True R-Values of Round Residential Ductwork

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1 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 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 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-199

2 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 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-200

3 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

4 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

5 = 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) 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 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 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-203

6 Btu/-ft 2 -F an 0.5 Btu/-ft 2 -F espectvely, wc gves an ute flm esstance f 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 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

7 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/ T = (Equatn 17) T 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 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 ut (Equatn 19) 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-205

8 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 ( 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 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 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 f te extenal flm 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-206

9 Nm. Duct Da. (n) Table 2. -Values an Intenal Flm esstance f 4 Nmnal Insulatn Levels 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 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 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 % 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 % 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 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 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-207

10 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 cmpae wt 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 t 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 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 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 = 1.74, teefe te flm ecease by te same fact fm t Te ttal -value canges fm 4.52 t 4.31 ( ). 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 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 f te extenal flm 2006 ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-208

11 Nm. Duct Da. (n) Table 4. -Values an Intenal Flm esstance f 4 Nmnal Insulatn Levels 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 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 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 = 0.86, s te ntenal flm esstance wll ncease fm t Te ttal -value wul ten be ajuste n te same fasn as abve fm t 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 Tey ae, f cuse, vey mptant n te case f unnsulate ucts ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-209

12 efeences [ADC] A Dffusn Cuncl Flexble Duct Pefmance an Installatn Stanas. 4 t etn. Scaumbeg, Ill.: A Dffusn Cuncl. [ASHAE] Amecan Scety f Heatng, efgeatng, an A-Cntnng Engnees ASHAE Hanbk: Funamentals. Atlanta, Ga.: Amecan Scety f Heatng, efgeatng, an A-Cntnng Engnees. Incpea, Fank P., an Dav P. DeWtt Intuctn t Heat Tansfe. 4 t etn. New Yk, N.Y.: Jn Wley & Sns. Katz, Alnz P., S. Knz, an.b. Engal Tempeatue Dp n Ducts f Fce- A Heatng Systems. Unvesty f Illns Bulletn. Bulletn Sees N May 2. Levnsn, nnen M., Wm. Wy Delp, Dayl J. Dckeff, an Mak P. Mea Effects f A Infltatn n Intenal Fbeglas Insulatn an n te Delvey f Temal Capacty Va Ducts. LBNL Bekeley, Calf.: Lawence Bekeley Natnal Labaty. [USSA] Unte States Stana Atmspee U.S. Gvenment Pntng Offce ACEEE Summe Stuy n Enegy Effcency n Bulngs 1-210