Question

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11.1 An industrial boiler consists of tubes inside of which flow hot combustion gases. Water boils on the exterior of the tubes. When installed, the clean boiler has an over- all heat transfer coefficient of 300 W/m2- K. Based on experience, it is anticipated that the fouling factors on the inner and outer surfaces will increase linearly with time as Rat and R = at where a;= 2.5 x 10-1" m2- K/Ws and a = 1.0 x 101" m2- K/W -s for the inner and outer tube surfaces, respectively. If the boiler 11.2 Problems Fouling R factors Tube, SS302 RT Water T75°C "=0.5 m/s D D V 20 m/s T15°C Air (a) Determine the overall heat transfer coefficient based on the outside area of the tube, U, Compare the thermal resistances due to convection, tube wall conduction, and fouling (b) Instead of air flowing over the tube, consider a situ ation for which the cross-flow fluid is water at 15°C with a velocity of V, = 1 m/s. Determine the overall heat transfer coefficient based on the outside area of the tube, p. Compare the thermal resistances due to convection, tube wall conduction, and fouling. (c) For the water-air conditions of part (a) and mean ' velocities, um of 0.2, 0.5, and 1.0 m/s, plot the overall heat transfer coefficient as a function of the cross-flow velocity for 5 s Vs 30 m/s (d) For the water-water conditions of part (b) and cross-flow velocities, V, of 1, 3, and 8 m/s, plot the overall heat transfer cocfficient as a function of the mean velocity for 0.5 s umi 5 2.5 m/s

Answer 1

Stainfess stil AJSI 302 (30Dk Waty (Tyi34ek) 21s k wimk Ko =0.02737 3. t46 X10 N-SIm 7 .35x1o 0.tos Ki o.668 Pri 2.354 =0.0002 m 0.0004m k 27mm Di22 Tmi7sc Umi0-Sm -20ms T-ISC Air overall Cofficient Can be expreused thurmal uistanes due to Conve ction ccv), tabe wall conductien (w) and baed upen the outr the Jum thhe fautang ) Riat Rey + R Revo Ai

RJn (D) conveitien Coelfieients apprioiate Coelations. Can be estimatd The Fetimeting For intnal ou thasactorize the Haw evaluating Thmaphyial propees mi Di at Tm with Repi 0 SX0.022 28625 3.746 6 974-8 0.8 0.3 0.083 Reni Pi nN ,d - 0.02 3 o 3 109.3 Nuki Di 2212 W m2k 109.3 x0.66l O.D 22 For extenal flou charactorie Eslimating ho the low with Repo 20 x 0.027 19.25x10 31,12y 6 esaluatng homhsal i p 7 when the dufaa tomperate at 11 thernal Cirtuit detormind fron Revi Tm,i R wMa MMo www ww

tima ToTp-T) Riot Rev,D the churhill- Beonstin Correlatien. wing 12 a62(Re ( ReDO 0.3+ + 1+ 0.4 12/3 4 Phe 282000 3r 062(21124) oas) 0-3 + 2/37/41+/ 31124 282000 + 102.6 wm-k 1o4 using the above valus for hi and and prescribed values, the thermal neitanes overall Coefficient tan be evaluatd and other and tabulated Revi tkiw) Ri (kiw) Rfo Reyp (k) (ki) 0.00578 -00216 0.00436 O.00236 o.l13y 92-1 Rtot (klu) C L

major thermal ruistance Outcide Cair) Convection actourting for o the total eetance The other thernal gusistances s due to The e timilan tines Smaller than Reyo ase magnitude naly 50 borWaty- Wlatoy tondition, the method of nalyus bellous that of past (a). For the intnal How, the estimated on Ve ctien Coelficient i the ame as For an auumed outoy pln Coefficient T29RK, the Comve ction Correlation fer the outey waty loo condition V = ms and past ). To Repp =26,260 Nupo 4914 시n-k 220.6 tabulatd The thermal rustances and oreal tofficient Revi CKIN) Ript Cklo) 0-b1귀 kho) (kIw) CKha) 0.002/6 0.00579 0.00236 0-00240 98h00. (wln 691

Note that the termal estances ave Similar magnitude raulty to the wator- aiy Condition of partla), the thermal esistane of the outide Conve cion protes the overall Coeffi cient for the waty water conditions the watey air condilion. In Cortbyast wi the nearly 50 times Jmalbr 5 times gruator than that fo7 tor the water aiy condition with tha (C) analyi o part a) was Cal tulatid function of aiy watey velocities Hao velouty for CYofs al a sehchd mean Imls Umi Unyi0mls 0.2 mls Uni 120 100 60 40 10 IS as 30 tfect of intuating the Cress tincreave dince the Reuo i the dominant thermal eistante for the ycam. elocly Revo this The air locty 4ohile ncreating the watey mean will increate he because Revi a dmall efect 22 jinCrease has on

analyes fun cton selectid aiy cvoss floa For the water watoy Condition wth (d) o part (b), U, was Cal tulatd a waty velo ay for of Nelouities mean mls 1000 -3l 700 600 1-S &.S 04S Water mean velouy ) mle