حل تحليلي لتوصيل الحرارة المتغير مع الزمن خلال مادة كروية مجوفة عازلة للحرارة ذات توصيل حراري متغير مع درجة الحرارة
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- Junior Evans
- 5 years ago
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1 Nu Vlu Jauay 4 Jual f Egg Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy D Mshaal Adula Adula LuMhaal Egg Dpa Cllg f Egg Al-Musasyah Uvsy Baghdad Ia dshal4@gal ABSUC h -dsal sphal da -la paal dffal ua f as ha du hugh a hllw sphal hal sula aal f a hal duvy pau dpd ppy ppsd y a avalal pal fu s slvd aalyally usg Khhff s asfa I s assud ha hs sulag aal s ally a a uf pau h s suddly sujd a s adus wh a sp hag pau Fu hal sula aals w sld A dal aalyal slu was ahvd wh pag h suls f pau dsu wh avalal aalyal slu f h sa fu as suds ha assu a sa hal duvy I s fud ha h haass f h hal sula aal ad h pssu valu w s pals hav a aj ff h a f ha asf ad pau pfl KEYWODS: Nla dffal ua aalyal slu hal duvy as Khhff s asfa حل تحليلي لتوصيل الحرارة المتغير مع الزمن خلال مادة كروية مجوفة عازلة للحرارة ذات توصيل حراري متغير مع درجة الحرارة د مشعل عبد الا مير عبد الكريم مدرس في قسم الهندسة الميكانيكية الجامعة المستنصرية / كلية الهندسة الخلاصة تم حل المعادلة التفاضلية الغير خطية الا حادية البعد ذو الا حداثيات الكروية لانتقال الحرارة المتغير مع الزمن خلال مادة كروية مجوفة عازلة للحرارة ذات خاصية توصيل حراري متغير مع درجة الحرارة ما خوذة من معادلة مختبريه متوفرة باستخدام تحويل كرشوف تم افتراض ا ن هذه المادة العازلة كانت في البداية بدرجة حرارة منتظمة وثابتة ثم تعرضت ا لى تغير مفاجي في درجة الحرارة وبقيمة ثابتة عند نصف قطرها الداخلي تم اختيار ا ربعة مواد عازلة مختلفة تم التوصل ا لى حل تحليلي مطابق عند المقارنة مع نتاي ج الحل التحليلي لتوزيع درجات الحرارة للحالات الا ربعة بافتراض ا ن المادة العازلة للحرارة ذو خاصية توصيل حراري ثابتة ولا تتغير مع درجة الحرارة تم استنتاج ا ن خواص المادة العازلة للحرارة وقيمة الضغط بين جزيي اتها له تا ثير مباشر على مقدار كمية الحرارة المنتقلة وتوزيع درجات الحرارة الكلمات الري يسية: معادلة تفاضلية غير خطية حل تحليلي توصيل حراري متغير مع الزمن تحويل كرشوف 78
2 Mshaal Adula Adula INODUCION h haass f h hal sulag aals ha a usd a spaa plas sag as asf ls ad asp vssls f yg luds ad lufd hydas aff h pfa f hs applas Ms f hs hal sulas pa ud asph du vauu pssu ad us h Pl a ls gaulad aal f vla glass g had a 85-9 C vapz h hgh wa ha s appd s suu ad allwg s vlu pus ad xpadd up 7 6 s s gal vlu al fs h f f shlls as Kpsh ad Bugs 96 Kaga 969 ad Vsh ad Gl 95 F spf applas wh ly a sall spa s avalal f hal sula a sys f ullayd fls s usd a hgh vauu I s pfd h fld f asf ls f lud hydg ad lud hlu as wll as ps h spa hlgy ad h fld f physal as xpal sah Hffa 6 A ppy f all yg hal sulag aals s ha pas ud hgh pau df w asph a ad yg flud paus hf fllg sd a vauud la gh aula spa spaag h asph f yg flud vssls s ssay avd h dp s ffy du h pa ad fz f wa vap ad a dxd h sudd fllg f a py yg lud sag a ally a asph pau wh a yg lud a s saua pau wll a a sudd hgh pau dff w h als f h aula spa ag h hal sulag aal hs hgh pau dff s hd h dpd f hal duvy f h hal sula aal s pau I add wll a a pal f h vapa f yg lud du h as ha asf Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy 79 sd h yg lud sag a hs gy lss s f a ga s spally wh h sz f yg lud sag a s lavly g Zvv al hav usd h PAK- sfwa paag whh s asd h f l hd usg h Gal appah slv h -la as w-dsal ha du hugh a sula wall f a f aspa f lud aluu h jv was pz ud a uday ds h hss f h sula aal whh s hal pps s a pau dpd Sgh Ja ad zwa-udd 8 psd a aalyal dul-ss slu f as ha du pla das -D yldal f ul-lay da h adal d wh spaally -uf u dpd vlu ha sus Ihgus uday ds f h hd d a appld h d ppdula h lays Oly hgus uday ds f h fs sd d a applal θ sa sufas Ja Sgh ad zwa-udd psd a aalyal ss slu f as uday-valu pl f ha du θ sphal das h ppsd slu s applal sphal pa-sphal ullay gs whh pau ds dpd up h φ d suh as: sphal hsph sphal wdg full sph Spaally -uf ly ad θ -dpd dpd vlu ha sus ay ps h lays Ihgus dpd θ -dpd uday ds f h fs sd hd d ay appld h ad u adal udas ad ly hgus uday ds f h fs sd d ay appld h θ -d uday sufas
3 Nu Vlu Jauay 4 Jual f Egg A Kayha ad Nuz hav vsgad aalyally h usady ha du ps f wdd yldal shap laas hs slu s vald f h s galzd uday ds ha h ffs f du v ad ada h sd ad usd h yldal ps laas h Lapla asfa has usd hag h pl da f fuy A apppa Fu asfa has dvd usg h Su-Luvll h Du h dffuly f applyg h vs Lapla asfa h Mph fu hd s ulzd fd h as pau dsu laa I hs pap h -dsal sphal da -la paal dffal ua f as ha du hugh a hllw sphal hal sula aal f a hal duvy pau dpd ppy ppsd y a avalal pal fu a Hffa 6 s slvd aalyally usg Khhff s asfa hs sulag aal s ally a a uf pau h s suddly sujd a s al adus wh a sa pau < Fu hal sula aals w sld Hffa 6 ah f usd adus f h fs s Pl f hss 5 wh a haas a pal da f d 5 ad dsy f 5 ρ 64g / a Pa asph pssu h sd s Pl f hss wh a haas a pal da f d 5 ad dsy f ρ 5g / a a gas pssu Pa h hd s Mglass sphs f hss wh a haas a pal da f d ad dsy f 5g / Pa ρ a a gas pssu h fuh s f Fglass as f hss wh a a f da f d 4µ ad dsy f ρ 4g / a a gas pssu Pa valda h suls h pau dsu wll pad wh a avalal aalyal slu f h sa fu as suds ha assu a sa hal duvy A suy al wll ps h gal aalyal slu f h hsy f pau pfls ad ha asf as f ay sz ad yp f hal sula aal ha s sujd a wh a sa pau < SAEMEN OF HE POBLEM Csd a sphal sag a f lufd yg flud s hally sulad wh a hllw sphal sup sulag aal f pau dpd hal duvy ppsd y a avalal pal fu a ad f sd adus ad usd hs sulag aal s h wh a sa pau < as shw Fg I s ud fd h as pau dsu f h sulag aal ad h a f ha asf adus ally a a uf pau s suddly sujd a ANALYICAL SOLUION slv hs pl h fllwg assups a sdd: h pau s a fu f ly as O-dsal slu ad ha asf θ ad φ ds h pau dpda hal duvy f h sulag aal s ppsd y a avalal pal a fu 8
4 Mshaal Adula Adula h a spf ha apay C ad h dsy ρ f h sulag aal a pau dpd pps 4 h al pau f h sulag aal s sa 5 h sulag aal s suddly wh a sa sujd a pau ad hld a s al pau valu sufa a a s usd 6 N v ada ha asf a h udas 7 N al ha ga S all f h hal pps f h sulag aal a pau dpd xp f h hal duvy whh s a pau dpd ppy ad h s ha ga ad v ada ha asf a h udas hf h sphal das -dsal -la as ha du paal dffal ua wh s al ad Dhl uday d a gv as fllws: ρc Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy Susug sys ad aagg ylds; ψ ρc ψ ψ ψ ψ ψ ψ ψ µ d d ψ ψ µ ψ hgz sys assu; ψ β ψ 4 Susu 4 sys ad aagg ylds; β ρc β β µ β β 5 la h sys 5 assu; laz h -la paal dffal ua sys a d Khhff s asfa ada h z lw l f h aslu pau sal as shw Fg s usd as fllws: θ β 6 Susu 6 sys 5 ad aagg ylds; ψ d 8
5 Jual f Egg Vlu Jauay 4 Nu 8 θ µ θ θ θ θ 7 d C C d C µ ρ slv sys 7 assu h fllwg: θ θ θ 8 θ 9 Susu h uday ds f sys 7 9 ad aagg ylds; µ θ Assu; τ θ Susug sys 7 ad usg h hd f spaa f vaals h aagg ylds; λ λ s s λ τ Susu ad 8 ylds; [ ] λ λ λ µ θ s s 4 Susu h uday d f sys 7 4 ad aagg ylds; [ ] s s λ λ λ µ θ 5 λ 6 s µ 7 Susu 6 ad 7 5 ylds; s µ θ S; ψ ψ θ β s µ ψ ψ Assu;
6 Mshaal Adula Adula Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy 8 s φ s d d d 8 alz 8 assu h fllwg: F 9 H susug 9 8 ad aag ylds h gal aalyal ls f slu f usady pau dsu hugh h sphal hal sula aal as fllws; s F d d d h usady ha asf hugh h sphal hal sula aal s gv as: A 4 A Dffag 8 ad aagg ylds: s s d Susu ad ad aag ylds: s s 4 d 4
7 Jual f Egg Vlu Jauay 4 Nu 84 alz 4 susug 9 4 ad aag ylds: F d s s 4 5 Ad h ha asf a h sufa f h hal sula aal s gv as: 4 F d h gal aalyal ls f slu f usady ha asf hugh h sphal hal sula aal s gv as fllws: s s F F Cas sudy : pau pfl: Susu h valu f ad aagg ylds; s F Ha asf: Susu h valu f 5 ad aagg ylds; F s s 4 Cas sudy : a pau pfl: Susu h valu f a ad aagg ylds; η a a a a Wh: s F η 6 slv 6 assu; a g [ ] [ ] g g g g f η 7 h f 7 s fud usg h appxa ual av Nw Mhd Gald 989; d dg d df f
8 Mshaal Adula Adula Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy w w ld ld f f ld ld [ g g ] η[ g g ] ld ld Ha asf: Susu h valu f a 5 ad aagg ylds; 4 [ g g ] s s F 4 HEMAL CONDUCIVIY h dpd f hal duvy pau s suggsd y h pal fu a Hffa 6 h valus f a f h fu sld hal sula aals a gv al hs pal fu s vald a pau ag f 77 4 K h hal duvy f h fs sula aal 5 Pl a a Pa asph pssu s laly dpd pau Pl Isu hal Daa Sh 97 I h laus Chsas ad Hllgwh 958 ad Chsas Hllgwh ad Mash 959 asus f h hal duvy f f Fglass as a pulshd hs aal sss f fs yp AA f Ows-Cg Fglass Cpa h hav f h hal duvy ad s a valu f ah f hs hal sulag aals f a pau ag 77 K s shw Fg f 5 SPECIFIC HEA CAPACIY Eah f h fu sld hal sula aals s gally ad f Quaz glass hf h pau dpd f spf ha apay f Quaz glass f a pau ag f 77 K s gv al Cu ad Gw 96 I d valua h a valu f spf ha apay C f Quaz glass s la wh pau s psd usg a 4 h Dg plyal f as shw al ad s pld wh s a valu Fg 4 6 HEMAL DIFFUSIVIY h hav f hal dffusvy ad s a valu f ah f h fu sld hal sula aals f a pau ag f 77 K s shw Fg 5 7 ESULS AND DISCUSSION Csd fu py sphal sag as f lud g f sa Eah f hs as s hally sulad wh a hllw sphal sup sulag aal f usd adus ad ally a K h fs hal sula aal s Pl f hss 5 wh a haas a pal da f d 5 ad dsy f 5 ρ 64g / a Pa asph pssu h sd s Pl f hss wh a haas a pal da f d 5 ad dsy f ρ 5g / a a gas pssu Pa h hd s Mglass sphs f hss wh a haas a pal da f d ad dsy f ρ 5g / a a gas pssu Pa h fuh s f Fglass as f hss wh a a f d 4µ ad dsy f da f 85
9 Nu Vlu Jauay 4 Jual f Egg 4g / ρ a a gas pssu Pa h hal duvy f h fu sld hal sula aals s pau dpd ad s ppsd y a avalal pal fu a Hffa 6 h valus f a a gv al h ah f hs as s suddly flld wh sauad lud g a 77 K hf ah f h fu sld hal sula aals s sujd a wh a sa pau f 77 K Fg 6 shws h pau pfls f ah f h fu sld hal sula aals f w as suds h fs sds a sa a valu f hal duvy ag K f h pau 77 h gal aalyal ls f slu f h fs as sudy s dal h slu f Caslaw ad Jag 959 usg h sa assups hf h valda f h aalyal slu s aplshd pfly h sd as sudy s f a pau dpd hal duvy ppsd y a avalal pal fu a Hffa 6 Eah pfl f h sd as sudy was vgd af a axu f 5 as f a pau sdual valu f 6 C al 4 shws h suy f h ps w aalyal slus f h as suds Fg 7 shws h ha asf pfls f ah f h fu sld hal sula aals I s la ha h hal sula aal ha has h lws valu f hal duvy has h lws ha asf valu al 4 shws h suy f h ps w aalyal slus F h Fg 6 ad 7 s la ha h haass f h hal sula aal ad h pssu valu w s pals hav a aj ff h a f ha asf ad suly h pau pfl F sa h da ha asf d wh hsg 5 Pl a Pa asph pssu s y ha du f h sal gas w h pals whas h ha asf y ada s glgl Wh h pssu wh a hal sula aal s lwd a valu h pag f ha asf y ha du f h sal gas w h pals s glgly sall wh pad wh h pag ha asf y ada ad du v h ul aal h gas pssu a whh hs s ahd dpds h haas da f h hal sula aal F Pl wh a haas a pal da f d 5 a gas pssu f Pa s suff f Mglass sphs wh a haas a pal da f d ad f f Fglass wh a a f da f d 4µ s Pa spvly Fgus 8 ad 9 shws h hsy f pau pfls ad a f ha asf f ah f h fu sld hal sula aals f a pau dpd hal duvy ppsd y a avalal pal fu a Hffa 6 h gal aalyal slu f h hsy f pau pfls ad ha asf as f ay sz ad yp f hal sula aal ha s sujd h assups ha a lsd al s gv al 4 ad s pld Fg ad spvly 8 CONCLUSIONS h pu sl f hal sulag aal f a spf sphal sag a f lufd yg flud s ha wh a u ha laag u l ff a f yg flud a u au f sulag aal u s ad a axu sag apay f h sag a u hss f h hal sulag aal hs pu sl s aplshd 86
10 Mshaal Adula Adula wh hsg h f Fglass as wh pad wh h h h hal sulag aals O h h had s fud ha h haass f h hal sula aal ad h pssu valu w s pals hav a aj ff h a f ha asf ad pau pfl h da d f ha asf wh hsg a spf hal sula aal a asph pssu s y ha du f h sal gas w s pals whas h ha asf y ada s glgl Wh h pssu wh a hal sula aal s lwd a vauu lvl h pag f ha asf y ha du f h sal gas w s pals s glgly sall wh pad wh h pag ha asf y ada ad du v h ul aal ACKNOWLEDGEMENS h auh wuld l ha M Hfa A A fly Ld AG Gshäfsh LE Gay f hs valual hal dals dug al uas Whu hs u hs pap uld d EFEENCES A DA Kayha MH Nuz M Exa aalyal slu f usady axsy duv ha asf yldal hp ps laas Iaal jual f ha ad ass asf ELSEVIE Caslaw HS ad Jag JC Cdu f Ha Slds d d Oxfd Uvsy Pss Nw Y 959 Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy Chsas M Hllgwh JM ad Mash JHN Lw pau sula syss Adv Cyg Eg 9595 Cu J ad Gw JJ Spf Has ad Ehalps f hal Slds a Lw paus NBS Mgaph 96 Gald CF ad Whaly PO Appld Nual Aalyss 4 h d Adds- Wsly Nw Y 989 Hfa A h hal duvy f yg sula aals ad s pau dpd Elsv Cygs Ja PK Sgh S ad zwa-udd A xa aalyal slu f wdsal usady ullay ha du sphal das Iaal jual f ha ad ass asf ELSEVIE 5-4 Kaga hal Isula Cyg Egg Isal Pga f Sf aslas 969 Kpsh H ad Bugs W Pl f yg sula Adv Cyg Eg 968:S45 Pl Isu Nw Y hal Daa Sh N Sgh S Ja PK zwa-udd Aalyal slu as ha du pla das wh ulpl lays adal d Iaal jual f hal ss ELSEVIE Chsas M ad Hllgwh JM h pfa f glass f sula ud hgh vauu Adv Cyg Eg 9584:S4 Vsh ad Gl Ha asf y gas du ad ada fus sulas asas f ASME Pap N 5-A
11 Nu Vlu Jauay 4 Jual f Egg Zvv MM Nl AV Slavv B ad Zv F N-La as ha du aalyss f sula wall f a f aspa f lud Aluu hal S Vl 4 Suppl S99-S NOMENCLAUE A Css s aa C Spf ha Capay J/gK d Pal da F Fu u hal duvy W/K a f ha asf W Dsa alg h -d I u adus spvly pau K sd GEEK SYMBOLS hal dffusvy /s β Aa ud h Khhff s asfa uv W/ φ Dslss paa η Dslss paa λ valus f ua 6 - µ Aa ud h Khhff s asfa uv W/ θ Paa W ρ Dsy g/ a f u adus ψ Aa ud h Khhff s asfa uv W/ SUBSCIPS Ial Ma I sufa SUPESCIPS Dslss sg Aay 88
12 Mshaal Adula Adula Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy ρ ρ al Suggsd pal fu ad sa valus f h sld hal sula aals Hffa 6 Isulag aal Pl a 5 64 g / d 5 p Pa Pl - vauu 5 g / d 5 p Pa Epal fu a 85 W / K a Mglass sphs vauu ρ 5 g / d p Pa Fglass vauu ρ 4 g / d 4 µ p Pa al Daa valus f spf ha apay f Quaz glass wh pau Cu ad Gw 96 K C J/gK al Daa valus f a 4 h dg plyal f f spf ha apay f uaz glass wh pau β J / g K C 4 β β β β β
13 Jual f Egg Vlu Jauay 4 Nu 9 al 4 Suy f aalyal slus Cas sudy hal duvy ] / [ K W pau pfl ] [ K Ha asf ] [ W s F d d d s s F F s F F s s 4 a s F a a a a F a a s s 4 Wh: 4 F d / / / F
14 Mshaal Adula Adula Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy 9
15 Nu Vlu Jauay 4 Jual f Egg 9
16 Mshaal Adula Adula Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy 9
17 Nu Vlu Jauay 4 Jual f Egg Fg 8 Hsy f pau pfls 94
18 Mshaal Adula Adula Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy Fg 9 Hsy f ha asf pfls 95
19 Nu Vlu Jauay 4 Jual f Egg Fg Hsy f pau pfls 96
20 Mshaal Adula Adula Aalyal Slu f as Ha Cdu hugh a Hllw Sphal hal Isula Maal f a pau Dpda hal Cduvy Fg Hsy f ha asf pfls 97
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