ME 35 Fal Eam BSIC EQUION SHEE Cevat aw Ctl Vlume Eegy Balae: E E ut + E ge E t E d t mc E dt ge V Sufae Eegy Balae: E E ut Cdut Fue aw: d d Heat ffu Euat: Catea Cdate: + + + ρc y y z z t Cyldal Cdate: + ρc + + φ φ z z t Sheal Cdate: ρc + + + φ φ t d d hemal tae: Cdut tae: Plae wall: R Sheal hell: R t d Cvet tae: R Radat tae: R ( ( t ad 4π hv h t v ad t d Cyldal hell: R t d ( l πl hemal Eegy eeat: Plae wall wth ufm eegy geeat gve temeatue at bth ufae wdth ad at the ete f the wall: ( eeal lut f lae wall wth ufm eegy geeat: ( + C + C
Cylde wth ufm eegy geeat ufae temeatue : ( 4 eeal lut f a yldal hell wth ufm heat geeat: ( + Cl + C 4 Eteded Sufae/F: Cvetve : dabat : ( h m( + ( h m h m( b h ( m + ( h m h ( m / h ( m + ( h m h ( m ( hp h ( m + ( h m h ( m ( h m( ( / hp b tah ( m b h ( m ( ( b h ( m + h m( b h ( m / h ( m ( b ( hp h ( m ( m e ( / b Pebed emeatue: b Itely g F: hp b b hp whee m b b v ufae + v t e e e + e h h Rt v bae F Effetvee: ε ε h R F Effey: η b b b t d h tah h h v t h f adabat t m η a eteded legth f a m ( m tah ( tah ug adabat t + η P m F aay: N ttal η ( η Rt d h η h R ttal b ttal t d aay η h ttal
w meal Steady Cdut: Cdut Shae Fat: R t d S Fte Vlume Methd: F ufm meh te t eegy geeat teady tate + + + 4 + j j j+ j j aet Cdut: Rt d hv umed Caatae aly: B Rt v ld t ρvc e τ t Ct ld Rt v τt hv hv F e e ( B( F ld hemal dffuvty α ρc ue B t etmate the amat f the umed Caatae Methd f lae lab f ylde / f hee /3. alytal Slut f aet Cdut wth Satal Effet: t Q ( ρcv h Plae Wall: Ce ( ζ F ( ζ F t* B Q Cete temeatue at : ( ζ Ce ( ζ F Q ζ h g Cylde: Ce ( ζ F J( ζ F t* B Q Cete temeatue at : J( ζ Ce ( ζ F Q ζ Shee: Ce ( ζ F ( ζ h F t* B ζ Q Ce ζ F 3 Q Cete temeatue at : ( ( ζ ζ ( ζ 3 ζ J( ad J( ae the th ad t de Beel fut f the ft d ad the value wll be vded f eeded.
d Sem-Ite Sld: Smlaty vaable η 4 dη Ctat Sufae emeatue (: Ctat Sufae Heat Flu ( : Sufae Cvet ( h ( t ( t ef 4 d η dη ( ( t π ( t e ef π 4 4 : ( t ef e + ef + 4 4 h h h Cvet Newt aw f Clg: v hv ( Ma afe: hm( ρ ρ v v eva hfg veage Heat afe Ceffet: hv hvd S veage Ma afe Ceffet: hm hmd S mele Paamete: ρu u yld Numbe: Padtl Numbe: P µ ν ν α Shmdt Numbe: S ew Numbe: e B B hv h m Nuelt Numbe: Nu Shewd Numbe: Sh δ Buday aye he: P δ δ S t δ δt e δ Nu P h Heat-Ma algy: ρc e Sh S h e Eteal Flw: flud m B ν α B Flat Plate 5 Flat Plate (ama al: δ / / C f.664 / /3 Nu.33 P
/ Flat Plate (ama veage: C f.38 Sh.664 S / /3.37 Flat Plate (ubulet al: δ C /5 /5 Flat Plate (ubulet veage: C f.74 Flat Plate (Med veage: Cylde flw: Nu Shee: Nu ( Nu.664 P / /3 /5.59 4/5 /3 Nu.96 P f C.74 74 /5 f Nu.37 P 4/5 /3 (.37 87 / /3 5/8.6 P.3 + /3 /4 + + 8 (.4 P µ / /3.4 +.4 +.6 P µ /4 Nu P 4/5 4/5 /3 f P>. Iteal Flw: ρu ( d ula Mea Velty: um um u ( d ρ yld Numbe: u m h 4 ula h h u m 4m ν P ν π µ ubulet: 3 Hyddyam Etae egth: lama fd hyddyam tubulet.5 fd hyddyam 6 > > fd themal hemal Etae egth: ama flw:.5p ubulet flw: fd themal 6 > > ρuc d ula Mea (Bul emeatue: m (. m u d mc u m v m m. m. P P Ctat Heat Flu: ( + + v ( P mc mc Ctat Sufae emeatue: m P e. h m mc m P e. h v m mc Ctat Outde Fee Steam emeatue: v M l. v hv M mc ( m m
m P e. U e. v U M m mc mcr tt U aveaged veall heat tafe effet. Cula Pe Fag Ft Fat : la m a 64 f f.36 f < 4 tubulet /4 f.84 f > 4 tubulet ama Fully-develed g: Nu 4.36 Nu 3.66 tat tat ama Etae g: tat.668( P Nu 3.66 + /3 +.4 ( P 4/5 ubulet Fully-eveled g: Nu.3 P.3 flud heatg.4 (lable t bth tat ad tat Fee Cvet: /4 y Buday aye Paamete: ν η 4 u f gβ ( 3 gβ ( 3 Ra P ν να /6 Vetal Flat Plate:.387Ra Nu.85 + 9/6 8/7 + (.49 P Blg: /5 flud lg ( / ' ( η /4 4 7 Hztal Flat Plate: P Nu.54 Ra f < Ra < /3 7 ue ht/ lweld Nu CRa /4.589Ra 9/6 4/9 / ue ht lweld /4 Nu.5 Ra f < Ra < Nu.7Ra Hztal Cylde: Shee: Nu + + (.469 P C ad deed Ra. lwe ht/ ueld Ba Euat: h h ( blg blg e blg at g Nuleate Blg: ( ρl ρv / l e µ lhfg σ C f hfg Pl Ctal heat flu: ( /4 π σg ρl ρv h ρ 4 ρv ma fg v 3
Mmum Heat Flu: σg ( ρl ρv m.9hfg ρv ( ρ + ρ l v Flm Blg: h g( ρl ρv fg Nu C ν ( Cdeat: ' 3 h v v v at ( h h +.8C C.6 C.67 ' fg fg v at ylde /4 /4 hee. mdeat ' h Ba Euat: h h ( deat deat d deat at deat Flm Cdeat Vetal Flat Plate lama: h g( ρl ρv fg Nu.943 l ν ll ( at ' h h +.68C ( fg fg l at ' 3 h fg /4 Radat Radat leavg e ufae ad teeted by a ed ufae: d mal Ie ( dω dω π π / Emve Pwe: Setal: ( ( E E d tal: ( E dffue emtte ( πi ( e π π / E dφ I φ d dffue emtte E π I e Iadat: ( ( e dφ I φ d dffue adat ( πi ( d tal: ( dffue adat π I π π / Radty: ( ( J J dφ I φ d dffue emtte ( ( πi ( dffue eflet e+ e+ J dffue emtte π Ie + dffue eflet J J d (aue ufae ( ( 4 Bla Bdy Em: C E b ( Eb E b d σ 5 C e 898 µ mk We dlaemet law ma Eb π Ib
Radatve Pete: Emvty: etal detal: I e ( φ ε I ( Setal hemheal: tal hemheal: ε π π / eb e E π π / E b eb ( b b ( ( dφ I φ d ( dφ I d ( E d ε E d ε E d σ I btvty: etal detal: abbed ( φ α I ( φ Setal hemheal: abbed ( α ( tal hemheal: abbed α α 4 π π / abbed π π / ( dφ I φ d ( α d ( ( dφ I φ d d I fletvty: Setal detal: efleted ( φ ρ I ( φ Setal hemheal: efleted ( ρ ( efleted tal hemheal: ρ ρ π π / efleted π π / ( dφ I φ d ( ρ d ( ( dφ I φ d d I amvty: Setal detal: tamtted ( φ τ I ( φ Setal hemheal: tamtted ( τ ( tal hemheal: tamtted τ τ π π / tamtted π π / ( dφ I φ d ( τ d ( ( dφ I φ d d Sem-taaet Sufae: α + ρ + τ α + ρ+ τ
Oaue Sufae: α + ρ α + ρ Khhff aw: ε α ffue ufae: ε α ε f α f ay Sufae: ( ( ffue-ay Sufae: ε α Vew Fat: F j j j d dj J π j ty: F j jfj N Summat: Fj j ve ufae F F lae ufae Sufae wth multle ub-ufae: F F j j j d dj J j j π j ave ufae ( j F Radatve Ehage: Bla elue: ( 4 4 j F jσ j ffue-gay elue: E b ( ε J ε J J N j j F j Radat betwee tw aallel tely lage ufae: Eb Eb + + ε F ε Sgle Sheld Radat Sheld: Eb Eb ( ε ( ε3 ( ε3 ( ε + + + + + ε F 3 3ε3 3ε3 F 3 3 ε Net Radat eavg a Sufae: ad J εe α 4 age themal uudg: J σ u εσ ( ( ( ( lage themal 4 4 ad u ad u h h εσ + + ad u u Ueful Ctat σ Stefa-Bltzma Ctat 5.67 W m K Ru Uveal a Ctat 8.34 J mlk 8 4 ( ε ( ε emety Cylde: π l V π l Shee: 4π V agle: bh/ b: bae h: heght 4 π 3 3