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Pg0105im - PRfllLEM 1.29 EHflWH Cylindricsl systdm with...

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Unformatted text preview: PRfllLEM 1.29 EHflWH: Cylindricsl systdm with negligihl: W vstiltidts its the r; dis'dcfidtts. FIND: {I} Hut dqusdutt basil-mitt: with I matted? dtfimd MIDI swim. {It} Twins-stun dimihuddn TH!) f-fl' study-stat: cunditiuns with no intern-1 hut gamut-an and W! ptuptrlins. in] Hunt rste fur Pitt (11} mndiduns. SWTIE: Inwhhm __ _ . a” it: ASSUMPTIONS: t' I} T is independdnt of rd. {21th: trri'i] 1: n. ANALI'SIS: [all Dcftnr: the control volume as V = admit-1.. whm: L is list-lath urn-tun! II} pals. Apply I11: cansdwitidn of may tsquirsmt. Eq. 1.1 ll+ Eh-Emn+fil=fifl qg-qulV—sp‘iic—EE [1.21 ET B = r — = —a - +4 what: I]. -it{.fl.tLi Ha Hm q.+ [MIMI l3} Eqs. {3} and [4] follow ftum Fmr'tsr's Inst-r. Eq. ll. and from Eq. 23?. mspcctiwly. Cmbitu'ttg Eqs. [3”: anti {4] with Eq. {1} and cuddling 1th: sums. find 1 a 31' HT 15);] Cunsidttring that 1:: an: wnsmnt. this farm syncs with Eq. 2.20. {Isl Fur steady-stat: :uttditiuns wilh II] = U, the heat aquatiun. {5]. hummus s tiT_ sl—]-- With Dunsunt pmptmitss. 1| I'nlltms that .1de is sunstsnt which implies TWIJ is lindar in i. That is. dT _ Tt-T. _ I _ l E‘ tau—m -+flrr1 Tit m Titti-T1+EIZT3 Tm. {Tfiifl in The hit“ rat: fur tit: dmditidns nf Part {h} fiJIJIIWE frat-n Fanisr's law. Eq. (It. using mt: tcmpcrtttun: gradient of Eq. {7]. That is. :4; [:r‘] Lm—Tlt. [gist] IS]: = ‘k‘lfir‘I—J Ti' I —T-*T +1“: I] CflMHEI-FI'S: Nut: tit: csptcssiun far this map-tram indict-it it: Faut-icr's law, Eq. [3}. is th'nEl nut EITt'BqI. For tin: candititms at Pat-t {b} and is]. nut: that qfl] is indcpcndcnt of tit: this is first nutcd in Eq. {45) Ind finally unfit-mud in Eq. t9]. ...
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