Characterization of the heat transfer in open-cell metal foam

Transcription

1 Characterization of the heat tranfer in open-cell metal foam C. Briano-Calcagno, J. Fontánez-Delgado & N. Dukhan Department of Mechanical Engineering, Univerity of Puerto Rico Mayagüez, Mayagüez, P.R., U.S.A. Abtract The material characterization of open-cell aluminum foam in term of heat tranfer i preented. A one-dimenional heat tranfer model for the combined convection and conduction in the foam i ummarized. The model ue the foam parameter that are uually reported by the manufacture uch a: the urface area, the relative denitie, the ligament diameter and number of pore per inch. The model predict the temperature profile in the foam. The model wa applied uccefully to a ample of aluminum foam having ten pore per inch and wa verified by direct experiment. Excellent agreement between the prediction of the model and the experimental data wa obtained. The aumption of a onedimenional heat tranfer wa validated. The effect of the air flow rate on the heat tranfer i alo tudied in order to further characterize the heat tranfer behavior of the foam. The reult for an aluminum foam ample of 10 pore per inch are preented at thee flow rate. Keyword: heat tranfer, open-cell metal foam, air flow rate. 1 Introduction Metal foam are a relatively new cla of material with novel propertie and a promie for ignificant performance gain. They have been ued in aeropace geothermal operation, petroleum reervoir, high-power batterie for lightweight cordle electronic and compact heat ink for power electronic [1,, 3]. The open poroity, low relative denity and high thermal conductivity of the cell edge, the large acceible urface area per unit volume, and the ability to mix the cooling fluid by promoting eddie [4]; all make metal foam heat exchanger efficient, compact and light weight. Current model for

2 44 High Performance Structure and Material II packed bed are not applicable to high poroity metal foam due to the difference in poroity and geometry [3, 5]. The porou matrix conit of tortuou, irregularly haped flow paage. The flow re-circulate at the back of the olid fiber, and for pore-cale Reynold number greater than 100, turbulence and unteady flow occur [6]. The geometric complexity prevent exact olution of the tranport equation inide the pore [3, 7, 8]. Due to their novelty metal foam are till incompletely characterized. Reliable model of the heat tranfer in foam would certainly help the engineering reearch community. A number of tudie were undertaken to fill thi gap, [9, 10, 11]. The preent work provide a macrocopic lumped-parameter treatment to determine the temperature ditribution in open cell metal foam in a forced convective mode. The analyi ue the typical parameter reported by the foam manufacturer. The implicity and applicability of the preent approach eliminate the need for rigorou microcopic analytical or numerical modeling of the flow and the heat tranfer in and around the pore. Another advantage i that the current model i eaily verified by imple experiment, a decribed below. Once validated, the model can be ued to tudy the effect of the flow rate on the temperature profile. Heat tranfer model Conider a one-dimenional olid fin of length L, width W and thickne t a hown in fig. 1. Let the bae temperature be T b. The governing equation for the heat tranfer through the fin i readily available [1]: d θ m = 0 θ, (1) dx where θ = T T and m the fin parameter. For an inulated tip, dθ /dx = 0 at x = L, the olution to eqn. (1) i [1]: θ coh m ( L x) =, () θ b coh m L where θ b = T b T. Figure 1: Schematic of a contant cro-ectional area fin.

3 High Performance Structure and Material II 45 The tudy develop imilar cloed form reult for a thin piece of porou foam having a contant cro-ectional area and an inulated tip. Unlike the olid fin cae, the coolant flow through the foam, a hown in fig. 1. Thi condition give rie to forced convection heat tranfer inide the pore of the foam. The heat tranfer coefficient for thi convection, h, i availble [4, 8] and i different than h. For the foam, conider now a control volume of thickne dx in the x- direction, a hown in fig.. Figure : Control volume for the foam. The conervation of energy i applied for teady-tate condition to thi control volume and neglect radiation. The conduction term are readily given by Fourier law; the convection term by Newton law of cooling: dt dt k A cond = k A cond + h A ( T T ) (3) x x + dx conv dx dx where k i the conductivity of the olid fiber and A cond i the area for conduction given by: A cond = A c A, (4) p where A c i the cro-ectional area and A p i the area occupied by the pore. The area wa approximated by []: A cond = A c ( 1 ε ), (5) where ε i the poroity. For the control volume of fig., the area for convection i imply given by: A conv = σ. A c dx, (6) where σ i the urface area per unit volume, which i uually reported by the foam manufacturer. Subtituting for the area, implifying and rearranging, eqn. (3) then become: d θ m = 0 θ, (7) dx where θ i analogou to θ above and m i a new foam parameter given by:

4 46 High Performance Structure and Material II m = k h σ ( 1 ε ). (8) For an adiabatic tip, the one-dimenional foam temperature ditribution i given by eqn. () except for replacing m with m : θ coh m ( L x) =. (9) θ coh m L 3 Experiment b To verify the model, one ample of commercially available aluminum, alloy 6101-T6, foam having ten pore per inch wa teted. The foam parameter were σ = 803 m /m 3 and ε = 0.918, [13, 14]. The dimenion of the ample were W = mm, t = 50.8 mm and L = 50.8 mm. The ample wa glued to a 1.7-mm thick olid aluminum bae uing thermal epoxy, fig. 3. Figure 3: Schematic of foam ample. The poroity of the ample wa calculated by uing the ma, the volume and the denity of aluminum alloy 6101-T6. Experiment were performed uing a wind tunnel in the Porou Media Reearch Lab of the Univerity of Puerto Rico at Mayagüez. The tunnel wa a mall open-loop tunnel hown chematically in fig. 4. The ize of the tunnel tet ection wa 14.9 cm by 30. cm. A thin thermfoil heater, with a urface area identical to the ample olid aluminum bae, wa placed at the bae of the foam. The heater wa connected to a DC power upply to provide a power of 197.6W. The four ide of the foam ample that contituted it outer perimeter were inulated uing Styrofoam inulation, and the ample wa placed in the tunnel tet ection. The other two ide were perpendicular to the flow direction and remained open to the airflow.

5 High Performance Structure and Material II 47 Thirteen thermocouple were ued to meaure the temperature at trategic location in the foam a well a the ambient and the bae temperature. Thee location are hown in fig. 3 by the mall circle and are lited in table 1. Smaller pacing of the thermocouple wa ued cloer to the bae to capture the teep drop in temperature. Thee were attached to an automatic data acquiition ytem which wa connected to a computer, a hown in fig. 4. Figure 4: Schematic of the experimental et-up. Table 1: Thermocouple location. Thermocouple No. Location, x, cm Ambient Table how the dynamic preure of the air for 10ppi, after traveling through the foam, which wa meaured uing the manometer. The preure wa ued to calculate the average velocity and the actual flow rate. The temperature meaurement for the ample were taken varying the exit opening of the tunnel at 5%, 50%, 75%, and 100%. The flow rate and correponding average velocity are hown in table. The temperature meaurement were taken at z = 0.64, 1.7,.54, 3.81 and 4.44 cm. The dependence of temperature on the y-direction wa eliminated baed on the ymmetry of the boundary condition, i.e., inulation at y = 0 and y = cm.

6 48 High Performance Structure and Material II The uncertainty in the location of the thermocouple wa ± 0.8 mm. A for the temperature, the combined uncertainty wa ± 1 o C [15]. Table : Dynamic preure. Flow Rate Dynamic Preure (Pa) Average Velocity (m/) Flow Rate (m 3 /) 5 % % % % Reult and dicuion The firt part of thi work wa concerned with validating the one-dimenional aumption, which i fundamental to the development of the analytical model. Fig. 5 and 6 are plot of the temperature ditribution a a function of the nondimenional ditance along the foam, at a flow rate of 0.1 m 3 / and 0.07 m 3 /, repectively. It i clear that, at a given flow rate, the temperature ditribution for the five different z-location 0.64, 1.7,.54, 3.81 and 4.44 cm are very imilar. Thi prove that the temperature i not a function of the flow direction (z), but a function of the direction perpendicular to the flow direction (x). The third direction (y) i eliminated due to the ymmetry of the boundary condition, i.e., inulation at y = 0 and at y = cm. Figure 5: Temperature ditribution (10ppi) at 100% flow rate. Equation (9) wa ued to generate the analytical curve hown by the olid line. The analytical model agree well with the experimental reult. The temperature ditribution along the foam decreae in exponentially with the ditance along the foam. It aymptotically reache zero a the ditance from the bae increae. Therefore, mot of the heat tranfer take place in the region cloe to the bae. Both the analytical and the experimental reult alo agree on

7 High Performance Structure and Material II 49 predicting thi phenomenon. A few point for the z = 3.81 mm cae lie below the zero temperature line, i.e., the temperature in the foam i le than that of the ambient, which i phyically impoible. Therefore thee point are attributed to experimental error. Figure 6: Temperature ditribution (10ppi) at 5% flow rate. Figure 7: 5% Flow rate on temperature ditribution. The validation of the one-dimenional aumption wa encouraging and it allow for the tudy of other phenomena that contribute to the characterization of the novel model. One of thee i the effect of the flow rate. The effect of the flow rate on the temperature ditribution can be een in fig. 7 and 8 for the 5% and 100% flow, repectively. The experimental data point are thoe for the central location in the foam, i.e., y = 50.8 mm and z = 5.4mm. Thee were choen a repreentative value for the one-dimenional temperature profile. The agreement between the experimental data and the analytical prediction i excellent. The experimental data how variou point that do not lie preciely on the analytical curve, epecially around a dimenionle ditance of 0.. Thee

8 50 High Performance Structure and Material II are due to random and ytematic experimental error. Even though thee diturbance occur, the data remain within the uncertainty. Since thee run repreent the maximum and the minimum flow rate, it i logical to conclude that the one-dimenional aumption and the model are valid for all flow in between. The next tep i to ae the effect of the flow rate on the temperature profile. Figure 8: 100% Flow rate on temperature ditribution. Figure 9 i a plot of the one-dimenional temperature profile according to the analytical model of the 10ppi ample for flow rate of 5%, 50%, 75%, and 100%. The temperature profile decay in an apparent exponential fahion. The curve for the 5% cae i higher than thoe for the 50%, 75%, and 100%; which indicate lower heat tranfer. The temperature ditribution for the 50, 75 and 100% flow cae are very imilar, which how a weak effect of the flow rate for The temperature of the foam reache that of the ambient at a dimenionle ditance of 0.6, approximately. Figure 9: 10ppi Temperature ditribution model.

9 High Performance Structure and Material II 51 Figure 10 how the experimental reult for 5%, 50%, 75%, and 100% flow. The trend can be identified among the firt ix point, x/l = 0.15, due to the high heat tranfer rate that occur near the bae of the fin, which i hown in the mall window on the figure. It can be een that a the flow rate i increaed, the level of the temperature ditribution curve decreae. Thi indicate a higher heat tranfer rate for higher flow rate. The ame obervation of fig. 9 can be made about fig. 10. The temperature ditribution for the 5% flow cae lie above all the other cae, with all other cae being imilar. Figure 10: Flow rate effect on temperature ditribution. 5 Concluion The combined convection and conduction heat tranfer in open-cell metal foam wa invetigated uing a one-dimenional model. One advantage of the model i that it ue the typical parameter reported by the foam manufacturer. The temperature profile wa determined for one aluminum foam, uing air a the fluid. The model and the one-dimenional aumption were verified by direct experiment. Preliminary reult howed excellent agreement between the model prediction and the experimental data. When the flow rate i raied, the convection in the foam ample increae, cauing an increae in the heat tranfer rate. The reult are encouraging and provide bai for further verification of the validity of the analytical model in term of the thickne of the foam in the flow direction. Reference [1] M. F. Ahby, A. G. Evan, N. A Fleck, L. J Gibon, J. W. Hutchinon, and H. N. G. Wadley, Metal Foam, A Deign Guide, Butterworth- Heinemann: Woburn, MA, Chapter 1, alo pp , 000. [] D. Sulline, and K. Daryabeige, Effective thermal conductivity of high poroity open cell nickel foam, Proc. of the 35th AIAA Thermophyic Conf., Anaheim, CA, 001.

10 5 High Performance Structure and Material II [3] K. Vafai, and C. L Tien, Boundary and inertia effect on convective ma tranfer in porou media, Heat and Ma Tranfer, 5(8), pp , 198. [4] A. F. Batawro, Effectivene of open-cell metallic foam for high power electronic cooling, Proc. of the Sympoium on the Thermal Management of Electronic: Anaheim, CA, [5] A. Bhattacharya, V. V Calmidi and R. L Mahajan, Thermophyical propertie of high poroity metal foam, Heat and Ma Tranfer, 5(8), pp , 00. [6] A. F Batawro, A. G. Evan and H. A. Stone, Evaluation of cellular metal heat tranfer media, Harvard Univerity Report, MECH 35, [7] S. Decker, S. Möβbauer, D. T Nemoda, and T. Zapf, Detailed experimental characterization and numerical modeling of heat and ma tranport propertie of highly porou media for olar receiver and porou burner, Lehrtuhl für Strömungmechanik Univerität Erlangen- Nürnberg Cauertr. 4, D Erlangen, Germany. /CleanAir6_NUMERIC.pdf [8] M. L. Hunt and C. L. Tien, Effect of thermal diperion on forced convection in fibrou media, Heat and Ma Tranfer, 31(), pp , [9] L. B. Youni, and R. Vikanta, Experimental determination of the volumetric heat tranfer coefficient between tream of air and ceramic foam, Heat and Ma Tranfer, 36(6), pp , [10] D. A. Zumbrunnen, R. Vikanta and F. P. Incropera, Heat tranfer through porou olid with complex internal geometrie, Heat and Ma Tranfer, 9(), pp , [11] H. L Pan, O. Pickenacker, K. Pickenacker, D. Trimi, S. Möβbauer, K. Wawrzinek, and T. Weber, Experimental determination of the effective heat conductivitie of highly porou media, Lehrtuhl für Strömungmechanik Univerität Erlangen-Nürnberg Cauertr. 4, D Erlangen, Germany. erlangen.de/ber/pdf/effwl.pdf [1] F. P. Incropera, and D. P De Witt, Fundamental of Heat and Ma Tranfer, John Willey and Son: New York, pp , 00. [13] B., Ozmat, B., Leyda and B. Benon. Peronal communication, 00, ERG Material and Aeropace Corp, Oakland, CA. [14] ERG Material and Aeropace, Oakland, CA, [15] R. Figliola and D. Bealy, Theory and Deign for Mechanical Meaurement, John Wiley and Son: New York, pp.