Tue -Values f un esental Ductwk Lay Palmte an En Kuse, Ectpe, Inc. ABSTACT It s a cmmn mscnceptn tat te actual -value f flexble uct s smla t te ate -value. Ts s appxmately tue f lwe nmnal -values. F nstance, une typcal cntns, a sx-nc amete, nmnal -4.2 uct as an actual -value f 3.41 nt cuntng flm esstances. In ts case, nclung te flm esstances me tan cmpensates f ts lss, wt te ttal -value beng 4.34. Te cmbnatn f bt facts es nt always esult n an mpve ttal -value weve, an te scepancy between nmnal an actual - value gets lage wt ge -values an/ smalle ametes. F example, a sx-nc amete, nmnal -8 flex uct as an actual -value f nly 5.62 nt cuntng suface flms. Wt te flm esstances te ttal -value f 6.45 s 19% less tan te nmnal value. F -11 ucts (sx-nc amete) te -value wt flms s nly 7.81, 29% less tan te nmnal value. Te pmay cause f ts scepancy s tat te ate -value s measue wt te nsulatn flat. Wen n use, t s wappe n a cylne aun te uct, esultng n a euce -value. Ts pape evews te basc cncepts an equatns f cect calculatn f eat lss n a cylncal gemety nclung te effects f amete an nsulatn tckness an ensty. Te effects f uct a velcty, tempeatue an ensty n te ntenal flm ceffcent ae gven, as well as a scussn n te effect tat a ensty canges ue t elevatn ave n uct effcency. Tables ae gven t smplfy te estmatn f actual -values. Stana atng Met Flexble, nsulate uct as a ate -value tat s pnte n te ute jacket. It s a cmmn msunestanng tat ts atng takes nt accunt te effects f te cylncal gemety n te eat tansfe ate. Hweve, t es nt. Ts pape scusses te cnseatns apppate f estmatng actual -value f flexble uct, wc as n ecent yeas becme vey cmmn n bt esental an small cmmecal applcatns. Vey smla cnseatns apply f te un uct applcatns suc as ang an nsulatng wap jacket t un metal uct. Te stana atng met publse by te A Dffusn Cuncl (ADC) eques ne t etemne te nstalle tckness f nsulatn n te fnse puct by cmpasn f te a ametes f te nne an ute jackets (ADC 2003). Te stana ten eques te nsulatng mateal (usually fbeglass) t be teste flat at te nstalle tckness n a stana guae tbx test met. Te esultng teste -value must meet ne f te allwe atng values f -4.2, -6, -8, an -11. Te ate -value es nt nclue any effects f te cylncal gemety te suface flm esstances n te nse an utse sufaces f te uct. Ntce tat te manufactue s fee t use fbeglass f ffeng enstes an fbe amete, esultng n a ffeent -value pe nc. Tus ne ban f flexble uct ate -4.2 may ave an nstalle tckness f 1.5 nces wle ante may ave an nstalle tckness f 1.25 nces. Ts wul cespn clsely t te ffeence exstng between -11 batts an - 13 batts f 2x4 wall nsulatn. Ts effect s llustate n te tables belw. 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-199
Ante gemetc fact ases fm te fact tat te ADC stana allws flexble uct t ave an nne amete tat s vesze by as muc as 3/8 nc fm te nmnal value t allw f easy nstallatn ve stana metal uct fttngs. Many manufactues f flexble uct nt state te actual nne ametes f te pucts. Because te ate -values nt nclue te effects f te gemety an te flm ceffcents, t s nt pssble t use tem ectly n calculatng te eat lss fm te uct. Te mst mptant effect s te cylncal gemety causng te actual -value f te nsulatn t be less tan te ate (flat) value, especally f g -values. Ts pape utlnes te evatn f te stana eat lss calculatn f cylnes, an als scusses te apppate values f te flm ceffcents. Temal Lss Equatns Te veall temal esstance f a un uct can be expesse as te sum f tee cmpnent esstances. Tese ae 1.) a esstance ue t te nse suface flm f a; 2.) te actual esstance f te cylncal nsulatn; an 3.) a esstance ue t te utse flm. We can expess ts n equatn fm as fllws: = + + (Equatn 1) ttal n actual ttal = ttal -value f uct n = -value f nse suface cnvectn eat tansfe actual = actual -value f nsulatn n cylncal nstallatn = -value f ute suface eat tansfe ut ut Apppate calculatn mets f eac f tese cmpnents ae pesente n any ntucty eat tansfe textbk (e.g., Incpea & DeWtt 2002) an n many engneeng anbks (e.g., ASHAE 1993). Tese mets ae evewe belw. Actual -Value f Insulatn Te nmnal -value f uct nsulatn s etemne f flat nstallatn; teefe we must fst calculate te actual -value f nsulatn nstalle n a un uct. Te key assumptn n te etemnatn f te nsulatng value f cylncally-nstalle nsulatn s tat une steay-state cntns te same quantty f eat flws tug any aus, nclung te nne an ute suface a. F a gven small tckness f nsulatn, te eat flw s pptnal t te temal esstance pe unt aea (wc s pptnal t te tckness) an t te aea f te annulus. Snce te aea nceases as te aus becmes geate te effectve esstance t eat flw eceases. Tus, te cylncal gemety esults n a euce -value elatve t te same tckness la flat. Te basc gemety s llustate n Fgue 1. 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-200
Fgue 1. Cylncal Gemety f Heat Flw Q states: Fue s law f cnuctn n cylncal cnates, n any cnsstent set f unts, Q A k T T Q = A k (Equatn 2) = utwa eat flux = suface aea at aus = temal cnuctvty f nsulatn = ate f cange f tempeatue wt aus It sul be nte tat te appaent temal cnuctvty k s epenent n te bulk tempeatue f te nsulatn. Unlke te epenence n tempeatue f te cnuctvty f a tself, tat f te nsulatn as a wle s vey cmplex an epens n fbe ensty, fbe amete, te gas cnuctvty, an te aatve ppetes f te fbe. In ts pape, we gne ts epenence. Expanng te aea tem n Equatn 2 an eaangng yels te fllwng ffeental equatn: L Q ( kt ) = 2 πl (Equatn 3) = any aus between nne an ute nsulatn a = uct lengt Integatng fm te nne aus t te ute aus gves: Q ( T ) ln = kl T 2π (Equatn 4) = ute nsulatn aus = nne nsulatn aus 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-201
T T = tempeatue at ute suface f nsulatn = tempeatue at nne suface f nsulatn eaangng an multplyng numeat an enmnat by te nne aus gves te equatn n tems f te nne suface aea: A Q = A k ( T T ) ln = suface aea at nne aus, (Equatn 5) gves: Dvng tug by te nne suface aea an tempeatue ffeence an nvetng A ( T T ) Q = 1 ln k (Equatn 6) Nte tat te left se f te equatn epesents te actual -value an te tem 1/k, n te gt se f te equatn, s te nsulatn -value pe unt tckness. Als nte tat we ae evelpng an actual -value tat s t be apple t te aea f te nne suface f te uct. In (ASHAE 1993) an -value s evelpe tat s t be use n cnjunctn wt te aea f te ute suface f te nsulatn laye. Equatn 6 can be ewtten as: = actual nsul ln (Equatn 7) nsul = nmnal -value f nsulatn pe unt tckness (flat) Cnvetng t uct amete specfcatn, as s te me cmmn pactce, gves: actual = nsul ln 2 = nne uct amete = ute amete f nsulate uct (Equatn 8) Ntng tat te ute amete can be wtten n tems f te nne amete an te ffeence between te nsulate amete an uct amete ( ) as: = + (Equatn 9) 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-202
= ffeence between nsulate amete an uct amete Nte als tat s twce te nstalle tckness f te nsulatn. ewtng Equatn 8 usng Equatn 9 gves: = + actual nsul ln 1 2 (Equatn 10) Outse Flm Ceffcent Te eat tansfe ceffcent f te utse f te uct s calculate as: = + (Equatn 11) ut c ut = veall ute suface eat tansfe ceffcent = aant eat tansfe ceffcent = cnvectn eat tansfe ceffcent c F te ange f ametes, ute a an suface tempeatues fun n esental cnstuctn, te ute cnvectn ceffcent can be estmate usng te smplfe equatn f lamna natual cnvectn n a gven by (ASHAE 1993). 0.25 T = 0.27 c (Equatn 12) c = te cnvectn eat tansfe ceffcent (Btu/-ft 2 -F) T = te tempeatue ffeence between te ute suface an te suunng a (F) = te utse amete f te uct (ft) Wt a T f 10 F an an ute amete f 1.0 ft., we get 0.48 Btu/-ft 2 -F f te cnvectn eat tansfe ceffcent. F lamna flw tee s a weak epenence n te ute amete f te uct an te tempeatue ffeence. F nstance, f we uble te amete te cnvectn ceffcent wll ncease by a fact f 2 0.25 abut 1.2. Tus te cnvectn ceffcent mgt ncease fm, say, 0.5 t 0.6. Usng a typcal value f 1.0 Btu/-ft 2 -F f te aant tansfe ceffcent, ts wll ncease te veall ute suface flm ceffcent fm 1.5 t 1.6 abut 6.6%. F a sx-nc uct wt -4.2 ate nsulatn, as swn n Table 1, ts wll cange te veall -value by 0.02 fm 4.34 t 4.32 abut 0.6%. F bette-nsulate ucts, te cange n veall -value wll be even smalle. Snce te ute aant an cnvectn ceffcents ae bt epenent upn unspecfe tempeatues, we ave f pupses f ts pape assume cnstant values f tese ceffcents. In Engls unts, typcal values f te aant an cnvectve eat tansfe ceffcents ae 1.0 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-203
Btu/-ft 2 -F an 0.5 Btu/-ft 2 -F espectvely, wc gves an ute flm esstance f -0.667 - ft 2 -F/Btu. F a uct wt a sny fl galvanze exte, sul be euce t values n te ange f 0.2 t 0.6 Btu/-ft 2 -F. See (Katz, Knz & Engal 1944) f measue emssvtes f new an age galvanze metal. Inse Flm Ceffcent Te eat tansfe ceffcent f te nse f te uct s calculate as (ASHAE 1993): n = knu / (Equatn 13) n = nse cnvectn eat tansfe ceffcent k = temal cnuctvty f uct a Nu = Nusselt numbe (mensnless eat tansfe ceffcent) In ts pape, we use te fllwng celatn f te Nusselt numbe (ASHAE 1993; Incpea & DeWtt 2002): e P X Nu 5 X = 0.023e 4 / P (Equatn 14) = eynls numbe (mensnless) = Pantl numbe (mensnless) = 0.30 f flu beng cle, 0.40 f flu beng eate F ts pape we assume a cnstant Pantl numbe f 0.711 f y a at 20 C an use an expnent f 0.35 as an aveage between te values f eatng an clng. Te celatn gven abve s val f fully evelpe flw n a un uct wt pefectly smt walls. Lack f fully evelpe flw an ugness f te uct walls eac esult n a lage eat tansfe ceffcent an a smalle flm esstance. Usng any cnsstent set f unts, te eynls numbe s efne as: e = ρ V / µ (Equatn 15) ρ = uct a ensty V = uct a velcty = nne uct amete µ = uct a vscsty Te epenence f te ntenal eat tansfe ceffcent n e 0.8 sws tat t wll be stngly affecte by velcty f a fxe amete an flu ppetes. If we uble te velcty, te ntenal flm esstance wll be almst alve. Te vscsty epens n abslute tempeatue. An accuate met f calculatng te vscsty f a s te Sutelan equatn. In te fm use n (USSA 1962) te vscsty n SI unts s gven by: 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-204
3 2 T µ = β (Equatn 16) T + S µ = uct a vscsty (N-s/m 2 ) β = 1.458x10-6 N-s/m 2 -K 1/2 (exact) T = uct a tempeatue (K) S = Sutelan cnstant f a (110.4 K) (exact) In e t calculate n, we nee t knw te temal cnuctvty f a, wc epens n tempeatue. A cnvenent an accuate fmula f te temal cnuctvty f y a (USSA 1962] n SI unts f W/m-K s: T 3 3/ 2 2.648 10 T = (Equatn 17) T + 245.4 10 k 12 / T = abslute uct a tempeatue (K) As was te case f te extenal cnvectn ceffcent, te epenence f te ntenal cnvectn ceffcent n te uct amete s weak. It vaes nvesely wt -0.2. F unnsulate metal ucts te ente temal esstance s ue t te ntenal an extenal flm ceffcents. An excellent efeence f measue tempeatue ps n unnsulate ucts tat sw g ageement wt tempeatue ps usng calculate ntenal an extenal flm ceffcents s (Katz, Knz & Engal 1944). Ante me ecent ept cntanng gaps f measue values f nsulate flex uct s (Levnsn et al. 2000). In geneal, ne f te avantages f nsulatng ucts, s tat te effect f vaatns n tese cnvectn an aatn ceffcents ue t ffeng emssvty, bulk a ppetes, suface tempeatue, an tempeatue ffeence between te suface an ambent a ave nly a mn effect n te ttal -value. Te Ttal -Value Fnally we can nset te esults abve nt Eq. 1. Te ttal -value f te uct, n any cnsstent set f unts, s ttal 1 = n + actual 1 + ut (Equatn 18) Ntce te utse flm esstance as t be multple by te amete at t ppely accunt f te lage utse suface aea. Expanng an tanslatng t Amecan Scety f Heatng, efgeatn, an A-cntnng Engnees (ASHAE) IP unts, te ttal -value f te uct nclung suface flms can be wtten as: ttal 1 = n + nsul 1 ln 1+ + 2 ut (Equatn 19) 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-205
esults ttal = ttal -value f uct (-ft 2 -F/Btu) nsul = -value f flat nsulatn pe nc tckness (-ft 2 -F/Btu-n) n = nse cnvectn eat tansfe ceffcent (Btu/-ft 2 -F) ut = veall ute suface eat tansfe ceffcent (Btu/-ft 2 -F) = nne uct amete (n) = ute amete f nsulate uct (n) Te auts ave mplemente te calculatns utlne abve n a speaseet. Te emane f ts pape s evte t selecte esults fm te speaseet. Unless specfcally state tewse, all f te esults belw ae f stana sea level pessue (101325 Pa) an a uct a tempeatue f 69 F. Ts esults n a ppetes vey clse t ASHAE stana a, efne as a wt a ensty f 0.075 lbm/ft 3. Unless state tewse te velcty s 500 FPM wc cespns t abut 98 CFM n a sx nc amete uct. Tables 1 tug 4 all ave te same fm. Te fst clumn lsts te avalable nmnal nne ametes f flexble un ucts n nces. Te secn clumn gves te uct suface aea n squae feet pe ft f lengt. Te t clumn gves te ntenal flm esstance, wc epens n amete an velcty but s nepenent f te uct nsulatn. Fu pas f clumns fllw ts, ne f eac f te stana -value atngs f -4.2, -6, -8, an -11. Als swn n te eangs s te nstalle tckness eque t puce te nmnal -value. In eac pa f clumns ae swn te actual -value f te nsulatn n ts cylncal fm an te ttal -value afte ang te ntenal an extenal flm esstances calculate as explane n te peceng sectn. Te veall cnuctance (UA) f te uct nsulatn can be calculate as LA / ttal L s te lengt n feet an A s te ntenal suface aea pe ft f lengt. Table 1 sws sea level -values f an a velcty f 500 FPM. Te nsulatn s assume t be -2.8 pe nc, wc gves an nstalle tckness f exactly 1.5 nces f nmnal -4.2 nsulate flexble uct. Nm. Duct Da. (n) Table 1. -Values an Intenal Flm esstance f 4 Nmnal Insulatn Levels -2.8 pe nc, 0 uct amete vesze nmnal : 4.2 nmnal : 6 nmnal : 8 nmnal : 11 Actual Duct Aea (ft 2 pe ft lengt) Tckness: 1.50 n Tckness: 2.14 n Tckness: 2.86 n Tckness: 3.93 n n actual ttal actual ttal actual ttal actual ttal 4 1.05 0.45 3.13 3.97 4.08 4.85 4.97 5.69 6.09 6.76 5 1.31 0.47 3.29 4.18 4.33 5.16 5.33 6.12 6.61 7.34 6 1.57 0.49 3.41 4.34 4.53 5.40 5.62 6.45 7.03 7.81 7 1.83 0.50 3.50 4.47 4.68 5.60 5.85 6.72 7.38 8.19 8 2.09 0.52 3.57 4.57 4.80 5.76 6.04 6.94 7.66 8.52 9 2.36 0.53 3.62 4.65 4.91 5.89 6.19 7.13 7.91 8.79 10 2.62 0.54 3.67 4.73 4.99 6.00 6.33 7.29 8.12 9.03 12 3.14 0.56 3.75 4.84 5.13 6.18 6.54 7.56 8.46 9.43 14 3.67 0.58 3.81 4.93 5.23 6.32 6.71 7.76 8.73 9.74 16 4.19 0.59 3.85 5.01 5.32 6.44 6.84 7.93 8.95 9.99 18 4.71 0.61 3.88 5.06 5.38 6.53 6.95 8.06 9.13 10.20 20 5.24 0.62 3.91 5.11 5.44 6.61 7.04 8.18 9.28 10.38 24 6.28 0.64 3.96 5.19 5.52 6.73 7.18 8.36 9.52 10.66 28 7.33 0.66 3.99 5.26 5.58 6.83 7.28 8.50 9.70 10.88 Nte: All -values ae n -ft 2 -F/Btu. n s te ntenal flm esstance, actual s te actual -value f te nsulatn laye nly an ttal s te veall -value nclung te ntenal flm an -0.667 f te extenal flm 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-206
Nm. Duct Da. (n) Table 2. -Values an Intenal Flm esstance f 4 Nmnal Insulatn Levels -3.36 pe nc, 0 uct amete vesze nmnal : 4.2 nmnal : 6 nmnal : 8 nmnal : 11 Actual Duct Aea (ft 2 pe ft lengt) Tckness: 1.25 n Tckness: 1.79 n Tckness: 2.38 n Tckness: 3.27 n n actual ttal actual ttal actual ttal actual ttal 4 1.05 0.45 3.26 4.12 4.29 5.09 5.27 6.02 6.52 7.22 5 1.31 0.47 3.41 4.32 4.53 5.39 5.62 6.43 7.03 7.79 6 1.57 0.49 3.51 4.47 4.71 5.61 5.89 6.75 7.44 8.24 7 1.83 0.50 3.59 4.59 4.85 5.79 6.10 7.00 7.77 8.61 8 2.09 0.52 3.65 4.68 4.96 5.94 6.28 7.21 8.04 8.92 9 2.36 0.53 3.71 4.76 5.05 6.06 6.42 7.39 8.27 9.18 10 2.62 0.54 3.75 4.82 5.13 6.16 6.54 7.54 8.46 9.41 12 3.14 0.56 3.82 4.93 5.25 6.33 6.74 7.78 8.78 9.77 14 3.67 0.58 3.86 5.01 5.34 6.45 6.89 7.96 9.02 10.06 16 4.19 0.59 3.90 5.07 5.42 6.56 7.00 8.11 9.22 10.29 18 4.71 0.61 3.93 5.13 5.47 6.64 7.10 8.23 9.38 10.48 20 5.24 0.62 3.96 5.17 5.52 6.71 7.18 8.34 9.52 10.64 24 6.28 0.64 4.00 5.24 5.59 6.82 7.30 8.50 9.73 10.89 28 7.33 0.66 4.02 5.30 5.65 6.90 7.39 8.62 9.88 11.09 Nte: All -values ae n -ft 2 -F/Btu. n s te ntenal flm esstance, actual s te actual -value f te nsulatn laye nly an ttal s te veall -value nclung te ntenal flm an -0.667 f te extenal flm Te ffeence between te nmnal an actual -values f te nsulatn laye tself ae stkng, especally f small ametes an lage nstalle tckness. F nstance, 4-nc flexble uct ate at -11 as an actual -value f nly 6.09 55% f te nmnal value. Even wt te flm esstances ae te ttal -value s nly 6.76, wc s stll nly 61% f te nmnal value. Te scepancy gws smalle as te nne uct amete nceases. Cnse 20-nc amete uct, wc s abut te lagest amete seen n esental cnstuctn. In ts case, -11 ate flexble uct as an actual -value f 9.28, wc s 84% f te ate value an a ttal -value f 10.38 94% f te ate value. Ntce f 5- an 6-nc ucts ate at -4.2, te ttal -value s clse t te ate value, tat s, te ae flm esstances appxmately cancel te lss ue t te cylncal gemety. Fbeglass nsulatn s manufactue wt vayng -values pe nc, angng fm abut -2.5 up t almst -4 (ASHAE 1993). Table 2 sws te same vaables as Table 1, but assumes a ge ensty fbeglass f -3.36 pe nc. Ts esults n an nstalle tckness f 1.25 nces f an -4.2 ate uct. Because te nstalle tckness s less f a gven nne amete an nmnal -value, te penalty ue t te cylncal gemety wll be smalle. Tus n geneal lwe cnuctvty nsulatn wll yel bette veall -values f a fxe nmnal atng. F nstance, -11 ate 4-nc uct as an actual -value f 6.52 vesus 6.09 n Table 1, abut a 7% mpvement. Te ttal -value f 7.22 vesus 6.76 n Table 1 sws a 6.8% mpvement. At lage ametes te beneft f usng nsulatn wt a geate -value pe nc eceases. Tables 3 an 4 sw te same nfmatn as Tables 1 an 2 espectvely, weve te ntenal amete s ncease by 3/8-nc. It was mentne eale tat mst flexble uct s manufactue wt a slgtly vesze nne ce t allw easy cnnectn t stana metal fttngs. Te ADC stana allws f a maxmum f 3/8-nc vesze n te nne amete. Teefe a gven nstalle tckness f nsulatn s apple t a slgtly lage nne amete, wc wll cause a slgt mpvement n te actual -value an als n te ntenal flm esstance. 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-207
Hweve, te ntenal suface aea s ncease by a lage amunt tan te -value s te veall cnuctance UA f te uct s lage tan befe tus nceasng te eat lss. F nstance n Table 3 we see tat nmnal -11 uct wt a 4 nc amete as a ttal -value f -6.99 cmpae wt -6.76 n Table 1, a 3.4% ncease n -value. Te ntenal suface aea pe unt lengt nceases fm 1.05 squae feet t 1.15 squae feet, an ncease f abut 9.5%. Te veall eat lss pe unt lengt teefe nceases fm 0.155 t 0.164 Btu/-F, abut 5.8%. Tus mst flexble uct as a lage eat lss tan expecte tewse because f te ncease nne amete. A fact tat affects ttal -value s te velcty f a n te uct, wc can ave a lage mpact n te ntenal flm esstance. esental uct systems typcally ave velctes angng fm abut 500 FPM (feet pe mnute) t abut 1000 FPM. Te value ecmmene by ASHAE f esences s 600 FPM. Small amete unuts t nvual egstes ten t be n te 500 FPM ange wle tunk ucts nea te a anle may ave ge velctes. Small cmmecal uctwk fequently as smewat ge esgn velctes. Te velcty nly affects te ntenal flm ceffcent, s s f less mptance f well-nsulate ucts. Te values n Tables 1 tug 4 can be easly ajuste f te velctes. F nstance suppse we ae nteeste n a 6-nc nmnal uct, 3/8-nc vesze, usng -3.36 pe nc flexble uct, wt a nmnal atng f -4.2, an aflw wt a velcty f 1000 FPM. We stat wt Table 4. Te ntenal flm esstance gven n te table s -0.49 f a velcty f 500 FPM. Fm Equatns 13 an 14, we knw tat ntenal flm ceffcent s pptnal t te velcty ase t te 0.8 pwe. Te velcty at n u case s 2, s te ntenal eat tansfe ceffcent wll ncease by a fact 2 0.8 = 1.74, teefe te flm ecease by te same fact fm -0.49 t -0.28. Te ttal -value canges fm 4.52 t 4.31 (4.52-0.49+0.28). Nm. Duct Da. (n) Table 3. -Values an Intenal Flm esstance f 4 Nmnal Insulatn Levels -2.8 pe nc, 3/8 uct amete vesze nmnal : 4.2 nmnal : 6 nmnal : 8 nmnal : 11 Tckness: 1.50 n Tckness: 2.14 n Tckness: 2.86 n Tckness: 3.93 n Actual Duct Aea (ft 2 pe ft lengt) n actual ttal actual ttal actual ttal actual ttal 4 1.15 0.46 3.20 4.05 4.18 4.98 5.12 5.87 6.30 6.99 5 1.41 0.48 3.34 4.24 4.41 5.26 5.45 6.25 6.78 7.53 6 1.67 0.49 3.44 4.39 4.59 5.48 5.71 6.56 7.17 7.96 7 1.93 0.51 3.52 4.51 4.73 5.66 5.92 6.81 7.49 8.32 8 2.19 0.52 3.59 4.60 4.85 5.81 6.10 7.02 7.76 8.63 9 2.45 0.53 3.64 4.68 4.94 5.93 6.25 7.19 7.99 8.89 10 2.72 0.55 3.69 4.75 5.02 6.04 6.37 7.35 8.19 9.11 12 3.24 0.56 3.76 4.86 5.15 6.21 6.58 7.60 8.52 9.49 14 3.76 0.58 3.81 4.95 5.25 6.35 6.74 7.79 8.78 9.79 16 4.29 0.60 3.86 5.02 5.33 6.46 6.86 7.95 8.98 10.03 18 4.81 0.61 3.89 5.07 5.39 6.54 6.97 8.09 9.16 10.24 20 5.33 0.62 3.92 5.12 5.45 6.62 7.05 8.20 9.30 10.41 24 6.38 0.65 3.96 5.20 5.53 6.74 7.19 8.37 9.53 10.69 28 7.43 0.67 3.99 5.26 5.59 6.83 7.29 8.51 9.71 10.90 Nte: All -values ae n -ft 2 -F/Btu. n s te ntenal flm esstance, actual s te actual -value f te nsulatn laye nly an ttal s te veall -value nclung te ntenal flm an -0.667 f te extenal flm 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-208
Nm. Duct Da. (n) Table 4. -Values an Intenal Flm esstance f 4 Nmnal Insulatn Levels -3.36 pe nc, 3/8 uct amete vesze nmnal : 4.2 nmnal : 6 nmnal : 8 nmnal : 11 Actual Duct Aea (ft 2 pe ft lengt) Tckness: 1.25 n Tckness: 1.79 n Tckness: 2.38 n Tckness: 3.27 n n actual ttal actual ttal actual ttal actual ttal 4 1.15 0.46 3.32 4.20 4.39 5.21 5.41 6.19 6.72 7.45 5 1.41 0.48 3.45 4.38 4.60 5.48 5.73 6.56 7.19 7.97 6 1.67 0.49 3.54 4.52 4.76 5.69 5.97 6.85 7.57 8.39 7 1.93 0.51 3.62 4.62 4.89 5.85 6.17 7.09 7.87 8.74 8 2.19 0.52 3.68 4.71 5.00 5.99 6.33 7.28 8.13 9.02 9 2.45 0.53 3.72 4.78 5.08 6.10 6.47 7.45 8.34 9.27 10 2.72 0.55 3.76 4.85 5.16 6.20 6.58 7.59 8.53 9.48 12 3.24 0.56 3.83 4.94 5.27 6.35 6.77 7.81 8.83 9.83 14 3.76 0.58 3.87 5.02 5.36 6.47 6.91 7.99 9.06 10.10 16 4.29 0.60 3.91 5.08 5.43 6.57 7.02 8.14 9.25 10.33 18 4.81 0.61 3.94 5.14 5.48 6.65 7.11 8.25 9.41 10.51 20 5.33 0.62 3.96 5.18 5.53 6.72 7.19 8.35 9.54 10.67 24 6.38 0.65 4.00 5.25 5.60 6.83 7.31 8.51 9.74 10.92 28 7.43 0.67 4.03 5.30 5.65 6.91 7.40 8.63 9.90 11.11 Nte: All -values ae n -ft 2 -F/Btu. n s te ntenal flm esstance, actual s te actual -value f te nsulatn laye nly an ttal s te veall -value nclung te ntenal flm an -0.667 f te extenal flm Ante fact wc canges te ntenal flm ceffcent at a gven uct a tempeatue s te atmspec pessue, eflecte n te ensty f te a. F nstance n Denve, CO at 5000 feet elevatn te a pessue an te ensty f te a n a uct at a gven tempeatue s 83.2% f tat at sea level. A fce a stbutn system s, t a easnable appxmatn, a cnstant vlume evce, meanng tat te same system wt te same fan tunng at te same spee wll mve te same actual vlume f a. Te velctes evey n te uct system wll eman te same as at sea level. Te ntenal flm esstance nees t be ajuste f te new ensty. Usng te same uct as te velcty example, we wul calculate te ntenal eat tansfe ceffcent t cange by a fact f 0.83 0.8 = 0.86, s te ntenal flm esstance wll ncease fm -0.49 t -0.57. Te ttal -value wul ten be ajuste n te same fasn as abve fm -4.52 t -4.60. Cnclusns Falng t euce te ate -value f un uct nsulatn t accunt f te cylncal gemety can lea t sgnfcant es. F nstance, nceasng te nmnal -value f sx-nc uct fm -4.2 t -11 nly nceases te ttal -value by a fact f 1.80 nstea f a fact f 2.62 base n te nmnal values, tus gvng an e f abut 31% n te mpvement. Use f nsulatn wt a geate -value pe nc wll esult n geate actual an ttal - values f te same nmnal ate -value, because te gemetc penalty s euce. Te vaatn n flm ceffcents n te nte an exte sufaces f te uct becmes elatvely mn wt nmnal -values geate tan -4.2. Tey ae, f cuse, vey mptant n te case f unnsulate ucts. 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-209
efeences [ADC] A Dffusn Cuncl. 2003. Flexble Duct Pefmance an Installatn Stanas. 4 t etn. Scaumbeg, Ill.: A Dffusn Cuncl. [ASHAE] Amecan Scety f Heatng, efgeatng, an A-Cntnng Engnees. 1993. ASHAE Hanbk: Funamentals. Atlanta, Ga.: Amecan Scety f Heatng, efgeatng, an A-Cntnng Engnees. Incpea, Fank P., an Dav P. DeWtt. 2002. Intuctn t Heat Tansfe. 4 t etn. New Yk, N.Y.: Jn Wley & Sns. Katz, Alnz P., S. Knz, an.b. Engal. 1944. Tempeatue Dp n Ducts f Fce- A Heatng Systems. Unvesty f Illns Bulletn. Bulletn Sees N. 351. May 2. Levnsn, nnen M., Wm. Wy Delp, Dayl J. Dckeff, an Mak P. Mea. 2000. Effects f A Infltatn n Intenal Fbeglas Insulatn an n te Delvey f Temal Capacty Va Ducts. LBNL-42499. Bekeley, Calf.: Lawence Bekeley Natnal Labaty. [USSA] Unte States Stana Atmspee. 1962. U.S. Gvenment Pntng Offce. 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-210