Hat Exangr April 8, 007 Hat Exangr Larry artt Manial Engrg 375 Hat ranfr April 8, 007 Outl Bai ida f at xangr Ovrall at tranfr ffiint Lg-man tmpratur diffrn mtd Efftivn NU mtd ratial nidratin Hat Exangr Ud t tranfr nrgy frm n fluid t antr ypially n fluid i ld wil t tr i atd May av pa ang: tmpratur f n r bt fluid i ntant Simplt i dubl pip at xangr aralll flw and untr flw 3 Figur - frm Çngl, Hat and Ma ranfr 4 mpat Hat Exangr Hav larg urfa ara fr at xang pr unit vlum Aivd by u f f ar and truk radiatin bt xampl Oprat r flw Fluid aid t b mixd r unmixd Mixd: n flw paag fr t fluid Unmixd: vral flw paag mpat Hat Exangr II mpat at xangr m air nditinr Rfrigrant tub, air trug f 5 Figur - frm Çngl, Hat and Ma ranfr 6 ME 375 Hat ranfr
Hat Exangr April 8, 007 mpat Hat Exangr III Sll-and-ub Exangr untr flw xangr wit largr urfa ara; baffl prmt mixg Figur -3 frm Çngl, Hat and Ma ranfr 7 Figur -4 frm Çngl, Hat and Ma ranfr 8 ub and Sll a Sll and ub a II rviu art wd n ll pa and n tub pa N a wr flw angd dirtin mpltly Numbr f ll r tub pa i t numbr f tim a fluid t ll (r tub flw a rvr dirtin Exampl nxt art ub flw a n mplt ang f dirtin givg tw tub pa 9 Figur -5(a frm Çngl, Hat and Ma ranfr 0 Sll and ub a III ub flw a tr mplt ang f dirtin givg fur tub pa Sll flw ang dirtin t giv tw ll pa Figur -5(b frm Çngl, Hat and Ma ranfr Ovrall U U i vrall at tranfr ffiint Analyzd r fr dubl-pip at xangr R + Rwall + i Ai A U A U A UA Figur -7 frm Çngl, Hat and Ma ranfr i i ME 375 Hat ranfr
Hat Exangr April 8, 007 Hat Exang Analyi Hat tranfr frm t t ld fluid m& UAΔ ( Firt law p nrgy m& balan p, Aum n at l t urrundg Subript and dnt ld and t fluid, rptivly Altrnativ analyi fr pa ang 3 Analyi Fr n xtrnal at tranfr, mb tr quatin fr diffrntial ara, da, and tgrat frm t d U d m& d m& Figur -4 frm Çngl, Hat and Ma ranfr p p d d da 4 Δ i lgman dlta Analyi Rult aralll flw at xangr wit n xtrnal at tranfr UAΔ Δ Δ Δ Δ Δ Δ Δ Δ Δ Δ and Δ ar Analyi Rult II aralll flw UAΔ at xangr Δ Δ Δ Δ Δ Δ Δ Δ Δ bt,, 5 6 Figur -4 frm Çngl, Hat and Ma ranfr Figur -4 frm Çngl, Hat and Ma ranfr Δ Δ Δ untr Flw Sam bai quatin Δ Diffrn Δ and Δ dfitin Δ Δ UAΔ UA Δ Δ Figur -6 frm Çngl, Hat and Ma ranfr 7 Wat if Δ Δ? Apply l Hpital rul t w tat Δ Δ Δ ti a Δ Δ Δ Δ Lim Δ Lim 0 0 Lim Δ Δ Δ Δ Δ 0 Δ Δ + Δ Δ Δ Δ Δ Δ Δ Lim 0 Lim Δ Δ Δ Δ Δ 0 + Δ Δ Δ Δ Δ + Δ Δ Lat tp tak drivativ f numratr and dnmatr wit rpt t Δ Δ fr ntant Δ dnmatr 8 ME 375 Hat ranfr 3
Hat Exangr April 8, 007 Hat Exangr rb Wit Δ mtd w want t fd U r A wn all tmpratur ar knwn If w knw tr tmpratur, w an fd t furt by an nrgy balan wit knwn ma flw rat (and p & an fd Q m& p (, & frm tw, tmpratur fr n & m& tram and tn fd p (,, unknwn tmpratur Q Q rb An untrflw at xangr wit U 00 W/m i t b ud t l kg/ f il ( p 000 /kg frm 00 t 30 ug 3 kg/ f watr ( p 484 /kg at 0. Wat ara i rquird? Givn: 00, 30, 0, U 00 W/m, p, 484 /kg, p, 000 /kg, m& kg/, and m& 3 kg/. Fd: A 9 0 Slutin Equatin:,, UAΔ UA m& m& p p,, ( ( kg 000 ( 00 30 m& p 40000 kg 40000 + 3. m & 3 kg 484 p kg Δ Slutin II ( 30 0 ( 00 3. 30.5 30 0 00 3. W 40000 A UΔ 00W 30.5 m ( A.9 m Otr nfiguratin U rrtin fatr Δ F rr Δ,F Δ,F i Δ fr untr flw Δ, F F rr dpnd n tmpratur n tub id (t and t and ll id ( and trug tw paramtr, R and 3 rrtin Fatr rrtin fatr paramtr, R and Sll and tub dfitin blw tub, tub, t t ll, tub, t ( m p ll tub &,, tub R t t m & tub, tub, ( p ll rrtin fatr art w diagram tat illutrat t quatin fr and R 4 ME 375 Hat ranfr 4
Hat Exangr April 8, 007 rrtin Fatr art I Figur -8 frm Çngl, Hat and Ma ranfr 5 Figur -8 frm Çngl, Hat and Ma ranfr 6 Figur -8 frm Çngl, Hat and Ma ranfr 7 Figur -8 frm Çngl, Hat and Ma ranfr 8 Efftivn-NU Mtd Ud wn nt all tmpratur ar knwn Bad n rati f atual at tranfr t imum pibl at tranfr Maximum pibl tmpratur diffrn, Δ i Only n fluid, t n wit t mallr valu f m& p, an av Δ Df ( m& p and ( m& p 9 ε Efftivn, ε m. (, In fftivn-nu mtd w fd ε, tn fd Q & ε Q & U m Δ t fd Q & bau Δ Δ r Δ Δ / If Δ Δ and / >, Δ > Δ m Δ i imum at tranfr tat an ur wit impibl < m m 30 ME 375 Hat ranfr 5
Hat Exangr April 8, 007 Max In xampl, Δ Δ il and Δ watr (9 Δ / 04.5 If w ud Δ t gt Q (04.5 (0,495 kw tn Δ il (04.5(0/(9 Fd ε Exampl art fr fdg fftivn frm NU UA/ m and m / rati Fr NU.5 and m / 0.5, ε?.7 4.9 > Δ Figur -6 frm Çngl, Hat and 3 Ma ranfr 3 Efftivn Equatin Dubl pip paralll flw NU ε + Dubl pip untr flw ε NU NU NU ( + ( ( 33 Figur frm Figur -6 frm Çngl, Hat and Ma ranfr UA m m Mr Efftivn Equatin Sll and tub On ll pa and, 4, 6, tub pa + ε + + + Any gmtry wit 0 ε NU NU NU + + NU 34 Figur frm Figur -6 frm Çngl, Hat and Ma ranfr m UA m rb An 5 m untrflw at xangr wit U 00 W/m i t b ud t l kg/ f il ( p 000 /kg at 00 ug 3 kg/ f watr ( p 484 /kg at 0. Wat i t il lt tmpratur. Givn: 00, 0, U 00 W/m, A 5 m, p, 484 /kg, p, 000 /kg, m& kg/, and m& 3 kg/. Fd: 35 Slutin kg 000 000 m& p kg 3 kg 484 55 000 m m& p kg 00 W ( 5 m 000 UA NU m.5 m 000 W m 55 0.593 36 ME 375 Hat ranfr 6
Hat Exangr April 8, 007 art ε Frm art fr untr flw: NU.5 m / 0.6 ε 0.89 37 Efftivn Equatin Fr untrflw at xangr ( m / NU ( ε NU (.5( 0.593 ε ( 0.895.5 0.593 0.593 Q & 000 εq & εm. 0.895 00 0 ( ( 5.43x0 43 kw 38 Outlt mpratur U bai nrgy balan quatin t fd lt tmpratur frm Q & 5 x.43 0 + 0 + m& 3 kg 484 p kg 5 x.43 0 00 m& 3 kg 484 p kg 3.4 8.4 rb mparin mparg xampl Δ and ε-nu xampl ad t am ma flw rat, at apaiti and U valu ε-nu xampl ad A 5 m mpard t A.9 m fr Δ A xptd, ligtly largr ara giv a ligtly largr tmpratur ang Oil l frm 00 t 30 wit A.9 m and t 8.4 wit A 5 m 39 40 ME 375 Hat ranfr 7