THERMAL/FLUID CHARACTERISTICS OF ISOTROPIC PLAIN-WEAVE SCREEN LAMINATES AS HEAT EXCHANGE SURFACES

Transcription

1 AIAA THERMAL/FLUID CHARACTERISTICS OF ISOTROPIC PLAIN-WEAVE SCREEN LAMINATES AS HEAT EXCHANGE SURFACES Ji-Wook Park *, Dan Ruch *, an R. A. Wirtz Mechanical Engineering Department/MS 31 Univerity of Nevaa, Reno Reno, NV ABSTRACT A imple-to-fabricate woven meh, coniting of bone laminate of two-imenional plain-weave conuctive creen i ecribe. Geometric equation how that thee porou matrice can be fabricate to have a wie range of poroity an a highly aniotropic thermal conuctivity vector. A mathematical moel of the thermal performance of uch a meh, eploye a a heat exchange urface, i evelope. Apparatu to meaure both the preure rop an heat tranfer coefficient are ecribe. Meaurement of preure rop an overall heat tranfer rate are reporte an ue with the performance moel to evelop correlation equation of meh friction factor an Colburn j-factor a a function of coolant propertie, meh characteritic an flow rate through the meh. A heat exchanger performance analyi elineate conition where the creen-laminate technology offer uperior performance. J = moifie Colburn j-factor k = thermal conuctivity ke = effective thermal conuctivity M = meh number n = number of creen layer of the lamination P = preure Pr = Prantl number q = heat tranfer rate q = heat flux Re = Reynol number St = Stanton number t = thickne of meh creen T = temperature U = effective conuctance of meh creen W = with of meh creen β = heat tranfer urface area to volume ratio P = preure rop = poroity ρ = flui enity µ = flui vicoity A A c cf c D h f G h H j NOMENCLATURE = face area of meh creen, WH = cro-ection area of meh creen, tw = compreion factor = flui pecific heat = wire iameter of meh creen = hyraulic iameter of meh creen = friction factor = flui ma velocity = unit urface conuctance = height of meh creen = Colburn j-factor Subcript f = flui i, o = inlet, outlet = oli x, y, z = coorinate INTRODUCTION Kay an Lonon [1984] have pointe out that a mot effective way to increae the performance of a heat exchanger i to increae it urface area to volume ratio, β. 7 Small-particle packe be an foame metal are * Grauate Stuent, Department of Mechanical Engineering. Member AIAA. Profeor, Department of Mechanical Engineering. Member AIAA. Copyright 00 The, Inc. All right reerve. 1

2 expane material having large value of urface area to volume ratio (β). Unfortunately, ue to the tortuoity effect in conjunction with the high poroity () of thee material, their effective thermal conuctivity (ke) i relatively mall o that much of the gain in performance obtaine by having a large urface area to volume ratio i lot by having a relatively mall effective thermal conuctivity. Typical value of effective thermal conuctivity in pherical particle packe be are 10% - 15% of the particle thermal conuctivity [Kaviany, 1995]. 5 Commercially available metal foam uch a aluminum foam ha an effective thermal conuctivity that range from only % to 6% of the bae metal value [Ahby et al, 000]. 1 An aniotropic porou matrix having a large urface area to volume ratio an high effective thermal conuctivity in a particular irection will reult in a very effective heat exchange urface. Such a matrix can be fabricate by layering an boning plain-weave creen to form a three-imenional matrix. Xu an Wirtz [00] 15 have hown that plain-weave creen laminate can be configure to have a large urface area to volume ratio an high effective thermal conuctivity in a particular irection, with effective thermal conuctivitie of aniotropic creen laminate approaching 78% of bae material value. In aition, creen laminate are imple to manufacture an can be fabricate to have a wie range of poroity. They can be incorporate into the eign of a flow-through moule or col plate heat exchanger, reulting in a compact, high-flux evice with reaonable preure rop characteritic. Tong an Lonon [1957] 11 reporte meaurement of friction factor an meh heat tranfer coefficient for inline plain weave laminate an taggere cro-ro matrice (no interweaving). They ue a calorimetric metho to meaure the local heat tranfer coefficient of one heate filament inie the array. Since other filament uptream of the meaurement filament were not heate, their correlation are expecte to preict heat tranfer coefficient that are higher than woul be expecte if all wire filament of the array were heate. Miyabe et al. [198] 9 report heat tranfer coefficient correlation for plain-weave creen laminate that are in cloe agreement with thoe of Tong an Lonon. However, they o not ecribe their meaurement technique. Armour an Cannon [1968] report preure rop correlation for plain-weave creen, but not lamination of creen. Xu an Wirtz [00] 15 evelop a moel for the in-plane effective thermal conuctivity of creen-laminate, an Koh an Fortini [1974] 8 report an empirical correlation for the cro-plane component. Previou correlation for the wire-element heat tranfer coefficient in creen laminate may preict overly high value, an there oe not appear to be a preure rop atabae for laminate ytem. The objective of the preent work i to ocument thermal/flui characteritic of plain-weave creen laminate an to evelop woven meh heat exchanger technology with particular attention to ingle-flui parallel plate heat exchanger. In thi paper we preent an analytical moel for heat tranfer in creen laminate ytem. Laboratory experiment leaing to meh preure rop an heat tranfer correlation are ecribe. A heat exchanger performance analyi i ue to elineate operating regime where the creenlaminate ytem offer uperior performance. THEORETICAL BACKGROUND Geometry of creen laminate Fig. 1 Screen laminate geometry. Figure 1 how two-imenional plain-weave creen tacke together to form a creen laminate. Each creen ha woven wire of iameter y an z, with axi parallel to the y-an z-axi, repectively. Wire pacing i eignate by the meh number, M y an M z. The laminate ha thickne, t = cf n( y + z ), where n i the number of creen layer of the lamination, an cf i the compreion factor. cf account for interleaving of wire filament of ajacent creen, an wire crimping at wire interection. Succeive creen can be arrange inline a hown in Figure 1, or in taggere configuration, where alternate creen layer are offet in the y an z irection by 0.5 M -1.

3 In thi work we conier only iotropic creen laminate, o y = z = an M y = M z = M. Uner thee conition, Xu an Wirtz [00] 15 how that the poroity (), pecific urface area (β), an effective thermal conuctivity of the laminate (ke y ) are given a cf ke cf y ( ) = π C M 1 (1) C K f π M (1 K β = 4(1 ) / () k 160 π M = [ f ( K f 1) C ) + C cf 1 ] + C K 4 where C = 13( M ) 384 ( M ) 640 f f f an cf K = k / k. The quantity cf (1-) i calle the reuce metal fraction. We note, in eq. (1) that the reuce metal fraction i olely a function of the wire iametermeh number prouct (M). Furthermore, M 1 eignate a tightly woven creen. In actuality, there i a phyical limit on the magnitue of M. For iotropic plain-weave creen where the thickne i limite to, M (max) = 1/ o that the = poroity i limite uch that 0 < cf (1-e) < Compreion factor, cf range in value from unity own to about 0.7, o the poroity of thee tructure can range from 100% own to approximately 47%. 1 (3) Fortini [1973]. 8 The Figure emontrate that the lamination can be tructure to have highly aniotropic effective thermal conuctivity with ke y /ke x approaching a maximum value of 6.. Furthermore, the ytem can be tructure to have a very large urface area. Eq. () ha the pecific urface area approaching 556 m -1 at maximum metal fraction when cf =1 with a wire iameter of mm (0.016 ). Thi i compare with a typical offet trip-fin array a ue in many highperformance exchanger application, which ha β(offet)= 54 m -1 [Kay an Crawfor, 1993]. 6 Heat Exchanger Implementation Fig.3 Heat exchange implementation of creen laminate an Schematic of tet ection. Fig. Thermal conuctivity ratio v. reuce metal fraction of plane-weave laminate. Figure plot the in-plane to cro-plane ratio of effective thermal conuctivity, ke y /ke x veru reuce metal fraction, cf (1-) for iotropic plane weave laminate. The cro-plane component i etermine uing an empirical correlation evelope by Koh an 3 Figure 3 how a woven meh creen laminate implemente a a heat tranfer urface in a parallel plate exchanger. The laminate, hown in ege-view in a channel having half-height H, an with, W act a a porou wall of poroity an thickne t. The laminate i oriente o that the large component of effective thermal conuctivity facilitate conuction away from the plate. A coolant approache the creen-laminate tructure at ma velocity G i an temperature T f,i. Heat (q) i conucte from the heate plate (at temperature T b ) into the creen meh, an then by convection to the flui flowing through the meh. The ketch at the right of the figure how the expecte creen-laminate an exit-plane coolant temperature itribution, T (y) an T f,o (y), repectively. The heat tranfer rate i given by [ T b T ] q U ( tw ) f, i = (4) where U i the effective conuctance of the porou wall an (tw) i the bae area.

4 Thin Porou Wall Heat Tranfer Moel The porou wall effective conuctance, U can be relate to the thermal an phyical characteritic of the woven tructure. The flui flow path length through the porou wall i hort an flow rate are relatively high, o local thermal equilibrium between the flui an oli phae i probably not achieve; a two energy equation moel i calle for. Wirtz [1997] 14 aume that the oli phae temperature i only a function of y, an the local heat flux between the flui an oli phae i characterize by Newton cooling law [ ( y) T ( x, y) ] q = h T (5) where h i the meh heat tranfer coefficient. Eq. (5) couple the oli an flui phae energy equation. Wirtz aume that T x, y) = ( T + T )/. Thi f f ( f, i f, o unneceary aumption lea to cloure of the two energy equation. The following i an extenion of the above-ecribe moel, which oe not make thi aumption. Aume the oli phae temperature i a function of y only. An energy balance on a y t lice of oli phae material, which balance the increae in internal energy of the flui phae with the net conuction in the oli phae, lea to the following energy equation cg [ T ( y) T ] i = (6) f, o f, i keyt y T with bounary conition: ( ) b T T 0 = T an = 0 y (ymmetrical heating aume). An energy balance on a x y element of flui, which introuce the particle heat tranfer coefficient through eq. (5), give θ βst + θ = 0 x where θ = T ( y) T ( x, y), with bounary conition f h θ ( 0, y ) = T ( y) T f, i. St = i the creen meh cg i Stanton number. Aume the porou wall ha uniform poroity an thickne. Then, the flui flowing through the porou wall will follow parallel treamline (y = contant) o that a parcel of flui will be expoe to oli phae material at a fixe temperature. Further aume that h = contant. Then eq. (7) can be integrate acro the porou wall y=h (7) to give T f, o ntu [ T ( y) T ](1 e ) ( y) T f, i = f, i (9) β t with ntu = St the number of tranfer unit of the meh. Subtitution of eq. (9) into eq. (6) an integration give the olution for the oli phae temperature itribution where T ( y) T T b T f, i [ m( H y) ] [ mh ] f, i coh = coh ntu ( ) (10) mh = Gˆ i 1 e (11) cg H Gˆ i i = i a imenionle coolant ke t y uperficial ma velocity. Then, the heat flux T q b = key may be etermine by y y=0 ifferentiating eq. (10). Subtitution of the reult into eq. (4) give UH key ( ) = mh tanh mh (1) Finally, recognizing that the maximum heat tranfer rate occur when all the coolant i heate to the bae temperature of the porou wall, we can write an expreion for the effectivene of the creen meh ntu qb 1 e η = tanh( mh ) (13) q (max) Gˆ b i T ( y) T f, o T ( y) Tf, i θ θ β St = t 0 x y= cont. (8) Fig. 4 4 Comparion of porou moel.

5 Figure 4 compare the effectivene of the preent moel, eq. (13) with that of Wirtz, [1997]. 14 The figure plot the exchange matrix effectivene veru number of tranfer unit for two repreentative imenionle uperficial ma velocitie. The figure how that the new moel give a mooth variation in effectivene a a function of ntu, an it preict η about 0% lower than the previou moel. The effectivene i een to aymptote to unity a ntu increae when G ˆ 0. Typical value of ntu an Ĝ for the work reporte here i are: 0.0 < ntu < 0.0 an 18 < Ĝ i < Screen-Laminate Preure Drop Correlation We potulate that the preure rop acro the meh, P, i functionally relate to flui an flow propertie a follow: P = fn( ρ, G, µ,, β, t, ) (14) G where G = i i the internal ma velocity. Then imenional analyi give f = fn(re) (15) 0.4 ρ P 1 where f = i the friction factor, G β t GD an Re = h i the meh Reynol number, with µ D = 4 = h the meh hyraulic iameter. β 1 Screen-Laminate Stanton Number Correlation In a imilar way, we potulate that the meh heat tranfer coefficient, h i functionally relate to flui an flow propertie a follow: Dimenional analyi give ( ρ, G, µ,, β, t, ke) h = f, (16) St = fn(re, Pr, / t, ) (17) where Pr i the Prantl number of the coolant. In the following, we ecribe experiment to etermine the pecific form of eq. (15) an (17). EXPERIMENTAL CHARACTERIZATION OF SCREEN LAMINATES i Experiment are performe to meaure the preure rop an porou wall effective conuctance. Then, the meh Stanton number i etermine from eq. (1). Experimental Setup an Proceure Preure rop an heat tranfer experiment are one in two ifferent channel-flow apparatu. A chematic of the tet ection for each apparatu i hown in Figure 3. The figure how an ege view of a creen laminate, of thickne t, locate in a parallel-plate channel, which i approximately 18 mm high x 100 mm wie. A flui, at ma velocity (G i ) an temperature (T f,i ) pae through the tet article. In the cae of the preure rop experiment, the channel i of open-loop, inuce-raft eign. Laboratory air pae through a honeycomb flow traightener; the tet article; a econ flow traightener; a plenum chamber an uitably long pipe to a laminar flow element, which meaure the volumetric flow rate; an, then to a variable pee exhauter. The preure rop acro the creen laminate (meaure at four uptream/owntream wall-preure port-pair) i meaure with an electronic manometer having ±4% accuracy. The laminar flow element ha ±3% accuracy. Heat tranfer experiment are conucte in a cloe loop chille water-flow apparatu. The tet rig conit of pump, flow enor, flow recirculator, an ata acquiition ytem. The flow ma velocity i meaure by a turbine flow enor, an a refrigerate recirculator/heat exchanger hol the inlet flow temperature contant at about 1 C. Thi reult in experiment with the Prantl number, Pr 9. Coppercontantan thermocouple meaure the uptream flui temperature an the bae temperature of the creen laminate ample (four location). The approach flow temperature i monitore at four location acro the channel pan at mi-height about H uptream from the tet article. The creen laminate ample i heate ymmetrically with two guare flat-plate heater, which reuce heat loe. The heating rate i applie o o that Tb Tf, i 10 C. In thi cae we meaure the overall conuctance, U, an ue eq. (1) to backcalculate the wire-element heat tranfer coefficient, h. We etimate that temperature meaurement are accurate to ±0. C, an q i meaure to ±4%. Screen Laminate Tet Article 5

6 apparatu were plotte a hown in Fig. 7 an Fig. 8. The friction factor an Stanton number correlation are foun in the cae of inline an taggere configuration repectively. Preure-rop correlation Fig. 5 Inline tacke plainweave creen. Fig. 6 Staggere tacke plain-weave creen. Commercial grae copper creen (k = 400 W/mK) i pre-coate with a oler bearing pate-flux (95% Sn/5% Pb, k = 55-60W/mK). Screen layer are tacke in a fixture, an the aembly i re-flow olere at 30 C. Figure 5 an 6 how multi-ply prototype with = 0.43 mm (0.017 ), M = 0 in -1. Two ifferent creen alignment are invetigate: the in-line configuration ha ucceive creen with wire filament aligne a hown in Fig. 5, an the taggere configuration ha creen tacke omewhat ranomly, while wire filament are aligne with the y-an z-axi, a hown in Fig. 6. Figure 5 how an inline configuration with = 0.7, β = 700 m -1, an ke y = 50 W/mK. Figure 6 how a taggere tacke configuration with = 0.63, β = 3350 m -1, an ke y 6 W/mK. Data reuction A total of 31 ample were tete with the following parameter range: 0.18 M 0.41, 1 n 10, an 0.64 cf 1.0. The poroity of each ample wa meaure with a 95%-confience level uncertainty of ±3.5%. The poroity range from 0.53 to Eq. () give the pecific urface area range at 01 m -1 < β < 668 m -1. The ample effective conuctivity wa meaure with a 95%-confience level of ±5.% [Xu an Wirtz, 00]. 15 The flow rate wa varie over the following range: 10 Re 3000 (friction factor), 30 Re 500 (heat tranfer experiment). A Monte Carlo error propagation imulation inicate the following 95%- confience level tolerance on compute reult: Re le than ±11%; f le than ± 13%; St le than ±18% [Park, 001]. 10 RESULTS Both preure rop an heat tranfer are meaure for iotropic creen laminate. For each meh ample, the ata from the experiment performe in both tet 6 Fig. 7 Friction factor of inline an taggere tacke creen laminate. Figure 7 ummarize preure rop meaurement for inline-tacke an taggere-tacke creen-laminate. The taggere-tacke creen-laminate friction factor i much higher than the friction factor of the inline configuration. The preent ata for the inline correlation i correlate with the following expreion 4.5 f = (18) Re The expreion contain an inertial lo term an a vicou term. Thee reult are compare with Tong an Lonon [1957] ata. 11 The preent creen laminate are bone wherea thoe of Tong an Lonon are not; boning fillet at wire interection probably give rie to higher inertial loe at high Reynol number. Eq. (18) reprouce the ata that generate it with a tanar error of ±0%. Figure 7 alo how the friction factor v. Reynol number correlation for taggere creen laminate tacking. In thi cae, the ata i correlate a follow 55.3 f = (19) Re The ata how that taggere tacking reult in an approximate two-fol higher preure lo than inline tacking at the ame flow rate. Eq. (1) reprouce the ata that generate it with a tanar error of ±15%.

7 Heat tranfer correlation Fig. 8 Moifie Colburn j-factor of inline an taggere tacke creen laminate. We are correlating ata in term of Colburn j-factor o that a irect comparion can be mae with the ata reporte by Tong an Lonon, who experimente with air (Pr = 0.7). From the imenional analyi it i evient that j-factor i functionally relate to Re,, an /t. We have choen to correlate the ata with a powerlaw. A regreion analyi yiele the following reult. The moifie j-factor (J) correlation for the inline correlation i plotte a continuou line an compare with Tong an Lonon [1957] 11 correlation for air. Tong an Lonon ata are ajute to conform to the efinition in the preent cae an then plotte a a ahe line. Comparing the preent correlation with the Tong an Lonon ata, the magnitue of the preent ata i maller than the correlation of Tong an Lonon at the higher Reynol number. Otherwie, the reult are in fairly cloe agreement. Thi implie that the preent correlation i applicable to coolant with 0.7<Pr<9.0. Eq. (1) reprouce the ata that generate it with a tanar error of ±18%. Alo hown in the Fig. 8 i the correlation of ata for taggere tacke laminate. At the ame Reynol number, the taggere configuration prouce a lower moifie j-factor than oe the inline configuration. Thi i a omewhat urpriing reult. j = St J = j Pr 3 =.63 Re t 0.65 =.63 Re t () (3) Eq. (3) reprouce the ata that generate it with a tanar error of ±10%. j = St Pr 3 = 5.86 Re t (0) Figure 8 ummarize heat tranfer ata (both inline an taggere configuration) in term of moifie j factor a a function of Reynol number. J = j 1 0. t 0.68 = 5.86 Re (1) Table 1 External an Internal Characteritic for PEC Analyi. 7 DISCUSSION Screen-laminate offer conierable eign flexibility. Ajutment of wire iameter an wire pitch allow for control of the tructure poroity, heat tranfer urface area to volume ratio, an effective thermal conuctivity. However, the friction factor an Stanton number of the heat exchange matrix are comparable to thoe of other heat tranfer urface. The quetion that mut be aree i: uner what conition oe the Characteritic Screen-Laminate Sphere External Characteritic Internal Geometric = 0.4, t = 4.3mm, H = 6.35mm Copper oli phae (k = 400 W/mK) Coolant i 300K (Pr = 5.9) M=0.63, cf=0.9 n =3, M=7.87cm mm <, = 0.8mm < 1.14mm Effective Conuctivity 83 W/mK, Xu an Wirtz [00] 38 W/mK, Haley [1986] Specific Surface Area β = 3000m -1, Eq. () 3158m -1 < β < 594m -1 Preure Drop Eq. (18) Ergun Corr. Dullien [1979] Matrix Heat Tranfer Coefficient Eq. (1) Wakao an Kaguei [198]

8 creen-laminate technology offer uperior performance. In the following, we ecribe a fixe outer geometry comparion [Webb, 1994] 13 of the performance of a creen-laminate exchange matrix with an exchange matrix coniting of an unconoliate be of pherical particle having the ame ma (poroity) an face area. The particle be i electe ince both exchange matrice can then be treate a porou meia, o that the thin-fin moel (eq. 5 13) can be ue to preict overall thermal performance. In thi way, performance moel election will not influence the ranking of performance. The theoretical poroity of a packe be of unconoliate phere epen on the packing arrangement [Kaviany, 1995]. 5 It can range from = 0.6 for face centere cubic packing to = for imple cubic. However, the poroity of a packe be i ifficult to control. A typical poroity for an unconoliate be i 0.4. Therefore the thermal performance of a plain-weave creen laminate having the ame poroity ( = 0.4) i compare with the pherical be ytem. Thi can be achieve with a creen-laminate ytem having M=0.63 with cf=0.9. Thi will reult in the two ytem having the ame ma an external imenion. However, we note that thi comparion i omewhat artificial in that M=0.63 cannot be achieve with plain-weave. The etail of the two ytem are ummarize in Table 1. We efine the heat uty ratio a U(creenlaminate)/U(packe be), an the preure rop ratio i efine a P(creen-laminate)/ P(packe be). Figure 9 plot the preure rop ratio a a function of uperficial ma velocity of coolant comparing the creen laminate matrix to pack be with phere iameter of 0.68 mm, 0.98 mm an 1.14 mm. In every cae, the creen laminate preure rop i ignificantly lower than that of the packe be. The creen laminate preure rop range from approximately 4-time maller than the packe be preure rop own to approximately 7-time le. The correponing heat uty ratio are plotte in Fig. 10. Figure 10 how that the heat uty ratio ecreae with increaing uperficial ma velocity. It alo ecreae with ecreaing phere iameter. For the cae coniere, the creen laminate provie uperior heat tranfer at lower uperficial ma velocitie an larger phere iameter. The break-even phere iameter increae with increaing uperficial ma velocity. We note that the creen-laminate wire iameter wa electe arbitrarily. A maller wire iameter woul reult in an increae in pecific urface area (β), meh Fig. 9 Fig PEC analyi in preure rop ratio. PEC analyi in heat uty ratio. heat tranfer coefficient (h), an the friction factor (f). A a conequence, the number of tranfer unit, an hence the effectivene of the heat exchange matrix woul increae leaing to an increae in the heat uty ratio at the expene of a proportional increae in preure rop ratio. CONCLUSIONS Screen laminate can be contructe to have a wie range of poroity, heat tranfer urface area an effective thermal conuctivity. The in-plane effective thermal conuctivity can be a much a 6. time greater than the cro-plane effective thermal conuctivity. Screen-laminate matrice can be moele a a porou meia. Since the flui flow path length through the porou wall i hort an flow rate are relatively high, local thermal equilibrium between the flui an oli phae i probably not achieve; o a two-energy equation moel i calle for. The preent

9 moel offer a phyically well-groune ecription of the heat tranfer procee in thin porou matrice. Dimenional analyi i ue to etablih the efinition of the imenionle group that characterize the preure rop an local heat tranfer coefficient. The preure rop relationhip conit of two parameter, f(re) while the heat tranfer coefficient relationhip conit of five parameter St(Re,Pr,t.,). Experiment with air an water have been ue to etablih correlation for the friction factor an meh Stanton number. A PEC performance comparion how that creen laminate ytem can generally be configure to offer thermal an preure rop performance uperior to unconoliate packe be matrice. ACKNOWLEDGEMENT/DISCLAIMER The Ballitic Miile Defene Organization through the Air Force Office of Scientific Reearch, USAF, ponor thi work uner contract number F The view an concluion containe herein are thoe of the author an houl not be interprete a necearily repreenting the official policie or enorement, either expree or implie, of the Ballitic Miile Defene Organization, the Air force Office of Scientific Reearch, or the U.S. Government. 9 Miyabe, H., Takahahi, S., an Hamaguchi, K., An approach to the eign of tirling engine regenerator matrix uing pack of wire gauze, Proc. 17 th IECEC, 198, pp Park, Ji-Wook, Thermal/flui characteritic of Iotropic plain-weave creen laminate a heat exchange urface, M.S. Thei, 001, Mechanical Engineering Department/MS 31, Univerity of Nevaa, Reno, NV Tong, L. S. an Lonon, A. L., Heat-tranfer an flow-friction characteritic of woven-creen an croe-ro matrixe, Tran. ASME, 1957, pp Wakao, N. an Kaguei, S., Heat an Ma Tranfer in Packe Be, Goron an Breach Science Pub., Webb, R. L., Principle of Enhance Heat Tranfer, John Wiley an Son, Wirtz, R. A., A emi-empirical moel for porou meia heat exchanger eign, Proc. 3 n National Heat Tranfer Conference, ASME HTD-Vol. 349, 1997, pp Xu, J. an Wirtz, R. A., In-Plane Effective Thermal Conuctivity of Plain-Weave Screen Laminate, Proc. Therme 00, Santa Fe, NM, 00. REFERENCES 1 Ahby, M., Evan, A., Fleck, N., Gibon, L., Hutchinon, J., an Waley, H., Metal Foam, A Deign Guie, Butterworth Heinemann., 000. Armour, J. C. an Cannon, J. N., Flui flow through woven creen, AIChE J., Vol. 14, 1968, pp Dullien, F. A. L., Porou Meia: Flui Tranport an Pore Structure, Acaemic Pre, Haley, G. R., Thermal conuctivity of packe metal power, Int. J. Heat Ma Tranfer, Vol. 9, 1986, pp Kaviany, M., Principle of Heat Tranfer in Porou Meia, n e., Springer, Kay, W. M. an Crawfor, M. E., Convective Heat an Ma Tranfer, 3 r en., McGraw Hill, Kay, W. M. an Lonon, A. L., Compact Heat Exchanger, 3 r en., McGraw-Hill, Koh, J. C. Y. an Fortini, A., Preiction of thermal conuctivity an electrical reitivity of porou metallic material, Int. J. Heat Ma Tranfer, Vol. 16, 1973, pp