) x 4π x x 0.4 I R p Cosφ + I XpSinφ Per uni regulion Ω ka x x 0 I 7.88A x Since copper loss iron loss xiu efficiency, Losses W Cu + W i W Cu x (0.85 I ) -η R p oupu η x 750 x 0 x.0 Therefore R p Ω x x 7.88 x x.0 x x 8. x 0.6 Per uni regulion L b S H b P 6 5.Esie he percenge regulion full lod 0.8 pf lg for 00 ka, /400, del-sr conneced core ype rnsforer wih he following d. Dieer Cross-secionl re of inside ouside he conducor H winding 9.5 c 6 c 5.4 L winding c 6.5 c 70 Lengh of coils 50 c, vol/urn 8, Resisiviy 0.0 Ω / / I R p Cosφ + I XpSinφ Soluion: Percenge regulion x 00 ka x 0 00 x 0 I 5.5A x R p r p + r s r p + r s (T p / T s )

15 Probles_Trn_winding 5 ρ Lp Resisnce of he priry r p Tp ( ) L p π x en dieer of priry i.e., H winding π 0.9 c (0.0 x.09 x 85) T p 85. Therefore, r p. Ω E ρ L s Resisnce of he secondry r s Ts (6.5 + ) L s π x en dieer of secondry i.e., L winding π 76. c 400 / ( 0.0 x 0.76 x 9) - T s 9. Therefore, r s 6.6 x 0 Ω E 8 70 R p x 0-85 x 8.66 Ω 9 b L p bs X p f Tp 0 Lc π µ + + L Men lengh of urn of boh priry & secondry ogeher π x en dieer of boh coils ( + 6) π x 9. c or cn be ken s 89.6 c widh of priry or H winding b p.5 c 6.5 widh of secondry or L winding b s.5 c widh of insulion or duc or boh beween L & H i.e, c X p π x 50 x 85 x 4π x x Ω x 8.66 x x 6. x 0.6 Percenge regulion x Design of cooling nk nd ubes. Design suible cooling nk wih cooling ubes for 500 ka, /440, 50Hz, phse rnsforer wih he following d. Diensions of he rnsforer re 00 c heigh, 96 c lengh nd 47 c bredh. Tol losses 7 kw. Allowble eperure rise for he nk wlls is 5 0 C. Tubes of 5 c dieer re o be used. Deerine he nuber of ubes required nd heir possible rrngeen. Tnk heigh H rnsforer heigh + clernce of 0 o 60 c c Tnk lengh L rnsforer lengh + clernce of 0 o 0 c c widh or bredh of he nk W rnsforer widh or bredh + clernce of 0 o 0 c clernce of c Losses.5 S θ A θ

16 Probles_Trn_winding 6 Dissiping surfce of he nk (neglecing he op nd boo surfces) S H (L + W ) x.5 ( ) x 5. x A x 5 Are of ll he ubes A 5.6 Dissiping re of ech ube π x dieer of he ube x verge heigh or lengh of he ube π x 0.05 x 0.9 x.5 0. A & is no possible. Le i be 74. Nuber of ubes n 0. If he ubes re plced 7.5 c pr fro cenre o cenre, hen he nuber of ubes h cn be 0 60 provided long 0 c nd 60 c sides re 5 nd 8 respecively Therefore nuber of ubes h cn be provided in one row ll-round (5 + 8) 46. Since here re 74 ubes, ubes re o be rrnged in nd row lso. If 46 ore ubes re provided in second row, hen ol nuber of ubes provided will be 9 nd is uch ore hn 74. Wih & 6 ubes long 00 c & 60 c sides s shown, ol nuber of ubes provided will be ( + 6) 76 hough 74 re only required. x ubes in rows 0 c 60 c 0 ubes in rows Pln showing he rrngeen of ubes. A phse 5 MA, /6.6 k, 50 Hz, sr/del core ype oil iersed nurl cooled rnsforer gve he following resuls during he design clculions. Lengh of core + ies heigh of yoke 50 c, cenre o cenre disnce of cores 80 c, ouside dieer of he H winding 78.5 c, iron losses 6 kw, copper loss in L nd H windings 4.5 kw & 57.5 kw respecively. Clcule he in diensions of he nk, eperure rise of he rnsforer wihou cooling ubes, nd nuber of ubes for eperure rise no o exceed 50 0 C. Coen upon wheher ubes cn be used in prcicl cse for such rnsforer. If no sugges he chnge. H 50 + clernce of (0 o 60) c c L x clernce of (0 o 0) c c W clernce of (0 o 0) c c Wihou ubes, losses.5 S θ

17 Probles_Trn_winding 7 S H (L + W ) x ( ) 0.4 ( )0 0 θ 490 C.5 x 0.4 wih cooling ubes, losses.5 S θ A θ ( )0 -.5 x 0.4 x 50 A x 50 Wih 5 c dieer ubes π x 0.05 x 0.9 x n Tn 50 H 78.5 H W L All diensions re in cs. If ubes re provided 7.5 c pr fro cenre o cenre, hen he nuber of ubes h cn be provided long 50 c nd 90 c sides re 50 / 7.5 nd 90 / 7.5 respecively. Nuber of ubes in one row ( + ) 90. Therefore nuber of rows required 60 / As he nuber ubes nd rows increses, he dissipion will no proporionely increse. Also i is difficul o ccoode lrge nuber of ubes on he sides of he nk. In such cses exernl rdior nks re preferble & econoicl.. The nk of 50 ka nurl cooled rnsforer is 55 c in heigh nd 65 c x 85 c in pln. Find he nuber of recngulr ubes of cross secion 0 c x.5 c. Assue iproveen in convecion due o siphoning cion of he ubes s 40%. Teperure rise 40 0 C. Neglec op nd boo surfces of he nk s regrds cooling. Full lod loss is. kw. Loss.5 S θ +.4 x 6.5 A θ 00.5 x [ x.55 ( ) ] x x 6.5 x A x 40 A 5.4 dissiping perieer of he ube x verge heigh of he ube (0 +.5) x 0 - x 0.9 x

18 Probles_Trn_winding 8 A 5.4 n If he ubes re provided 5 c pr (fro cenre o cenre of he ubes) hen he nuber of 85 ubes h cn be provided long 85 c side re 7. Wih 6 ubes on ech side of 85 5 c nk lengh, nuber of ubes provided x 6 7, s required. 85 Heder Tubes spced 5 c pr