sm3_20 - PROBLEM 3.20 KNOWN: h-‘latet‘ials and...

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Unformatted text preview: PROBLEM 3.20 KNOWN: h-‘latet‘ials and dimensions ot‘a composite wall separating a combustion gas from a liquid coolant. FIND: to} Heat loss per unit area. and {b} Temperature distribution. SCH EMATIC: th=0fl5mz Beryllium and: Stainless 3+1:le504) firm, gases Efl=100 C EM =2600'C A; =I000 W/ml-K h; 'K EA E: E1 E: E: Tie—g." LA=10mm—I‘—+—'1—£5=20mm i g R“ IL:- if; ASSUh’IPTIONS: i l } Dne—dimensiomal heat transfer. {2} Steady—state conditions. {3] Constant properties. {4} Negligible radiation et‘t‘eets. PROPERTIES: liable :I—i‘. St. St. {3H4} [T a ltHNth}: k = 25.4 \N'..'in-K: liable x’t—S. Beryllium Oxide {T a 15!}{IK}:I~;= 2l.5 ‘i’i-".-'m-K. ANALYSIS: [a] The desired heat flux may be expressed as " T..,_ ‘l T12 (2mm liiiif C‘ q = =— L l I Rt 1: l LB I; l I “iii I” U; I {UH/l I i [112.K hi RA ‘ J~‘B h: 5n 21.5 ' ‘ 25.4 mm: W q"'=34_(\.l}{l \K-".-']]1‘1. < {b} The composite sut‘t‘aee temperatures may be obtained by applying appropriate rate equations. From the fact that q"'=li] [Till THAI it tollowstliat a . 3 g .. 3'.{1{}U _ . a . Tm =T.,_.‘l i=2tmu L 4—W=ians C. lll SI} Wsm“ I K With q"={l<A.-'LA‘_}{TM TR] it also t‘ollows that .. . a L. ' .. _ {mlm 3.4mm \K-fi-‘in‘ . 0 , TC1=TH Aq =1LmH’L' +=15~J2 ‘ “ ltA 21.3 \K—u‘m- K Similarly, with q"=iTL..] Tag] Rm. in2 - K W TIL; =TL..] Rtthrrzlsilffl' “1:5 “I x34fillll—j: 163°C- m“ Continued PROBLEM 3.20 (Cont) and with q"=[l<B.-'LB‘_}[ITC~2 Ti 1‘]. ..._. a " ., rm" 3' .iuu W; ' a _ T5 3 : Tag LBq = “121" M: 1341) L3 kg 25.4 \Rfl'm - K COMM ENTS: ij 1 ji The calculations may he cheelted by reeomputmg q" from q"=hg T52 —T.,_.Ll = 1(a):l‘tli-ir‘ttt2 .K {134_(1—]{}u:f (534.64}!th-fl-"inl {2} The initial estimates ot‘the mean material temperatures are in error. particularly tor the stainless steel. For imprm'ed accuracy the calculations should be repeated using. i; values corresponding to T a l‘JHHUL" tor the oxide and T a l 15°C tor the steel. {3} The major contributions to the total resistance are made by the combustion gas boundary layer and the contact. where the temperature drops are largest. ...
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sm3_20 - PROBLEM 3.20 KNOWN: h-‘latet‘ials and...

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