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Experimental heat transfer data for water flow in commercial open-cell aluminum foam cylinder heated at the wall by a constant heat flux, is presented. The foam had 20 pores per inch (ppi) and a porosity of 87%. The measurements included wall temperature along flow direction as well as average inlet and outlet temperatures of the water. Flow speeds were in the non-Darcy regimes (transitional and Forchheimer). Heat fluxes were 14,998 W/m2 and 26,347 W/m2. The behavior of the wall temperature clearly shows thermal fully-developed conditions. The experimental Nusselt number is presented as a function of axial distance in flow direction, and showed what seemed to be a periodic development. A correlation for the average Nusselt number as a function of flow Reynolds number is provided. The experimental data can be used for validation of other analytical solutions, numerical models and heat-exchange engineering designs based on metal foam. INTRODUCTION Open-cell metal foams are excellent candidates for heat exchange designs. The foams have relatively high conductivities and very large surface area per unit volume. The internal structure of the foam interferes with fluid flow and causes vigorous mixing, which enhances convection between the internal solid surface of the foam and the fluid. Boomsma et al. [1] have shown that compressed open-cell aluminum foam heat exchangers generated thermal resistances that were two to three times lower than the best commercially available heat exchanger, at the same pumping power. Due to the complexity of heat transfer phenomenon inside metal foam, researchers have solved simplified forms of the governing equations, and relied on numerical simulations. Calmidi and Mahajan [2] numerically studied forced convection of air flow in aluminum foam. Hwang et al. [3] indicated that the local Nusselt number for air flow in metal foam increased with increasing Reynolds number. Angirasa [4] numerically studied convection heat transfer due to water flow in metal foam heat dissipaters. He invoked local thermal equilibrium. The validity of the local thermal equilibrium assumption is questionable due to the difference in the thermal conductivities of the solid and fluid phases. Lu et al. [5] analyzed forced convection in a tube filled with metal foam subjected to constant wall heat flux. The twoequation model, which relaxes the thermal equilibrium assumption, was solved. They employed the Brinkmanextended Darcy momentum model. A closed-form solution for the solid and the fluid temperatures was presented. They exploited the solution for investigating the effect of various foam parameters in practical heat-exchange designs. Analytical solutions in porous media continue to be sought [6-8] due to their utility, identifying trends of critical variables, parametric studies and for validating numerical models. Research Article – JTEN – 2015 68 678 Direct comparisons to experimental values of key variables is lacking in many analytical porous media studies concerning heat transfer [6-8], and seem to be non-existent in the literature concerning heat transfer in metal foam. Experimental verifications, when possible, add confidence to analytical solution and validate numerical modeling and simulations. Experimental data also has intrinsic value and they can provide correlations for practical engineering design. In 2006, Lu et al. [5] stated that no experimental data was available for metalfoam-filled pipes. The circular geometry is preferred in many heat exchange applications. In a 2012 comprehensive review, Zhao [9] indicated that there has been a lack of reliable experimental heat transfer data for open-cell metal foam in general. A summary of available experimental data for heat transfer in metal foam will be summarized next. Studies with Air Calmidi and Mahajan [2], measured the wall temperature of aluminum foam sample bounded by substrates and heated. For comparing to their numerical results, they used the measured wall temperature to obtain the average surface heat transfer coefficient. Hwang et al. [3] obtained wall and exit temperature measurements for air flow through metal foam having dimensions 60 × 25.4 × 60 mm3. The data was used to investigate heat transfer in terms of Nusselt number. Bhattacharya et al. [10] used the same kind of temperature measurements to obtain the effective conductivity of metal foam, while Bhattacharya and Mahajan [11] used similar techniques to assess the thermal performance of a finned-metal-foam heat sink. Zhao et al. [12] tested convection due to air flow in several foam samples 127 × 127 × 12 mm3 each. Kurbas and Celik [13] published the results of an experimental study of forced and mixed convection heat transfer in a foam-filled rectangular channel for air as the working fluid. Similar measurements were conducted. Mancin et al. [14] presented experimental data for forced convection due to airflow in several samples of aluminum and copper foam. Overall and interstitial heat transfer coefficients were obtained; foam finned surface efficiency were investigated. Each foam sample was 100 mm long and had a cross section of 20 mm × 20 mm. Dukhan et al. [15] measured actual air temperature inside a cylinder of metal foam heated with constant heat flux and cooled by air. The tube had a length of 152.4 mm in the flow direction and an inside diameter of 255.6 mm. Wall temperature measurements were limited, and the Nusselt number was not discussed. Studies with Air Experimental studies concerning heat transfer in heated metal foam with water as the cooling fluid are few indeed. Water flow provide much higher heat transfer rates due to it higher thermal conductivity (relative to that of air) and also due to dispersion which is negligible for air flow in porous media. Boomsma et al. [1] experimentally investigated compressed aluminum foam performance as a compact heat exchanger using water as a coolant. The foam size was 40 mm × 40 mm × 2 mm. Hetsroni et al. [16] investigated the cooling of 40-ppi metal-foam heat sink for transmission window. The foam dimensions were 10 mm × 45 mm × 2 mm. Kim et al. [17] studies convection in a sample of metal foam 9 × 90 × 30 mm3. One common fact about these studies is that they employed small foam sample sizes (small length at least in one direction), which makes there results specific to the samples tested. In the current study, direct measurements of wall and inlet and outlet temperatures for water flow inside heated commercial aluminum foam are presented. The length of the foam cylinder tested is long to ensure full thermal development and minimize size effects. Flow velocities encountered Darcy and non-Darcy regimes. Such measurements have an intrinsic value. To the knowledge of the present authors, the experimental data are novel, and can be used for validation of analytical and numerical models of heat transfer in metal foam and for assessing the performance of heat-exchange engineering designs based on such media. EXPERIMENT The experimental heat transfer model was principally a cylindrical aluminum tube brazed to an aluminum foam core, Fig. 1(a). Brazing of the two similar materials is known to minimize thermal contact resistance, and hence facilitate heat transfer from the wall to the foam. The tube had a length of 30.50 cm in the flow direction, an inside diameter of 5.08 cm and a wall thickness of 0.63 cm. The foam was obtained commercially (ERG Materials and Aerospace [18]), and was made from aluminum alloy 6101-T6 and had 20 pores per linear inch (ppi). The porosity of the foam was 87.6 % (calculated from measurements of its volume and weight). Other geometric parameters can be found in [18]. For measuring the wall temperature, 17 holes were drilled. The diameter of each hole was 1 mm and the depth was 4 mm. The location of the first hole was 150 mm from the inlet of the foam tube; the rest of the holes were at 10 mm from each other along the length of the tube (the flow direction). This caused the last hole to be at 1 mm from the outlet of the foam tube. In each hole, a type-K thermocouple was inserted, Fig. 1(b). Thermal epoxy then filled the remaining volume of each hole, while ensuring that the bead of the thermocouple was touching the bottom of the hole. The epoxy guaranteed that there were no air pockets trapped in the holes. A surface band heater was wrapped around the outer surface of the aluminum cylinder. The heater had a sandwichlike inner structure consisting of a mica plate wrapped by resistance heater ribbons of 1.66 Ohm/m; two more mica layers on both sides for electrical insulation and steel sheet layers to cover the inner elements and to give structure to the heater. The heater had an electrical power of 1,780 Watts at 60 Volts; it was powered by two 40-VDC power supplies connected in series. Research Article – JTEN – 2015 68 679 Figure 1 Experimental model construction: (a) aluminum tube with brazed foam, (b) Thermocouple inserted into holes, (c) Heater wrapped around the pipe and (d) Heat transfer model insulated Thermal grease was placed between the heater surface and the pipe surface to minimize contact resistance. The heater covered the outside area, Fig. 1(c). The whole assembly was then covered with five layers of ceramic fiber paper (4-mm thick) with a thermal conductivity of 0.058 W/mK in order to insulate the test section from ambient air, Fig. 1(d). Experiments were performed in an open-loop water tunnel as shown in Fig. 2. The heat transfer test section was connected to two 51.4-mm-diameter 200-mm-long Polyethylene tubes at its two ends using specially-designed flanges, Fig. 1(d). Temperature probes were inserted in these tubes to measure the inlet and outlet temperature of the water. Each probe has five thermocouples spanning the cross section in order to obtain a good average value for the inlet and outlet temperatures. The outlets of the Polyethylene tubes were connected to stainless steel pipes 32

EXPERIMENTAL FULLY-DEVELOPED THERMAL CONVECTION FOR NON-DARCY WATER FLOW IN METAL FOAM