Heat transfer studies in a vertical channel filled with a porous medium

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1 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 Heat transfer studies in a vertical channel filled with a porous medium Pradeep M Kamath 1, C Balaji 2 and S P Venkateshan 1 Abstract: This paper reports the results of an experimental study on the enhancement in the heat transfer from a heated aluminium plate placed in a vertical channel and filled with an aluminium metal foam. Hydrodynamic and heat transfer experiments have been conducted for different foam thicknesses. The results of the hydrodynamic experiments show no significant variation in the pressure drop with an increase in the foam thickness. However, an increase in the foam thickness contributes an average heat transfer enhancement of 2 to 4 times over an empty channel for the same Reynolds number. Correlations for Nusselt number are also developed for porous and empty channels. From these correlations, the heat transfer coefficient on the heater wall is found to be proportional to the foam thickness for a given Reynolds number. However, for an empty channel, the heat transfer coefficient is found to be independent of the channel width for a given Reynolds number. Nomenclature C form drag coefficient, 1/m g acceleration due to gravity, m/s 2 h wall heat transfer coefficient, W/m 2 K H total thickness of metal foam, m k f thermal conductivity of air, W/m K K permeability, m 2 L length of metal foam in flow direction, m Nu H Nusselt number, hh/k f P pressure drop, Pa PPI number of pores per inch U inlet velocity, m/s Re H Reynolds number, UH/ν 1 Heat Transfer and Thermal Power Laboratory, Department of Mechanical Engineering, IIT Madras, Chennai INDIA 2 Corresponding author

2 112 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 T T avg T temperature excess above ambient, T avg -T, C average wall temperature, C ambient temperature, C Greek symbols ν kinematic viscosity of air, m 2 /s ρ density of air, kg/m 3 1 Introduction Compactness and high rates of heat removal of thermal system have emerged as a challenge to the electronic industry. A lot of research in convective cooling has been done in the area of electronic cooling. Use of metal foams in the convection cooling of electronic devices has gained attention due to the high surface area to volume ratio, light weight, high heat transfer enhancement per unit pressure drop associated with them. Several experiments and numerical studies to determine the role of metal foams in heat transfer enhancements are reported in literature. Boomsma, Poulikakos, and Zwick (2003), compressed open cell foams and used them as heat exchangers for heat transfer enhancement applications. The compressed aluminium foams performed well not only in heat transfer enhancement but also resulted in significant improvements in the efficiency when compared to commercially available heat exchangers, under identical conditions. Jeng and Tzeng (2007), experimentally, investigated convective heat transfer and pressure drop in a metallic porous block with confined slot air jet for various parameters such as, the ratio of the jet nozzle width to the porous block height, the ratio of the jet-to-foam tip distance to the porous block height, and the jet Reynolds number. Their results indicated that the average Nusselt number with a metal foam was 3-5 times than that without it. The average Nusselt number increased with the Reynolds number and decreased with the porous block height. Calmidi and Mahajan (2000), studied forced convection in metal foams both experimentally and numerically using a thermal non-equilibrium model. They concluded that the thermal transport effect is low for foam-air combination compared to the foam-water combination. Chein, Yang, Tsai, and Lu (2010), fabricated a copper foam using electro forming technique and used it as a heat sink material to study the performance of heat sinks. The thermal resistance of the metal foams was compared with the plate fin, pin fin and no fin arrangements. It was reported that the thermal resistance decreases with a decrease in the porosity of the foam material. In a recent study by DeGroot, Gateman, and Straatman (2010) and Jaeger, Joen, Huisseune, Ameel, Scham-

3 Heat transfer studies in a vertical channel filled with a porous medium 113 pheleire, and Paepe (2012) the significance of thermal contact resistance has been addressed. They have reported that even with a press fit significant heat transfer enhancement can be obtained. Brazing of metal foams is one of the best permanent bonding techniques, but is costly and requires highly skilled labour. Moreover, the metal foam cannot be reused once it is bonded to a surface. Hwang, Hwang, Yeh, and Chao (2002), carried out transient single blow experiments on metal foams (of porosities of 0.7, 0.8 and 0.95) filled in a horizontal channel and determined the interstitial convective heat transfer coefficient using an inverse method. They reported that for a given Reynolds number, the volumetric heat transfer coefficient inside an aluminium foam increases with a decrease in the porosity and increases with an increase in the Reynolds number, for a given porosity. The authors proposed a correlation for the Nusselt number based on the pore diameter in terms of the pore Reynolds number. Hunt and Tien (1988), studied the effect of thermal dispersion on forced convection in metal foams. They tested aluminium, nickel, and carbon foams to provide a range of thermal conductivities. All the tested samples had very high porosities in the range of They found that the heat transfer increased with decreased porosity and concluded that it was due to thermal dispersion. Salas and Waas (2007), experimentally, investigated in a horizontal channel, the effect of foam thickness on convective heat transfer of metal foam sandwich panels, with foam thicknesses ranging from 6.4 mm to 25.4 mm. The heat transfer coefficient was found to increase with an increase in the foam thickness. The rate of increase in the heat transfer was found to decrease with an increase in the foam thickness. Recently Mancin, Zilio, Rossetto, and Cavallini (2012) conducted experiments in a horizontal channel to study the effect of foam thickness on the pressure drop and heat transfer on 20 pores per inch (PPI) foams of same porosity with 20 and 40 mm foam thicknesses. The foam thickness was found to have no significant effect on the pressure drop, whereas the heat transfer coefficient of a 40 mm thick foam was found to be smaller than the heat transfer coefficient of a 20 mm thick foam. In all of the above cases, metal foams were brazed to the hot surface. There are very few studies that do not consider a permanent bonding between the hot surface and the porous medium. Venugopal, Balaji, and Venkateshan (2010), experimentally, studied the heat transfer enhancement in a vertical channel using porous inserts made from perforated brass sheets, with different porosities. These porous structures were mechanically pressed against the heat transfer surface. They concluded that, the low porosity inserts show better heat transfer performance due to fin effect, when compared with the high porosity inserts. Kim, Kang, and Kim (2001) studied the effect of presence of an aluminium foam on the flow and convective heat transfer in an asymmetrically heated channel. The metal foams were mechanically

4 114 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 pressed until the convective heat transfer rate reached an asymptotic limit. Correlations for the friction factor and the Nusselt number were reported as a function of the Darcy number. The review of literature shows that for best results the metal foam is to be brazed with the base surface. However, brazing is a challenging task due to the requirement of correct temperatures to be maintained during brazing. Howard and Korinko (2003) reported that high temperature brazing results in creep damage. Furthermore, brazing gives a permanent weld and prevents reuse of the metal foams. The study of enhancement in heat transfer with high porosity foams of 10 mm foam thickness has already been conducted by the authors in an earlier work Kamath, Balaji, and Venkateshan (2011). In the present study, the earlier work has been extended for different foam thicknesses to study the effect of foam thickness on the pressure drop and heat transfer. The goal is to quantify the heat transfer rate of a channel filled with a metal foam and compare with that of an empty channel. 2 Experimental Setup The experimental setup consists of a vertical wind tunnel with an axial fan mounted at the bottom, the test section, data acquisition system, and a desktop computer as shown in Fig. 1. Details of the vertical wind tunnel are given in Venugopal, Balaji, and Venkateshan (2010) and will not be elaborated here. The schematic diagram of the test section and the heater plate assembly are given in Kamath, Balaji, and Venkateshan (2011). A photograph of the front sectional view of the test section is given in Fig. 2 and the schematic diagram of the test section is shown in Fig. 3. The test section consists of a heater plate assembly placed in a vertical duct filled with metal foams. The heater plate assembly consists of two aluminium plates of 3 mm thickness with a flat heater sandwich between them. The inner surface of each aluminium plate has milled grooves to accommodate thermocouples. The heater is made by winding nichrome wire over mica sheet. The aluminium plates are fastened to each other with the heater at the center, and the heater plate assembly has a size of mm. The vertical duct is rectangular in cross section and is made up of non-rubberized cork wall of 25 mm. The cork is supported on plywood boxes of 12 mm wall thickness. The plywood boxes are clamped to the outer wooden wall of the test section by L clamps. The breadth (B) of the vertical channel is always fixed to be 250 mm and the width (W) of the channel is varied according to the foam thickness. Metal foams of 10, 20, 30 and 45 pores per inch (PPI) and of foam thickness H (please refer to Fig. 3 for the legends B, W and H) 10 and 20 mm are used in the present study. Metal foams of 30 mm are made by mechanically pressing 20 mm thick foam with 10 mm thick foam of similar porosity and PPI. Metal foams are made of AlSi7Mg aluminium alloy and

5 Heat transfer studies in a vertical channel filled with a porous medium 115 Test section Convergent section Settling Chamber Data logger Divergent section Data acquisition system Axial fan Fan speed control Air Inlet DC Power supply and Desktop PC Figure 1: Photograph of the vertical wind tunnel with the data acquisition system have been supplied by m-pore, Germany. Temperatures on the aluminium plate surface, cork inner surface and cork outer surface and air inlet are measured by K type thermocouples. The heat loss through the cork insulation is determined by a conduction analysis, and the estimated heat loss is accounted for the heat transfer calculations. The thermocouples have an uncertainty of ±0.2 C. The inlet velocity of air into the test section is measured at a distance of 10 mm from the upstream end. The inlet velocity is measured by thermal anemometer with an uncertainty of ± 0.1 m/s. Pressure drop across the metal foam is measured with a digital manometer. The power input to the heater is supplied from a stabilized DC power supply. The panel of the DC power supply shows the voltage and current supplied to the heater. The uncertainties in the voltage and current measurement are ±1 V and ± 0.01 A

6 116 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 Proving ring Outer wall Heater plate assembly Metal foams Cork wall L clamp Inner box Bell mouth Figure 2: Photograph of the front sectional view of the test section respectively. Metal foams are mechanically pressed against the heater plate assembly by tightening with the help of screws provided on the test section. The tightening load is chosen such that there is no significant variation in the heat transfer with tightening load. The tightening load is such that the metal foams are not compressed, but have a good contact with the aluminium plate surface. Hydrodynamic experiments have been conducted to study the variation of pressure drop with inlet velocity, to account for the pumping power. The hydrodynamic experiments have been conducted at ambient temperature without powering the heater. Pressure drop across the metal foam is measured, by varying the flow rates. The flow rates and hence the inlet velocity is varied by varying the rpm of the axial fan mounted on the bottom of the wind tunnel. The room temperature during the experiment was found to vary from 30 to 33 C. Heat transfer experiments have been conducted at steady state. A variation of temperature less than ±0.2 C in ten minutes, is assumed to indicate steady state. The heat transfer experiments have been conducted by varying the inlet velocity and the power input to the heater for different PPI and foam thicknesses. The foam thickness values for the hydrodynamic and the heat transfer experiments

7 10 Heat transfer studies in a vertical channel filled with a porous medium L= g W Air inlet Section A A 1 10 A B=250 A 8 9 H All dimensions are in mm Foam thickness 1. Inner wooden boxes 2. Pressure taps 3. Metal foam inserts 4. Aluminium plate 5. Heater 6. Location of inlet velocity measurement 7. Tightening screws 8. L clamps 9. Outer wooden box 10. Non-rubberized cork insulation Figure 3: Schematic diagram of the front and top views of the test section

8 118 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 have been chosen to be 10, 20 and 30 mm, resulting in channel widths of 27, 47 and 67 mm respectively. 3 Results and Discussion The metal foams are specified based on the Pores per inch (PPI) specified by the manufacturer. The metal foam can be further characterized by determining the porosity, the pore diameter and the fiber diameter. The porosity of the metal foams is defined as the ratio of void volume to the total volume. The porosity of the metal foam is determined by measuring the dry mass of the metal foams with a digital balance, and the porosity of the metal foams can be computed knowing the density of the metal foam material and the total volume of the metal foam. The pore diameter is the average diameter of the pores on the surface of the metal foam and the fiber diameter is the average diameter of the fiber or the struts or the ligaments connecting the pores. A photograph of the metal foam (refer Kamath, Balaji, and Venkateshan (2011)) is taken with a digital camera, and an image processing software is used to measure the average pore diameter and the average fiber diameter. The characteristics of the metal foams are reported in Tab Flow Characteristics The flow characteristics of the metal foams include the permeability and the form drag coefficient. The permeability (K) is a measure of the ability of a porous material to transmit the fluid through it. The form drag coefficient (C) is the resistance to fluid flow by the solid and is proportional to the square of the inlet velocity. While the permeability of the metal foam is associated with the viscous forces, the form drag coefficient is associated with the inertia forces, causing the pressure drop. The flow characteristics can be estimated by conducting a simple hydrodynamic experiment. The behaviour of metal foams in hydrodynamic experiments can be represented as a quadratic and is given as P L = µ K U + ρcu 2 (1) Eqn. 1 is generally known as Hazen-Darcy-Dupuit equation. The pressure drop data is used to determine the permeability and the form drag coefficient. Fig. 4 shows the variation of pressure drop with inlet velocity for the different metal foams tested. The legends in Fig. 4 are represented as a_b_c, where a is the PPI of foam, b is the foam thickness and c is the porosity of foam. The pressure drop is found to be inversely proportional to the porosity of the foam. For the case of 10 PPI, a variation in the pressure drop is found with the foam thickness, but this cannot be considered to be significant as explained below.

9 Heat transfer studies in a vertical channel filled with a porous medium 119 P/L Unit pressure drop, Pa/m 2,000 1,500 1, _10_ _10_ _10_ _10_ _30_ _20_ _20_ _20_ _20_ _30_ U, Inlet velocity, m/s Figure 4: Variation of unit pressure drop with inlet velocity for different metal foams Dukhan and Patel (2008) proposed an equivalent length scale in multiples of the cell size to measure the flow properties of metal foams accurately. They studied the effect of metal foam length along flow direction on flow parameters of the foam and concluded that an equivalent length of 100 cells in the flow direction is required for the accurate measurement of pressure drop and hence the flow properties. In the present study, the metal foams have a length of 150 mm along the flow direction with a cell size of 4.9 mm for 10 PPI foams. The equivalent length in terms of the number of cells turns out to be 30, which is only one third of the required length. This results in an increase in the form drag coefficient and a fluctuation is observed in the estimated permeability values. As the equivalent length of the number of cells in the flow direction is only 30, the variation in flow properties can be considered as insignificant. However for 45 PPI foam, the pore diameter is 1.6 mm and there are roughly 100 cells in the flow direction. The pressure drops for 45 PPI foam of 10 mm and 20 mm foam thickness are similar. Therefore, it is concluded that an increase in the foam thickness does not contribute to a significant increase in the pressure drop. Tab. 1 reports the measured and estimated parameters of the metal foams used in the present study.

10 120 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 Table 1: Measured characteristics of the the metal foams Foam Foam Pore Ligament Porosity Permeability Form drag thickness diameter diameter K 10 7 coeff. C PPI mm mm mm % m 2 m Heat Transfer Characteristics The heat transfer coefficient from the aluminium surface is given as h = Q Q loss 2A T where Q is the heat input to the heater, Q loss is the heat loss through the cork, and T is the excess temperature over ambient obtained as the difference of average surface temperature of the plate and the ambient temperature and 2A is the total surface area of the heater plate on both sides in contact with metal foams. To compare the experimental results with those in the open literature, the heat transfer coefficient obtained in the present study is converted to a dimensionless Nusselt number, with the total thickness of the foams as the characteristic length. The properties of air at the inlet temperature is used for all the calculations. The non dimensional numbers are defined as follows Nu H = hh k f Re H = UH ν For purpose of comparison with literature, Nusselt and Reynolds numbers retrieved from Kim, Kang, and Kim (2001) and Venugopal, Balaji, and Venkateshan (2010) are modified to Nusselt and Reynolds number based on the thickness of the metal foam. The flow parameters reported for comparison are given in Tab. 2. (2) (3) (4)

11 Heat transfer studies in a vertical channel filled with a porous medium 121 Table 2: Details of flow parameter in literature used for comparison with the present study K1 V1 V2 V3 Length (cm) Width (cm) Height (cm) Material Al-6101 Brass Brass Brass Pore density(ppi) Porosity Permeability, K 10 7 m Form drag coeff, C m Thermal conductivity ks W/mK reported by Kim, Kang, and Kim (2001) and by Venugopal, Balaji, and Venkateshan (2010) Nusselt number, NuH V1_10_0.92 V2_10_0.89 V3_10_0.85 K1_09_ _10_ _20_ _30_ ,000 1e+04 Reynolds number, Re H Figure 5: Comparison of Nusselt number with open literature (V1, V2, V3 are data reported by Venugopal, Balaji, and Venkateshan (2010) and K1 is the data reported by Kim, Kang, and Kim (2001))

12 122 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 Fig. 5 shows a comparison of the Nusselt number with the Reynolds number obtained by using the foam thickness as the characteristic length in the present study with data in literature. The legends in Fig. 5 are represented as a_b_c, where a is the PPI of foam or the author reference as given in Tab. 2, b is the foam thickness and c is the porosity of foam. Nusselt numbers from literature are found to be slightly higher than the corresponding values in the present study. This may be due to the higher thermal conductivity of the material of the foam used in literature. The thermal conductivity of metal foams used in the present study corresponds to the AlSi7Mg aluminium alloy and has a value of 165 W/mK. Fig. 6 shows the variation of Nusselt number with Reynolds number for different aspect ratios. In Fig. 6, the legends are represented as a_b_c, where a, b and c represents the PPI, thickness and the porosity of the metal foam respectively. All the metal foams tested have porosities in the range of 0.9 to It is seen that by increasing the foam thickness, the Nusselt number increases for a given Reynolds number. The experiments have been conducted for various inlet velocities and different heat input levels. The results of the experiments show that for a Reynolds number greater than 400, the heat transfer coefficient is independent of the heat input. The effect of buoyancy forces is thus negligible for Reynolds number greater than 400 and hence forced convection prevails. For a Reynolds number below 400, there is a small variation of Nusselt number with varying heat input showing the existence of mixed convection. The enhancement of heat transfer with foam thickness can be quantified based on Reynolds number of flow, aspect ratio L/H and the porosity for the forced convection dominant region. A correlation is developed for Nusselt number of porous channel and is given as. Nu H = 20.42Re H (L/H) 0.95 (1 φ) 0.35 (5) Eqn. 7 has a correlation coefficient of 0.97,an RMS error of 14% based on 168 data points. The exponent of aspect ratio (L/H) is which is close to one, which shows that the Nu H is proportional to foam thickness for a fixed value of Re H and heat transfer coefficient is approximately proportional to the square root of H (h H 0.44 ) for a given inlet velocity. The correlation is valid for Reynolds number in the range of 400< Re H <7300, porosity 0.9< φ <0.95, and aspect ratio of 2.5 to 7.5. Fig. 6 shows the solid lines corresponding to the correlated values of the 10 PPI foam for different aspect ratios. Experiments are also done in an empty channel without metal foams. The Nusselt number of empty channel is determined a correlation for Nu H is given as Nu H = 0.213(L/H) 0.37 Re 0.67 (6) The correlation is based on 73 data points with a correlation coefficient of 0.99 and has an RMS error of 5.75%. From Eqn. 7 it is seen that when the inlet velocity

13 Heat transfer studies in a vertical channel filled with a porous medium 123 is fixed, it is found that heat transfer coefficient h is independent of the channel width (h H 0.04 ). The empty channel correlation is also valid for the same range of Reynolds numbers and aspect ratios as for the porous channel. Fig. 6 shows the variation of Nu H for different foams for varying velocity. The curves correspond to Eqn. 5 for the case of 10 PPI foam alone. The enhancement in heat transfer refers to Nusselt number, NuH Al foam (PPI_t_Φ) 10_10_ _20_ _10_ _20_ _10_ _20_ _10_ _20_ _30_ _30_0.917 Empty_10_1 Empty_20_1 Empty_30_1 Eqn 5 Eqn ,000 1e+04 Reynolds number, Re H Figure 6: Variation of Nusselt number obtained from the correlation for metal foam and empty channel the additional increase in heat transfer of a porous channel compared to an empty channel for a given Reynolds number and surface temperature of the aluminium plate. As an example, for the case of 10 PPI foams, if the excess temperature on the surface of aluminium plate is to be maintained at 60 C, for different aspect ratios, the additional increase in heat transfer compared to an empty channel is shown in Fig. 7, along with the pumping power, for varying flow rate. The inlet velocity is varied from 0.4 to 2.5 m/s and the maximum pumping power is found to be 9 W for a heat transfer enhancement of 350 W over an empty channel. 4 Uncertainty analysis All the measurement devices used in the present study are calibrated with standard instruments. The uncertainties involved in the measurement of temperature, velocity, pressure, voltage and current are given in Tab. 3.

14 124 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , _10_ _20_ _30_ _10_ _20_ _30_ Qporous-Qempty, W Pumping power WP, W Volume flow rate, Q vol x 10 3 m 3 /s, Figure 7: Variation of additional heat transfer and pumping power for the case of 10 PPI metal foam with the volume flow rate (Solid line represents pumping power and dashed line represents excess heat transfer) Table 3: Uncertainties in measured quantities Quantity Uncertainty Units Temperature ±0.2 C Velocity ± 0.1 m/s Pressure ±1 % Voltage ±1 V Current ±0.01 A Table 4: Uncertainties in derived quantities Quantity Uncertainty% Heat transfer coefficient ±7.55 Nusselt number ± 7.55 Reynolds number ± 8.3

15 Heat transfer studies in a vertical channel filled with a porous medium 125 The uncertainties in the derived quantities are obtained using the relation ( ) Y 2 Y = X i (7) X i Where X i is the measured quantity and Y the derived quantity and X and Y are the uncertainties in the measured and derived quantities respectively. Based on Eqn. 7, the uncertainties in the derived quantities are determined and these are reported in Tab Conclusions Hydrodynamic and heat transfer experiments have been conducted in a vertical channel filled with metal foams of different foam thicknesses. The results of the hydrodynamic experiments show that the variation of pressure drop with the foam thickness is insignificant. However, an increase in the foam thickness results in an increase in the heat transfer compared to an empty channel of same channel width and Re H. The attendant increase in pumping power for a heat transfer enhancement of 350 W, over an empty channel is found to be only 9 W. References Boomsma, K.; Poulikakos, D.; Zwick, F. (2003): Metal foams as compact high performance heat exchangers. Mechanics of Materials, vol. 35, no. 12, pp Calmidi, V. V.; Mahajan, R. L. (2000): Forced convection in high porosity metal foams. ASME Journal of Heat Transfer, vol. 122, pp Chein, R.; Yang, H.; Tsai, T.-H.; Lu, C. (2010): Experimental study of heat sink performance using copper foams fabricated by electroforming. Microsystem Technologies, vol. 16, pp DeGroot, C. T.; Gateman, D.; Straatman, A. G. (2010): The effect of thermal contact resistance at porous-solid interfaces in finned metal foam heat sinks. ASME Journal of Electronic Packaging, vol. 132, no. 4, pp Dukhan, N.; Patel, P. (2008): Equivalent particle diameter and length scale for pressure drop in porous metals. Experimental Thermal and Fluid Science, vol. 32, no. 5, pp Howard, S. R.; Korinko, P. S. (2003): Vacuum furnace brazing open cell reticulated foam to stainless steel tubing. In 2nd International Brazing and Soldering Conference, San Diego, CA.

16 126 Copyright 2013 Tech Science Press FDMP, vol.9, no.2, pp , 2013 Hunt, M. L.; Tien, C. L. (1988): Effects of thermal dispersion on forced convection in fibrous media. International Journal of Heat and Mass Transfer, vol. 31, no. 2, pp Hwang, J. J.; Hwang, G. J.; Yeh, R. H.; Chao, C. H. (2002): Measurement of interstitial convective heat transfer and frictional drag for flow across metal foams. ASME Journal of Heat Transfer, vol. 124, no. 1, pp Jaeger, P. D.; Joen, C. T.; Huisseune, H.; Ameel, B.; Schampheleire, S. D.; Paepe, M. D. (2012): Assessing the influence of four bonding methods on the thermal contact resistance of open-cell aluminum foam. International Journal of Heat and Mass Transfer, vol. 55, no , pp Jeng, T. M.; Tzeng, S. C. (2007): Experimental study of forced convection in metallic porous block subject to a confined slot jet. International Journal of Thermal Sciences, vol. 46, no. 12, pp Kamath, P. M.; Balaji, C.; Venkateshan, S. P. (2011): Experimental investigation of flow assisted mixed convection in high porosity foams in vertical channels. International Journal of Heat and Mass Transfer, vol. 54, no , pp Kim, S. Y.; Kang, B. H.; Kim, J.-H. (2001): Forced convection from aluminum foam materials in an asymmetrically heated channel. International Journal of Heat and Mass Transfer, vol. 44, no. 7, pp Mancin, S.; Zilio, C.; Rossetto, L.; Cavallini, A. (2012): Foam height effects on heat transfer performance of 20 ppi aluminum foams. Applied Thermal Engineering, vol. 49, pp Salas, K. I.; Waas, A. M. (2007): Convective heat transfer in open cell metal foams. ASME Journal of Heat Transfer, vol. 129, pp Venugopal, G.; Balaji, C.; Venkateshan, S. P. (2010): Experimental study of mixed convection heat transfer in a vertical duct filled with metallic porous structures. International Journal of Thermal Sciences, vol. 49, pp