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Experimental heat transfer due to oscillating water flow in open-cell metal foam
International Journal of Thermal Sciences 101 (2016) 48e58
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Experimental heat transfer due to oscillating water flow in open-cell metal foam a € € lu a cı a, Nihad Dukhan b, *, Mustafa Ozdemir , Levent Ali Kavurmacıog Ozer Bag a b
Makina Fakültesi, Istanbul Technical University, Gümüs¸suyu, 34437 Istanbul, Turkey Department of Mechanical Engineering, University of Detroit Mercy, Detroit, MI 48221, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 December 2014 Received in revised form 20 October 2015 Accepted 21 October 2015 Available online xxx
While studies concerning heat transfer due to oscillating air (and few other gases) flow in metal foam are available, heat transfer due to oscillating water flow in metal foam has not been offered in the literature. This paper presents characteristics of heat transfer of oscillating water flow in commercial open-cell metal-foam pipe that were obtained experimentally, most likely for the first time. One main difference between gas and liquid flows in porous media is that dispersion is far more significant in the latter. Another difference is the length of the entrance region, which depends strongly on the Prandtl number. The trends in the cycle-averaged wall temperature, length-averaged wall temperature and cycleaveraged Nusselt number were similar to those for oscillating water flow in packed spheres and for oscillating air flow in aluminum, copper and graphite foams in a rectangular channel. For the higher flow frequency of the current study, the cycle-averaged Nusselt number was higher for higher flow displacement amplitude. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Oscillating heat transfer Porous media Metal foam Electronic cooling Regenerator
1. Introduction Open-cell metal foams are relatively new class of porous media that have been recently discussed in Ref. [1]. These foams have high porosity, permeability, thermal conductivity and surface area density. The web-like internal structure of metal foams promotes mixing of through flowing fluids. As such, metal foams are attractive for heat transfer enhancement systems. Some preliminary steady-state convection heat transfer results for water flow in metal foam were recently published [2]. It is well-established that heat transfer can be augmented substantially by employing time-dependent flow as compared to heat transfer due to steady-state flow. Oscillating (or reciprocating) flow is time-dependent periodic flow. Lambert et al. [3] proposed enhancing heat-transfer performance of solar devices by employing oscillating flow. He showed that for oscillating flow, the effective thermal diffusivity was several orders of magnitude higher € than the fluid molecular diffusivity. Pamuk and Ozdemir [4] indicated that heat transfer due to oscillating flow is comparable to that of heat pipes.
* Corresponding author. Tel.: þ1 313 993 3285. E-mail address: [email protected] (N. Dukhan). http://dx.doi.org/10.1016/j.ijthermalsci.2015.10.028 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
Oscillating flow and heat transfer in porous media occur in many applications, e.g., heat pipes, regenerators (e.g. in Stirling engines and cryocoolers), cooling designs of nuclear power plants and reciprocating internal combustion engines. Oscillating heat transfer in porous media can produce two advantageous effects: 1) a high heat transfer rate and 2) a more uniform temperature distribution on a hot substrate or surface due to the presence of two thermal entry regions. Therefore, oscillating heat-transfer designs can be used to cool modern high-speed devices (e.g., microprocessors and transistors). The reliability and operation speed of these devices depend not only on their average temperature, but also on their temperature uniformity. Transport phenomena due to oscillating flow are naturally complex; and they are not very well understood [5]. Heat transfer due to oscillating flow in traditional porous media (packed spheres, granular beds and mesh screens) has received considerable attention. Sozen and Vafai [6] numerically investigated forced convection due to oscillating compressible ideal gas (Refrigerant-12m) flow in a packed bed. The porosity of the bed was 39%. Byun et al. [7] analyzed heat transfer due to oscillating flow through infinitely large porous slab using the two-equation model (thermal nonequilibrium). Habibi et al. [8] solved the heat transfer equations for a two-dimensional channel partially filled with a porous medium subjected to reciprocating air flow. The channel was discretely heated on one side to simulate compact circuit boards.
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Nomenclature A Ao Iuni L Nu ppi q00 ReD Reu t U xmax
cross-sectional area of test section (m2) non-dimensional displacement index (for temperature uniformity) length of porous medium (m) local cycle-averaged Nusselt number number of pores per inch of foam heat flux (W m2) Reynolds number based on pipe diameter kinetic Reynolds number time (s) average velocity (m/s) maximum flow displacements (mm)
€ Pamuk and Ozdemir [4] presented experimental heat transfer results for oscillating water flow in two sets of mono-sized packed steel balls (1 and 3 mm). The porosity of the first set was 36.9%, while it was 39.1% for the other. The effect of various parameters on heat transfer was studied, e.g., frequency, flow displacement and heat input. Results were presented in terms of cycle-averaged local Nusselt number and space-cycle-averaged Nusselt number. The latter correlated well with the kinetic Reynolds number and nondimensional flow displacement. Recently, Dai and Yang [9] numerically studied oscillating gas flow and heat transfer in regenerative cryocoolers using the Lattice Boltzmann Method. They noted that the velocity and temperature profiles were mainly influenced by the Womersley number. Little vortices were observed near the surface of the solid phase. Pathak et al. [5] numerically studied oscillating flow and heat transfer in a 75%-porous medium composed of square cylinders. The working fluid was helium. The Nusselt number strongly depended on flow oscillation frequency and amplitude. Significant phase lag occurred among velocity, pressure, temperature and heat transfer processes. For heat transfer due to oscillating flow in metal foam, there are only few published studies. Leong and Jin [10] experimentally studied heat transfer due to oscillating air flow through a channel filled with aluminum foam and subjected to constant wall heat flux. The 90%-porous foam was produced by sintering and had 40 pore per inch (ppi). The cycle-averaged Nusselt number increased with both the kinetic Reynolds number and dimensionless amplitude of flow displacement. A correlation for the length-averaged Nusselt number as a function of these two non-dimensional parameters were provided. In a different investigation, Leong and Jin [11] conducted experiments to study the effect of frequency on heat transfer performance of metal foam heat sinks subjected to oscillating flow of air. The aluminum foam used in the heat sinks had 10, 20 and 40 ppi. The cycle-averaged temperature decreased with increasing kinetic Reynolds number while the Nusselt number exhibited the opposite trend. Better heat transfer was noted for foam with low pore density. In a third experiment, Leong and Jin [12] studied heat transfer of oscillating air flow in two porous channels having commercial aluminum (20-ppi) and copper (60-ppi) foams with porosities around 90%. The oscillating flow amplitude was larger than the length of the test section (in order to ensure proper cooling). The local wall temperature was maximum at the center of the test section, and the cycle-averaged wall temperature decreased with increasing Reynolds number. The cycle-averaged Nusselt number
z
49
coordinate along flow direction, distance from entrance
Greek
m u r
viscosity (Pa s) angular frequency (rad/s) density (kg/m3)
Subscripts f fluid i inlet max maximum min minimum w wall z flow direction, local
had a concave shape with a minimum at the center of the channel. Heat transfer was higher for the case of copper foam due to its higher conductivity, as expected. In a fourth paper, Leong and Jin [13] experimentally studied oscillating flow through a channel filled with metal foam. For fluid flow characteristics, these authors stated that the non-dimensional fluid displacement and the kinetic Reynolds number were the appropriate similarity parameters for oscillating flow in open-cell metal foam. No heat transfer information was given in Ref. [13]. Fu et al. [14] carried out experiments on heat transfer of oscillating air flow in channels filled with commercial aluminum (40ppi) and carbon (45-ppi) foams-each having a porosity around 90%. The uniformity of the surface temperature in oscillating heat transfer was displayed. Ghafarian et al. [15] conducted computational analysis of heat transfer for oscillating air flow through a metal-foam channel heated from one side. They invoked the local thermal equilibrium assumption between the solid and fluid phases of the foam. The effect of the porosity, thermal conductivity and solid-fluid thermal conductivity ratio of the foam on heat transfer was investigated. The main conclusion was that heat transfer increased by employing high amplitude and high frequency. € As indicated by Pamuk and Ozdemir [16], and by the literature review given above, all experimental studies in the literature concerning oscillating flow and heat transfer in porous media (including metal foam) used gases, mostly air, as the working fluid. Oscillating flow of liquid, e.g., water, in metal foam has only been presented recently [17,18]; no heat transfer findings were given. One main difference between gas and liquid flows in porous media is that dispersion is significant in the latter, while so weak in the former that it has been ignored [19]. Another difference is the length of the entrance region, which depends strongly on the Prandtl number of the working fluid. Both of these matters affect oscillating heat transfer significantly. The purpose of the current experimental study is to furnish heat transfer characteristics due to oscillating water flow in commercial open-cell metal foam in terms of pertinent parameters. The results of the current study will be contrasted to those in previous studies employing air flow in similar metal foam; and also to the oscillating flow heat transfer results obtained for different porous media (e.g., packed beds of spheres and screens). A comparison of oscillating water flow heat transfer and steady state heat transfer in the same metal foam of the current study will also be provided. The aim is to enhance fundamental understanding of heat transfer in oscillating liquid flow in metal foam in order to guide engineering design tools (analytical and numerical) for potential applications, e.g., cooling
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systems for high-power devices and regenerators based on metal foam. The new experimental results can be used for validation of analytical and numerical modeling of the complex heat transfer phenomenon generated by oscillating liquid flow. 2. Experiment Fig. 1 is a schematic of the experimental setup. The test section was made from an aluminum alloy (6061-T6) pipe having inner diameter of 50.80 mm, wall thickness of 6.35 mm and length of 305 mm. Commercial open-cell aluminum foam (ERG Materials and Aerospace) having 20 ppi and porosity of 87.6% was brazed to the inside surface of the pipe, Fig. 2. Brazing minimized thermal contact resistance. The brazing technique is used in intricate situations and is ideal for joining complex assemblies and geometries, e.g., porous metals, powder metals, etc. In the so-called aluminum dip brazing process, which was used in preparing the test section of the current paper, the parts to be brazed are chemically cleaned then assembled with braze foil (88% aluminum and 12% silicon) preplaced between the braze surfaces and joints. The assembly is then preheated in an air furnace to 552 C to insure uniform temperature of dissimilar masses in the assembly. The parts are then immersed in a molten salt bath (aluminum brazing flux). The bath is maintained at 590 C ± 2.5 C in a furnace. As the assembly is immersed or dipped, the molten flux comes in contact with all internal and external surfaces simultaneously. Since the bath is a flux, complete bonding on oxide-free surfaces assures extremely high quality joints. Multiple holes were drilled along the tube wall in a straight line. The diameter of each hole was 1 mm and the depth was 4 mm. The holes were spaced 10 mm from each other along the length of the tube. The first hole was 1 mm away from the inlet of the pipe. In each hole, a type-K thermocouple was inserted; thermal epoxy then filled each hole, which guaranteed that there were no air pockets trapped in the holes. As such, the wall temperature could be measured along the pipe.
Fig. 2. Photograph of metal-foam test specimen.
Fig. 1. Schematic of the experimental setup: 1. Test section (metal foam), 2. Polyethylene tubes, 3. Steel pipes, 4. Connecting hoses, 5. Oscillation generator, 6. Crank arm, 7. Flywheel, 8. Motoreductor, 9. Inductive proximity Sensor, 10. Thermocouple wires (from metal foam and polyethylene tubes), 11. Data logger, 12. Computer, 13. Cooling thermostats, 14. Water inlet for thermostats, 15. Water outlet.
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A surface heater was wrapped around the exterior of the tube. The heater was made of resistance heating ribbons each having 1.66 U/m. Mica layers on both sides of the heater provided electrical insulation; and steel sheet layers provided cover and structural support to the heater. The rating of the heater was 1780 W at 60 V; it was powered by two 40-VDC power supplies connected in series. To guarantee good insulation, the whole assembly was covered with five layers of ceramic fiber paper (4-mm thick) with thermal conductivity 0.058 W/m K. It must be noted that during preliminary unidirectional steady-state runs, an average random heat loss of approximately 8.2% was recorded. It was obtained by applying an overall energy balance to the test section. The test section was connected to two 51.4-mm-diameter 200mm-long Polyethylene tubes at its two ends via flanges. In each of these tubes, five thermocouples spanning the cross section were inserted to measure the inlet and outlet temperatures of the water. The outlets of these Polyethylene tubes were connected to stainless steel pipes 32 mm in diameter and 110 cm in length. The ends of these pipes were attached to an oscillating flow apparatus via hoses. The two steel pipes constituted inner tubes of two tube-intube heat exchangers. Two cooling thermostats (LAUDA Alpha RA 8) with a cooling capacity of 0.225 kW each provided cold water to these heat exchangers, in order to remove heat supplied to the test section. The main component of the oscillation generator was a doubleacting cylinder which was connected to an electrically driven 7.5kW motoreductor by means of a flywheel and a crank arm. The inner diameter of the hydraulic cylinder was 50 mm and the diameter of the piston installed inside it was 32 mm. This mechanism could produce a maximum stroke of 200 mm. The rotational speed of the motoreductor was controlled by a variable speed ACdrive (6.99e20.97 rpm). Additionally, an adjustment system mounted on a flywheel allowed changes in stroke. The set-up was fully charged with water and connected to the oscillating generator. In order to fill the system with water while avoiding entraining air, the whole system was vacuumed down to an absolute pressure of 221 mbar. Heavily-filtered water was allowed to flow into the system from taps at the two ends of the piston. Accidental air bubbles were removed from the system through a purger, by tilting the whole set-up and/or by dismantling and reassembling parts of the set-up. All sensors were connected to a data logger. For a given oscillating flow run, the water coolers were switched on until they could provide cooling water at about 17 C. The heater was then switched on to provide the desired constant wall heat flux of 15,519 W/m2 to the test section. The stroke length of the piston was set to a desired value, the oscillation generator was switched on, and the oscillation frequency was ramped to a targeted level. After the system stabilized (2.5 h approximately), a Keithley 2700 XLINX data acquisition system, which was installed in a computer, communicated with the data logger and recorded signals from all sensors. One signal came from a clicker that touched a bump on a flywheel (part of the oscillation system) once per cycle; this signal was used to calculate the angular speed. The sampling rate changed between 10 and 30 readings per second due to device limitations. The above was repeated for line frequencies 5 and 15 Hz, and stroke lengths (displacement of piston) 130 mm, 170 mm and 195 mm. It took about 30 min for the system to reach steady periodic conditions after each change in frequency. For a given oscillation frequency, the sampling rate for only one data point was 2.42 Hz. This value was more than three times higher than the highest oscillation frequency. Therefore the data logger was able to capture the actual frequency of the system and the temperature amplitude. Even though the data acquisition system was capable of working at higher sampling rates, higher
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frequencies were avoided due to the risk of noise. It also should be noted that higher line frequencies caused mechanical vibrations of the set-up and some buckling of the supporting metal frame, while lower line frequencies caused overheating of the motoreductor. 2.1. Data reduction The maximum fluid displacements are related to the displacements of the piston according to conservation of mass, and the fact that water is an incompressible fluid. The maximum flow displacements (xmax) at the entrance of the metal foam are calculated from the ratio of the cross-sectional areas of piston and entrance of porous pipe as
xmax ¼
2RAp A
(1)
where R is the flywheel radius and Ap and A are the cross-sectional areas of the double acting cylinder and metal-foam pipe, respectively. This calculation results in 74.4 mm, 97.2 mm and 111.5 mm for xmax. The non-dimensional displacement is defined as
Ao ¼
xmax D
(2)
where D is the pipe inner diameter. For each displacement, line frequency was changed from 5 Hz to 30 Hz by the servo drive of motor. Actual flow frequency, which was linearly proportional to the line frequency, changed from 0.116 to 0.348 Hz. The motoreductor operated at 69.7 rpm at 50 Hz line frequency. The displacement of the piston is taken as zero at the rear position inside the cylinder and as maximum (equal to the diameter of the flywheel) at the forward position. The piston displacement is essentially equal to the fluid displacement since the fluid is incompressible. Hence, at the entrance of the foam, the fluid displacement xm varies with angular frequency u and time t according to
xm ðtÞ ¼
xmax ð1 cos utÞ 2
(3)
The cross-sectional mean fluid velocity in the foam pipe is
uðtÞ ¼ umax sin ut
(4)
where umax ¼ uxmax/2. The kinetic Reynolds number is defined by
Reu ¼
ruD2 m
(5)
where r and m are the density and viscosity of water. Two values of the kinetic Reynolds number were realized: 1873 and 5619. These values correspond to flow frequencies 0.116 and 0.348 Hz. In some oscillating flow literature [8,9], the Womersley l number is used. This number is related to the kinetic Reynolds number by
l¼
1 pffiffiffiffiffiffiffiffi Reu 2
(6)
2.2. Uncertainty analysis Uncertainty in the directly-measured quantities, e.g., lengths and temperatures was based on errors provided by manufacturers of the measuring devices. The propagation of error in derived quantities, e.g., angular frequency, maximum fluid displacement
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and local cycle-averaged Nusselt number, was assessed via uncertainty analysis as described by Figliola and Beasley [20]. The uncertainties in length and diameter of the metal foam tube were 0.33% and 0.04%, respectively. As for the temperature, the error in the reading was ±1.1 C or 0.4%, whichever was greater, as provided by the manufacturer. As an example of uncertainty in derived quantities, the local cycle-averaged Nusselt number is calculated according to 00
Nu ¼
q D kf ðTw Ti Þ
(7)
where q00 is the heat flux, kf is the fluid conductivity, Tw is the local wall temperature and Ti is the inlet water temperature. As such the uncertainty in Nu is based on propagation of errors in the variables that are involved in calculating it, i.e., q00 , D, kf, Tw and Ti according to [20]:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 u 2 2 u d 00 dkf dTi dTw 2 dNu dD 2 q ¼ ±t þ þ þ þ 00 Nu q D kf Tw Ti
(8)
where d represents the uncertainty. The uncertainties in diameter and temperatures were stated above. The effective thermal conductivity was obtained from an analytical model published in Ref. [21]. These researchers indicated that this model was excellent in matching their measured values of the effective conductivities, with less than 10% error. Therefore, the uncertainty in the effective conductivity kf was conservatively assumed to be 10%. The uncertainty in voltage and current readings were taken as 0.1 V and 0.1 A, respectively. These are the accuracies of the digital readouts of the measuring devices of these quantities. If we further include the uncertainty of the outside surface area of the test section as 0.039%, we can calculate an uncertainty in the heat flux which is far below 10%. To be safe a much higher uncertainty in the heat flux (10%) was assumed. Putting all these values in Eq. (8), we obtain an uncertainty of 14.7% in Nu. In a similar manner, the uncertainties in the angular frequency and maximum fluid displacement were estimated as 0.43% and 0.51%, respectively.
3. Results and discussion In the presentation of the results, the starting time (zero) is taken at the end of transient behavior which lasted for about 2.5 h from applying heat and starting the oscillations.
3.1. Symmetry Fig. 3 shows the wall temperature at various locations along the foam tube for non-dimensional displacement 2.2 and kinetic Reynolds number 1837. The heat flux for this case was 8866 W/m2. The purpose of this run was to establish symmetry of the test section around the midpoint of the foam pipe. The wall temperature is seen to be maximum at the midpoint and it decays gradually to reach a minimum at the two inlets. The maximum error in the wall temperature is ±1.1 C, this error does not alter the statements made above regarding the trends in the wall temperature. The symmetric behavior about the middle of the test section (z/D ¼ 3.2) is also displayed in Fig. 4. The periodic patterns of equal-distance pairs of wall temperatures, i.e. z/D ¼ 1.62 and 4.77; z/D ¼ 0.04 and 6.36, and the regular phase shift within each pair further establish the symmetry. This regular phase shift is purely due to flow reversal. The amplitudes of the temperature in each pair are equal. In Fig. 4, the instantaneous velocity is plotted for reference. Due to symmetry, only one half of the test section was subjected to further measurements, which reduced the load on the limited data acquisition system, without loss of information. If only the maximum error in the wall temperature (±1.1 C) is considered, the periodic behavior of the wall temperature presented in Fig. 4 is not significant, since it lies within this error margin. However, based on the physics of oscillating flow and heat transfer, there is good reason to think that the periodic behavior is real, partly because it seems to be uniform and well ordered. If the maximum random error in the temperature readings was really present, no such ordered periodic behavior would show. 3.2. Instantaneous wall temperature The variation of wall temperature with time for the three locations on one half of the test section is plotted in Fig. 5. The nondimensional displacement Ao for this figure is 1.5; part (a) is for the low frequency, while part (b) is for the high frequency. The periodic behavior is obvious, especially for the locations 0.04 and 1.62 diameters from the entrance. The amplitude of the wall temperature is higher at 1.62 diameters since this location is inside the foam, while location 0.04 diameters is practically at the entrance of the foam. It should be noted that there is no oscillation of the wall temperature at the middle point of the test section (z/D ¼ 3.20) due to symmetry. The wall temperature oscillation is in phase with velocity for both low and high frequencies, indicating that thermal inertia for these flow frequencies does not play a significant role. € For 3-mm packed spheres, Pamuk and Ozdemir [4] reported a
Fig. 3. Wall temperature for Ao ¼ 2.2, Reu ¼ 1873, q00 ¼ 8866 W/m2.
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Fig. 4. Periodic behavior of wall temperature for Ao ¼ 2.2, Reu ¼ 1873, q00 ¼ 8866 W/m2.
phase shift or p radians between the velocity and wall temperature. This may be due to difference in porosity and thermal conductivity € of the steel spheres of Pamuk and Ozdemir [4] and the highlyporous open-cell aluminum foam of the current study. Significant phase shifts were also reported in the study of Pathak et al. [5] for heat transfer due to oscillating helium flow in a 75%-porous medium composed of square cylinders. There were no statements or evidence of the presence of a phase shift between velocity and wall temperature in the oscillating heat transfer studies due to air flow in metal and graphite foams [10e12,14]. Increasing the frequency, at the same displacement, is seen to cause a decrease in the wall temperature at the middle point of the test section, and an increase in the wall temperature close to the entrance. The higher frequency also reduces the amplitude of the wall temperature, which suggests that increasing the frequency leads to a more uniform wall temperature. At the low kinetic
Reynolds number, the wall temperature lies within the band 55e74 C, approximately, Fig. 5(a); while for high kinetic Reynolds number, this band narrows and ranges from 60 to 71 C, Fig. 5(b). These trends can be explained by considering the fact that increasing frequency amounts to higher fluid mean velocity [17], which enhances convection between the solid ligaments of the foam and the fluid; this in turn invites more heat transfer from the heated wall to the ligaments by conduction. The net effect is a decrease in the wall temperature at the center. The increase in the wall temperature close to the entrance at the higher frequency is due to a general increase in the bulk temperature in this region due to enhanced axial conduction. As the non-dimensional fluid displacement increases to 1.9 and 2.2, the same trends are present in the wall temperature, Figs. 6 and 7. However, the wall temperature in all locations is generally lower, indicating better rates of heat transfer for longer fluid
Fig. 5. Instantaneous wall temperature as a function of time for fluid displacement Ao ¼ 1.5: (a) for Reu ¼ 1873, (b) for Reu ¼ 5619.
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Fig. 6. Instantaneous wall temperature as a function of time for fluid displacement Ao ¼ 1.9: (a) for Reu ¼ 1873, (b) for Reu ¼ 5619.
Fig. 7. Instantaneous wall temperature as a function of time for fluid displacement Ao ¼ 2.2: (a) for Reu ¼ 1873, (b) for Reu ¼ 5619.
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displacements. For example, the wall temperature band for Ao ¼ 1.9 and Reu ¼ 1873 is 53e65 C, Fig. 6(a). For the maximum displacement Ao ¼ 2.2 and for Reu ¼ 5619, the wall temperature band is 51e58 C, approximately. The enhanced heat transfer is caused by the elongation of the two thermal entrance regions of the test section caused by increasing fluid displacement. Also for longer displacements, the fluid sweeps longer distances inside the test section and it removes more heat from the wall and eventually delivers this heat to the coolers. It can be stated here that one should not only consider the maximum error in the temperature readings (±1.1 C). The wellordered periodic behavior of the instantaneous wall temperature presented in Figs. 5e7 strongly suggests that this behavior is both real and consistent with the physics of oscillating flow and heat transfer. 3.3. Cycle-averaged wall temperature Fig. 8 shows the cycle-averaged wall temperature along the test section for the three displacements and two frequencies. The average wall temperature gradually increases as the distance from the entrance increases, and it reaches a maximum at the middle of the test section. This behavior is due to the presence of two thermal entry regions at both ends of the test section due to reversing flow direction in each oscillation. It is well known that heat transfer is maximum in the thermal entry region and it decreases as the distance from the inlet increases. This trend is similar to what was € presented in Pamuk and Ozdemir [4] for oscillating water flow in packed spheres (1 and 3 mm), Leong and Jin [10] for oscillating air
55
flow in 40-ppi aluminum foam in a rectangular channel, Leong and Jin [11] for oscillating air flow in 10-, 20- and 40-ppi aluminum foam in a rectangular channel, Leong and Jin [12] for oscillating air flow in 90%-porous 20-ppi aluminum and 60-ppi copper foams, and in Fu et al. [14] for oscillating flow of air in 40-ppi aluminum and 45-ppi graphite foams. In general, the wall temperature is seen to decrease as the displacement increases for both frequencies, which is consistent with [2,10,12]. This may be explained by the presence of a longer penetration zone of fresh fluid when the displacement is long. This fresh fluid can absorb more heat from the heated wall. Leong and Jin [11] tested only one displacement; and no statements were made by Fu et al. [14] regarding these effects. For the low frequency, there is a small difference between displacements 1.2 and 2.2, as seen is Fig. 8(a). The effect of displacement is more pronounced at the higher frequency, as shown in Fig. 8(b). And, the wall temperature is generally lower for the high frequency, which is the same observation made earlier. Higher frequency means higher mean flow velocity, which enhances convection (or reduces the thermal resistance) inside metal foam leading to a lower wall temperature. The combination of long displacement, Ao ¼ 2.2, and high frequency, Reu ¼ 5619, produces the lowest and most uniform wall temperature, as seen in Fig. 8(b). The interpretations of the behavior of the cycle-averaged wall temperature as presented in Fig. 8 are generally valid even when the maximum error in temperature (±1.1 C) is taken into account. The difference between the curves for various flow displacements is larger than the error in temperature, except perhaps for the curves representing displacements 1.9 and 2.2 for the lower frequency shown in Fig. 8(a). 3.4. Length-averaged wall temperature Fig. 9 is a plot of the wall temperature averaged over the length of the foam tube. The influence of both displacement and frequency can be ascertained quickly from this figure. Again, it can be stated that the longer the flow displacement and the higher the flow frequency, the lower the average wall temperature, with the influence of displacement being more pronounced at the higher frequency. The same trends were reported in other studies [4,10e12,14].
Fig. 8. Cycle-averaged wall temperature for (a) Reu ¼ 1873, (b) Reu ¼ 5619.
Fig. 9. Length-averaged wall temperature at low and high frequencies.
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One should bear in mind the maximum error in the wall temperature (±1.1 C). Considering this error, the length-averaged wall temperatures for the lower kinetic Reynolds number for fluid displacements 1.9 and 2.2 are practically the same. For all other cases, the temperatures spacing is well above the temperature measuring error, and thus the statements made above regarding the trends in the length-averaged wall temperature are well supported. 3.5. Temperature uniformity To assess wall temperature variations, Leong and Jin [12] and Fu et al. [14] defined the temperature uniformity index Iuni as
Iuni ¼
Tmax Tmin Tmax
(9)
where Tmax and Tmin are the wall maximum and minimum temperatures in K, respectively. A comparison of temperature uniformity for steady and oscillating flows is provided in Fig. 10. For this plot Reynolds number ReD was calculated as
ReD ¼
rUD m
(10)
where U is the average flow velocity for steady-state flow and is the time-averaged maximum velocity for oscillating flow:
U¼
2umax p
of length to hydraulic diameter of the pipe L/D [22]. If the channel is filled with a porous medium, other parameters are added to the list. For example Kim et al. [23] added Darcy number, the ratio of the effective thermal conductivity of the porous medium to that of the fluid keff/kf and the ratio of the effective heat capacity of the porous medium to that of the fluid ðrcp Þeff =3rcp . Habibi et al. [8] added the porosity of the porous medium 3. In the current study, only one fluid was used to oscillate in a single porous medium. In other words, the thermophysical properties and their ratios were fixed; similarly, the geometrical parameters of the test specimen were not varied. The two parameters that were varied were only the dimensionless displacement amplitude Ao and the kinetic Reynolds number Reu. These two parameters are most commonly used in probing and treating oscillating heat transfer data, e.g., Byun et al. [7], Leong and Jin [10,13], Pathak et al. [5] and Zhao and Cheng [22]. As such the current results will be interpreted based on these two key parameters, and their effects on flow and heat transfer. In oscillating-flow literature, e.g. Refs. [10,14], the local cycleaveraged Nusselt number is according to Eq. (7) above. This number decays in what seems to be an exponential fashion as the distance from the entrance increases, as shown in Fig. 11. It reaches a minimum at the middle point of the test section. These trends are valid for all fluid displacements and for the low and high frequencies. The presence of the thermal entrance region is responsible for the higher Nusselt number close to the inlet.
(11)
This is similar to what was employed by Fu et al. [14]. Fig. 10 is a plot of the temperature-uniformity index for steadystate and oscillating flows. Unfortunately, the steady-state and oscillating heat transfer data were not obtained at the same Reynolds numbers due to experimental limitations; as such no definite statements could be made. Leong and Jin [12] and Fu et al. [14] showed that the index is generally lower for oscillating flow indicating more uniform temperature, as compared to steady state heat transfer. Uniform surface temperature is desirable in electronic cooling to mitigate hot spots. 3.6. Cycle-averaged Nusselt number Heat transfer phenomenon due to oscillating flow in an open channel is described by the following similarity parameters: the dimensionless displacement amplitude Ao, the kinetic Reynolds number Reu (or Womersley number), Prandtl number and the ratio
Fig. 10. Temperature uniformity for steady and oscillating flows.
Fig. 11. Cycle-averaged Nusselt number for (a) Reu ¼ 1873, (b) Reu ¼ 5619.
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Longer fluid displacements seem to generally produce higher Nusselt numbers. The curves for displacements 1.5, 1.9 and 2.2 at the low kinetic Reynolds number of 1873 have some overlaps, especially close to the entrance of test section, Fig. 11(a). Considering the uncertainty in this Nusselt number (14.7%), one is unable to make any assertions. However, it is noticed that the effect of displacement is more severe when the frequency is high, Fig. 11(b). The highest Nusselt number is realized at the longest displacement and highest frequency, which is consistent with observations made earlier. The thermal entrance region for oscillating flow with large displacement amplitude is longer than that for the case with small amplitude. This means that higher heat transfer rates (higher Nusselt number) are obtained for larger displacement amplitude. As to the effect of frequency, higher frequency implies higher mean fluid velocity, which enhances the convection part of heat transfer, which is reflected in higher Nusselt numbers. The so-called annular effect simply means that the axial velocity near the wall is higher than the centerline velocity (with an inflection point in the velocity profile near the wall) [22]. Dai and Yang [9] indicated that there was annular effect in the temperature profile for oscillating flow in porous media, with this effect being more pronounced at higher kinetic Reynolds numbers. This basically signifies higher fluid temperatures close to the wall compared to the core region, and hence more heat transfer from the wall region to the core. The trends presented here are similar to what was presented for oscillating air flow in metal and graphite foam [10e14]. For oscillating water flow in packed steel spheres (1 and 3 mm), Pamuk and € Ozdemir [4] showed that the cycle-averaged Nusselt number increased along the porous medium for long displacements, and it decreased for short fluid displacements. These trends may be attributed to the large difference in porosity between the foam (around 90%) and packed spheres (36.9% and 39.1%). Another difference is in the thermal conductivity between aluminum foam and steel packed spheres. This is in addition to the vast difference in internal structure of the two porous media. € Pamuk and Ozdemir [24] experimentally showed that the transverse dispersion thermal conductivity increased linearly with the product AoReu for heat transfer due to oscillating water flow in steel balls. This added conductivity is responsible for heat transfer from the wall region to the core of the flow. Because transverse dispersion is directly proportional to AoReu, more heat transfer is expected for longer fluid displacements and higher frequency. This is consistent with the current results presented in Fig. 11.
57
Fig. 12. Length-averaged Nusselt number for current study and Leong and Jin [10].
only four foam cells, approximately. This indicates that there might have been considerable size effects in the results of [11]. Size effects in metal foam have been discussed in Refs. [25,26]. 4. Conclusion Characteristics of heat transfer due to oscillating water flow in commercial open-cell metal foam were experimentally acquired and presented for three flow displacements and two frequencies. The following statements can be made: For the frequencies encountered in this study, the wall temperature was in phase with flow velocity. Higher fluid displacements generally lowered the wall temperature and produced more uniformity in the wall temperature. The combination of long displacement, and high frequency produced the lowest and most uniform wall temperature. For the higher flow frequency case, the cycle-averaged Nusselt number was higher for higher flow displacement amplitude. This trend was not clear in the lower flow frequency case as Nusselt number curves for various flow displacement amplitudes overlapped and were not distinguishable considering the experimental uncertainty. To clearly establish the effect of frequency, more experiments are needed.
3.7. Comparison to Leong and Jin [11] Fig. 12 compares the results of the current study to those of Leong and Jin [11] who studied oscillating heat transfer in metal foam due to air flow. To have the most meaningful comparison, only the case for 20-ppi foam form [11] is used. The length-averaged Nusselt number for oscillating air flow of [11] is higher than that for oscillating water flow of the current study. A careful look at the study presented in Ref. [10] reveals significant differences between [11] and the current study: a) The foam channel of [11] was heated on one side only (heat sink arrangement). b) The non-dimensional displacement Ao employed in Ref. [10] was 4.08 (calculated based on the hydraulic diameter), while the maximum Ao for the current study was 2.2. The flow displacement has a strong effect on heat transfer, as was shown above in connection with Figs. 9 and 11(b). c) The height of the channel of [10] was only 10 mm. For commercial open-cell 20-ppi aluminum foam, this height contained
Acknowledgment This work was supported by the Scientific & Technological _ Research Council of Turkey (TUBITAK) under program 2221: 1059B211404522, for which the authors are very thankful. References [1] N. Dukhan (Ed.), Metal Foam: Fundamentals and Applications, DESTech, Lancaster, PA, 2013, p. xiv. € Bag € cı, M. Ozdemir, lu, Experimental fully[2] N. Dukhan, O. L.A. Kavurmacıog
[3] [4] [5]
[6]
developed thermal convection for non-Darcy water flow in metal foam, J. Therm. Eng. 2 (2) (2016) 677e682. A.A. Lambert, S. Cuevas, J.A. del Rio, Enhanced heat transfer using oscillatory flows in solar collectors, Sol. Energy 80 (2006) 1296e1302. € M.T. Pamuk, M. Ozdemir, Heat transfer in porous media of steel balls under oscillating flow, Exp. Therm. Fluid Sci. 42 (2012) 79e92. M.G. Pathak, T.I. Mulcahy, S.M. Ghiaasian, Conjugate heat transfer during oscillatory laminar flow in porous media, Int. J. Heat Mass Transf. 66 (2013) 23e30. M. Sozen, K. Vafai, Analysis of oscillating flow compressible flow through a packed bed, Int. J. Heat Fluid Flow 12 (1990) 130e136.
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[7] S.Y. Byun, S.T. Ro, J.Y. Shin, Y.S. Son, D.-Y. Lee, Transient thermal behavior of porous media under oscillating flow condition, Int. J. Heat Mass Transf. 49 (2006) 5081e5085. [8] K. Habibi, A. Mosahebi, H. Shokrouhmand, Heat transfer characteristics of reciprocating flows in channels partially filled with porous medium, Transp. Porous Media 89 (2011) 139e153. [9] Q. Dai, L. Yang, LBM numerical study on oscillating flow and heat transfer in porous media, Appl. Therm. Eng. 54 (2013) 16e25. [10] K.C. Leong, L.W. Jin, An experimental study of heat transfer in oscillating flow through a channel filled with an aluminum foam, Int. J. Heat Mass Transf. 48 (2005) 243e253. [11] K.C. Leong, L.W. Jin, Effect of oscillating frequency heat transfer in foam heat sinks of various pore density, Int. J. Heat Mass Transf. 49 (2006) 671e681. [12] K.C. Leong, L.W. Jin, Heat transfer of oscillating and steady flows in a channel filled with porous media, Int. Commun. Heat Mass Transf. 31 (1) (2004) 63e72. [13] K.C. Leong, L.W. Jin, Characteristics of oscillating flow through a channel filled with open-cell metal foam, Int. J. Heat Fluid Flow. 27 (2006) 144e153. [14] H.L. Fu, K.C. Leong, X.Y. Huang, C.Y. Liu, An experimental study of heat transfer of a porous channel subjected to oscillating flow, J. Heat Transf. 123 (1) (Jul 12 2000) 162, http://dx.doi.org/10.1115/1.1336510. [15] M. Ghafarian, D. Mohebbi-Kolhori, J. Sadegi, Analysis of heat transfer in oscillating flow through a channel filled with metal foam using computational fluid dynamics, Int. J. Therm. Sci. 66 (2013) 42e50. € [16] M.T. Pamuk, M. Ozdemir, Friction factor, permeability and inertial coefficient of oscillating flow through porous media of packed balls, Exp. Therm. Fluid Sci. 38 (2012) 134e139.
€ Bag € cı, N. Dukhan, M. Ozdemir, [17] O. Characteristics of oscillating liquid flow in foam-like highly-porous media: an experimental study, Exp. Therm. Fluid Sci. 60 (2015) 96e105. € [18] M.T. Pamuk, M. Ozdemir, Hydrodynamic aspects of oscillating flow through porous media consisting of steel spheres, in: I. Dincer, et al. (Eds.), Progress in Exergy, Energy and the Environment, Springer International, Switzerland, 2014, pp. 633e640, http://dx.doi.org/10.1007/978-3-319-04681-5_59. [19] V.V. Calmidi, R.L. Mahajan, Forced convection in high porosity metal foams, J. Heat Transf. 122 (2000) 557e565. [20] R. Figliola, D. Beasley, Theory and Design for Mechanical Measurements, John Wiley and Sons, New York, 2000, pp. 149e163. [21] V.V. Calmidi, R.L. Mahajan, The effective thermal conductivity of high porosity fibrous metal foams, J. Heat Transf. 121 (1999) 466e471. [22] T.S. Zhao, P. Cheng, Heat transfer in oscillatory flows, in: C.-L. Tien (Ed.), Annual Review of Heat Transfer, vol. IX, 1998 (Chap. 7). [23] S.Y. Kim, B.H. Kang, J.M. Hyun, Heat transfer from pulsating flow in a channel filled with porous media, Int. J. Heat Mass Transf. 37 (14) (1994) 2015e2033. € [24] M.T. Pamuk, M. Ozdemir, Transverse thermal dispersion in porous media under oscillating flow, Online J. Sci. Technol. 4 (4) (2014) 56e64. [25] N. Dukhan, M. Ali, Strong wall and transverse size effects on pressure drop of flow through open-cell metal foam, Int. J. Therm. Sci. 57 (July 2012) 85e91. [26] N. Dukhan, M. Ali, Effect of confining wall on properties of gas flow through metal foam: an experimental study, Transp. Porous Media 91 (1) (2012) 225e237.
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Experimental heat transfer due to oscillating water flow in open-cell metal foam a € € lu a cı a, Nihad Dukhan b, *, Mustafa Ozdemir , Levent Ali Kavurmacıog Ozer Bag a b
Makina Fakültesi, Istanbul Technical University, Gümüs¸suyu, 34437 Istanbul, Turkey Department of Mechanical Engineering, University of Detroit Mercy, Detroit, MI 48221, USA
a r t i c l e i n f o
a b s t r a c t
Article history: Received 15 December 2014 Received in revised form 20 October 2015 Accepted 21 October 2015 Available online xxx
While studies concerning heat transfer due to oscillating air (and few other gases) flow in metal foam are available, heat transfer due to oscillating water flow in metal foam has not been offered in the literature. This paper presents characteristics of heat transfer of oscillating water flow in commercial open-cell metal-foam pipe that were obtained experimentally, most likely for the first time. One main difference between gas and liquid flows in porous media is that dispersion is far more significant in the latter. Another difference is the length of the entrance region, which depends strongly on the Prandtl number. The trends in the cycle-averaged wall temperature, length-averaged wall temperature and cycleaveraged Nusselt number were similar to those for oscillating water flow in packed spheres and for oscillating air flow in aluminum, copper and graphite foams in a rectangular channel. For the higher flow frequency of the current study, the cycle-averaged Nusselt number was higher for higher flow displacement amplitude. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Oscillating heat transfer Porous media Metal foam Electronic cooling Regenerator
1. Introduction Open-cell metal foams are relatively new class of porous media that have been recently discussed in Ref. [1]. These foams have high porosity, permeability, thermal conductivity and surface area density. The web-like internal structure of metal foams promotes mixing of through flowing fluids. As such, metal foams are attractive for heat transfer enhancement systems. Some preliminary steady-state convection heat transfer results for water flow in metal foam were recently published [2]. It is well-established that heat transfer can be augmented substantially by employing time-dependent flow as compared to heat transfer due to steady-state flow. Oscillating (or reciprocating) flow is time-dependent periodic flow. Lambert et al. [3] proposed enhancing heat-transfer performance of solar devices by employing oscillating flow. He showed that for oscillating flow, the effective thermal diffusivity was several orders of magnitude higher € than the fluid molecular diffusivity. Pamuk and Ozdemir [4] indicated that heat transfer due to oscillating flow is comparable to that of heat pipes.
* Corresponding author. Tel.: þ1 313 993 3285. E-mail address: [email protected] (N. Dukhan). http://dx.doi.org/10.1016/j.ijthermalsci.2015.10.028 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
Oscillating flow and heat transfer in porous media occur in many applications, e.g., heat pipes, regenerators (e.g. in Stirling engines and cryocoolers), cooling designs of nuclear power plants and reciprocating internal combustion engines. Oscillating heat transfer in porous media can produce two advantageous effects: 1) a high heat transfer rate and 2) a more uniform temperature distribution on a hot substrate or surface due to the presence of two thermal entry regions. Therefore, oscillating heat-transfer designs can be used to cool modern high-speed devices (e.g., microprocessors and transistors). The reliability and operation speed of these devices depend not only on their average temperature, but also on their temperature uniformity. Transport phenomena due to oscillating flow are naturally complex; and they are not very well understood [5]. Heat transfer due to oscillating flow in traditional porous media (packed spheres, granular beds and mesh screens) has received considerable attention. Sozen and Vafai [6] numerically investigated forced convection due to oscillating compressible ideal gas (Refrigerant-12m) flow in a packed bed. The porosity of the bed was 39%. Byun et al. [7] analyzed heat transfer due to oscillating flow through infinitely large porous slab using the two-equation model (thermal nonequilibrium). Habibi et al. [8] solved the heat transfer equations for a two-dimensional channel partially filled with a porous medium subjected to reciprocating air flow. The channel was discretely heated on one side to simulate compact circuit boards.
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Nomenclature A Ao Iuni L Nu ppi q00 ReD Reu t U xmax
cross-sectional area of test section (m2) non-dimensional displacement index (for temperature uniformity) length of porous medium (m) local cycle-averaged Nusselt number number of pores per inch of foam heat flux (W m2) Reynolds number based on pipe diameter kinetic Reynolds number time (s) average velocity (m/s) maximum flow displacements (mm)
€ Pamuk and Ozdemir [4] presented experimental heat transfer results for oscillating water flow in two sets of mono-sized packed steel balls (1 and 3 mm). The porosity of the first set was 36.9%, while it was 39.1% for the other. The effect of various parameters on heat transfer was studied, e.g., frequency, flow displacement and heat input. Results were presented in terms of cycle-averaged local Nusselt number and space-cycle-averaged Nusselt number. The latter correlated well with the kinetic Reynolds number and nondimensional flow displacement. Recently, Dai and Yang [9] numerically studied oscillating gas flow and heat transfer in regenerative cryocoolers using the Lattice Boltzmann Method. They noted that the velocity and temperature profiles were mainly influenced by the Womersley number. Little vortices were observed near the surface of the solid phase. Pathak et al. [5] numerically studied oscillating flow and heat transfer in a 75%-porous medium composed of square cylinders. The working fluid was helium. The Nusselt number strongly depended on flow oscillation frequency and amplitude. Significant phase lag occurred among velocity, pressure, temperature and heat transfer processes. For heat transfer due to oscillating flow in metal foam, there are only few published studies. Leong and Jin [10] experimentally studied heat transfer due to oscillating air flow through a channel filled with aluminum foam and subjected to constant wall heat flux. The 90%-porous foam was produced by sintering and had 40 pore per inch (ppi). The cycle-averaged Nusselt number increased with both the kinetic Reynolds number and dimensionless amplitude of flow displacement. A correlation for the length-averaged Nusselt number as a function of these two non-dimensional parameters were provided. In a different investigation, Leong and Jin [11] conducted experiments to study the effect of frequency on heat transfer performance of metal foam heat sinks subjected to oscillating flow of air. The aluminum foam used in the heat sinks had 10, 20 and 40 ppi. The cycle-averaged temperature decreased with increasing kinetic Reynolds number while the Nusselt number exhibited the opposite trend. Better heat transfer was noted for foam with low pore density. In a third experiment, Leong and Jin [12] studied heat transfer of oscillating air flow in two porous channels having commercial aluminum (20-ppi) and copper (60-ppi) foams with porosities around 90%. The oscillating flow amplitude was larger than the length of the test section (in order to ensure proper cooling). The local wall temperature was maximum at the center of the test section, and the cycle-averaged wall temperature decreased with increasing Reynolds number. The cycle-averaged Nusselt number
z
49
coordinate along flow direction, distance from entrance
Greek
m u r
viscosity (Pa s) angular frequency (rad/s) density (kg/m3)
Subscripts f fluid i inlet max maximum min minimum w wall z flow direction, local
had a concave shape with a minimum at the center of the channel. Heat transfer was higher for the case of copper foam due to its higher conductivity, as expected. In a fourth paper, Leong and Jin [13] experimentally studied oscillating flow through a channel filled with metal foam. For fluid flow characteristics, these authors stated that the non-dimensional fluid displacement and the kinetic Reynolds number were the appropriate similarity parameters for oscillating flow in open-cell metal foam. No heat transfer information was given in Ref. [13]. Fu et al. [14] carried out experiments on heat transfer of oscillating air flow in channels filled with commercial aluminum (40ppi) and carbon (45-ppi) foams-each having a porosity around 90%. The uniformity of the surface temperature in oscillating heat transfer was displayed. Ghafarian et al. [15] conducted computational analysis of heat transfer for oscillating air flow through a metal-foam channel heated from one side. They invoked the local thermal equilibrium assumption between the solid and fluid phases of the foam. The effect of the porosity, thermal conductivity and solid-fluid thermal conductivity ratio of the foam on heat transfer was investigated. The main conclusion was that heat transfer increased by employing high amplitude and high frequency. € As indicated by Pamuk and Ozdemir [16], and by the literature review given above, all experimental studies in the literature concerning oscillating flow and heat transfer in porous media (including metal foam) used gases, mostly air, as the working fluid. Oscillating flow of liquid, e.g., water, in metal foam has only been presented recently [17,18]; no heat transfer findings were given. One main difference between gas and liquid flows in porous media is that dispersion is significant in the latter, while so weak in the former that it has been ignored [19]. Another difference is the length of the entrance region, which depends strongly on the Prandtl number of the working fluid. Both of these matters affect oscillating heat transfer significantly. The purpose of the current experimental study is to furnish heat transfer characteristics due to oscillating water flow in commercial open-cell metal foam in terms of pertinent parameters. The results of the current study will be contrasted to those in previous studies employing air flow in similar metal foam; and also to the oscillating flow heat transfer results obtained for different porous media (e.g., packed beds of spheres and screens). A comparison of oscillating water flow heat transfer and steady state heat transfer in the same metal foam of the current study will also be provided. The aim is to enhance fundamental understanding of heat transfer in oscillating liquid flow in metal foam in order to guide engineering design tools (analytical and numerical) for potential applications, e.g., cooling
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systems for high-power devices and regenerators based on metal foam. The new experimental results can be used for validation of analytical and numerical modeling of the complex heat transfer phenomenon generated by oscillating liquid flow. 2. Experiment Fig. 1 is a schematic of the experimental setup. The test section was made from an aluminum alloy (6061-T6) pipe having inner diameter of 50.80 mm, wall thickness of 6.35 mm and length of 305 mm. Commercial open-cell aluminum foam (ERG Materials and Aerospace) having 20 ppi and porosity of 87.6% was brazed to the inside surface of the pipe, Fig. 2. Brazing minimized thermal contact resistance. The brazing technique is used in intricate situations and is ideal for joining complex assemblies and geometries, e.g., porous metals, powder metals, etc. In the so-called aluminum dip brazing process, which was used in preparing the test section of the current paper, the parts to be brazed are chemically cleaned then assembled with braze foil (88% aluminum and 12% silicon) preplaced between the braze surfaces and joints. The assembly is then preheated in an air furnace to 552 C to insure uniform temperature of dissimilar masses in the assembly. The parts are then immersed in a molten salt bath (aluminum brazing flux). The bath is maintained at 590 C ± 2.5 C in a furnace. As the assembly is immersed or dipped, the molten flux comes in contact with all internal and external surfaces simultaneously. Since the bath is a flux, complete bonding on oxide-free surfaces assures extremely high quality joints. Multiple holes were drilled along the tube wall in a straight line. The diameter of each hole was 1 mm and the depth was 4 mm. The holes were spaced 10 mm from each other along the length of the tube. The first hole was 1 mm away from the inlet of the pipe. In each hole, a type-K thermocouple was inserted; thermal epoxy then filled each hole, which guaranteed that there were no air pockets trapped in the holes. As such, the wall temperature could be measured along the pipe.
Fig. 2. Photograph of metal-foam test specimen.
Fig. 1. Schematic of the experimental setup: 1. Test section (metal foam), 2. Polyethylene tubes, 3. Steel pipes, 4. Connecting hoses, 5. Oscillation generator, 6. Crank arm, 7. Flywheel, 8. Motoreductor, 9. Inductive proximity Sensor, 10. Thermocouple wires (from metal foam and polyethylene tubes), 11. Data logger, 12. Computer, 13. Cooling thermostats, 14. Water inlet for thermostats, 15. Water outlet.
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A surface heater was wrapped around the exterior of the tube. The heater was made of resistance heating ribbons each having 1.66 U/m. Mica layers on both sides of the heater provided electrical insulation; and steel sheet layers provided cover and structural support to the heater. The rating of the heater was 1780 W at 60 V; it was powered by two 40-VDC power supplies connected in series. To guarantee good insulation, the whole assembly was covered with five layers of ceramic fiber paper (4-mm thick) with thermal conductivity 0.058 W/m K. It must be noted that during preliminary unidirectional steady-state runs, an average random heat loss of approximately 8.2% was recorded. It was obtained by applying an overall energy balance to the test section. The test section was connected to two 51.4-mm-diameter 200mm-long Polyethylene tubes at its two ends via flanges. In each of these tubes, five thermocouples spanning the cross section were inserted to measure the inlet and outlet temperatures of the water. The outlets of these Polyethylene tubes were connected to stainless steel pipes 32 mm in diameter and 110 cm in length. The ends of these pipes were attached to an oscillating flow apparatus via hoses. The two steel pipes constituted inner tubes of two tube-intube heat exchangers. Two cooling thermostats (LAUDA Alpha RA 8) with a cooling capacity of 0.225 kW each provided cold water to these heat exchangers, in order to remove heat supplied to the test section. The main component of the oscillation generator was a doubleacting cylinder which was connected to an electrically driven 7.5kW motoreductor by means of a flywheel and a crank arm. The inner diameter of the hydraulic cylinder was 50 mm and the diameter of the piston installed inside it was 32 mm. This mechanism could produce a maximum stroke of 200 mm. The rotational speed of the motoreductor was controlled by a variable speed ACdrive (6.99e20.97 rpm). Additionally, an adjustment system mounted on a flywheel allowed changes in stroke. The set-up was fully charged with water and connected to the oscillating generator. In order to fill the system with water while avoiding entraining air, the whole system was vacuumed down to an absolute pressure of 221 mbar. Heavily-filtered water was allowed to flow into the system from taps at the two ends of the piston. Accidental air bubbles were removed from the system through a purger, by tilting the whole set-up and/or by dismantling and reassembling parts of the set-up. All sensors were connected to a data logger. For a given oscillating flow run, the water coolers were switched on until they could provide cooling water at about 17 C. The heater was then switched on to provide the desired constant wall heat flux of 15,519 W/m2 to the test section. The stroke length of the piston was set to a desired value, the oscillation generator was switched on, and the oscillation frequency was ramped to a targeted level. After the system stabilized (2.5 h approximately), a Keithley 2700 XLINX data acquisition system, which was installed in a computer, communicated with the data logger and recorded signals from all sensors. One signal came from a clicker that touched a bump on a flywheel (part of the oscillation system) once per cycle; this signal was used to calculate the angular speed. The sampling rate changed between 10 and 30 readings per second due to device limitations. The above was repeated for line frequencies 5 and 15 Hz, and stroke lengths (displacement of piston) 130 mm, 170 mm and 195 mm. It took about 30 min for the system to reach steady periodic conditions after each change in frequency. For a given oscillation frequency, the sampling rate for only one data point was 2.42 Hz. This value was more than three times higher than the highest oscillation frequency. Therefore the data logger was able to capture the actual frequency of the system and the temperature amplitude. Even though the data acquisition system was capable of working at higher sampling rates, higher
51
frequencies were avoided due to the risk of noise. It also should be noted that higher line frequencies caused mechanical vibrations of the set-up and some buckling of the supporting metal frame, while lower line frequencies caused overheating of the motoreductor. 2.1. Data reduction The maximum fluid displacements are related to the displacements of the piston according to conservation of mass, and the fact that water is an incompressible fluid. The maximum flow displacements (xmax) at the entrance of the metal foam are calculated from the ratio of the cross-sectional areas of piston and entrance of porous pipe as
xmax ¼
2RAp A
(1)
where R is the flywheel radius and Ap and A are the cross-sectional areas of the double acting cylinder and metal-foam pipe, respectively. This calculation results in 74.4 mm, 97.2 mm and 111.5 mm for xmax. The non-dimensional displacement is defined as
Ao ¼
xmax D
(2)
where D is the pipe inner diameter. For each displacement, line frequency was changed from 5 Hz to 30 Hz by the servo drive of motor. Actual flow frequency, which was linearly proportional to the line frequency, changed from 0.116 to 0.348 Hz. The motoreductor operated at 69.7 rpm at 50 Hz line frequency. The displacement of the piston is taken as zero at the rear position inside the cylinder and as maximum (equal to the diameter of the flywheel) at the forward position. The piston displacement is essentially equal to the fluid displacement since the fluid is incompressible. Hence, at the entrance of the foam, the fluid displacement xm varies with angular frequency u and time t according to
xm ðtÞ ¼
xmax ð1 cos utÞ 2
(3)
The cross-sectional mean fluid velocity in the foam pipe is
uðtÞ ¼ umax sin ut
(4)
where umax ¼ uxmax/2. The kinetic Reynolds number is defined by
Reu ¼
ruD2 m
(5)
where r and m are the density and viscosity of water. Two values of the kinetic Reynolds number were realized: 1873 and 5619. These values correspond to flow frequencies 0.116 and 0.348 Hz. In some oscillating flow literature [8,9], the Womersley l number is used. This number is related to the kinetic Reynolds number by
l¼
1 pffiffiffiffiffiffiffiffi Reu 2
(6)
2.2. Uncertainty analysis Uncertainty in the directly-measured quantities, e.g., lengths and temperatures was based on errors provided by manufacturers of the measuring devices. The propagation of error in derived quantities, e.g., angular frequency, maximum fluid displacement
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52
and local cycle-averaged Nusselt number, was assessed via uncertainty analysis as described by Figliola and Beasley [20]. The uncertainties in length and diameter of the metal foam tube were 0.33% and 0.04%, respectively. As for the temperature, the error in the reading was ±1.1 C or 0.4%, whichever was greater, as provided by the manufacturer. As an example of uncertainty in derived quantities, the local cycle-averaged Nusselt number is calculated according to 00
Nu ¼
q D kf ðTw Ti Þ
(7)
where q00 is the heat flux, kf is the fluid conductivity, Tw is the local wall temperature and Ti is the inlet water temperature. As such the uncertainty in Nu is based on propagation of errors in the variables that are involved in calculating it, i.e., q00 , D, kf, Tw and Ti according to [20]:
vffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi !2 u 2 2 u d 00 dkf dTi dTw 2 dNu dD 2 q ¼ ±t þ þ þ þ 00 Nu q D kf Tw Ti
(8)
where d represents the uncertainty. The uncertainties in diameter and temperatures were stated above. The effective thermal conductivity was obtained from an analytical model published in Ref. [21]. These researchers indicated that this model was excellent in matching their measured values of the effective conductivities, with less than 10% error. Therefore, the uncertainty in the effective conductivity kf was conservatively assumed to be 10%. The uncertainty in voltage and current readings were taken as 0.1 V and 0.1 A, respectively. These are the accuracies of the digital readouts of the measuring devices of these quantities. If we further include the uncertainty of the outside surface area of the test section as 0.039%, we can calculate an uncertainty in the heat flux which is far below 10%. To be safe a much higher uncertainty in the heat flux (10%) was assumed. Putting all these values in Eq. (8), we obtain an uncertainty of 14.7% in Nu. In a similar manner, the uncertainties in the angular frequency and maximum fluid displacement were estimated as 0.43% and 0.51%, respectively.
3. Results and discussion In the presentation of the results, the starting time (zero) is taken at the end of transient behavior which lasted for about 2.5 h from applying heat and starting the oscillations.
3.1. Symmetry Fig. 3 shows the wall temperature at various locations along the foam tube for non-dimensional displacement 2.2 and kinetic Reynolds number 1837. The heat flux for this case was 8866 W/m2. The purpose of this run was to establish symmetry of the test section around the midpoint of the foam pipe. The wall temperature is seen to be maximum at the midpoint and it decays gradually to reach a minimum at the two inlets. The maximum error in the wall temperature is ±1.1 C, this error does not alter the statements made above regarding the trends in the wall temperature. The symmetric behavior about the middle of the test section (z/D ¼ 3.2) is also displayed in Fig. 4. The periodic patterns of equal-distance pairs of wall temperatures, i.e. z/D ¼ 1.62 and 4.77; z/D ¼ 0.04 and 6.36, and the regular phase shift within each pair further establish the symmetry. This regular phase shift is purely due to flow reversal. The amplitudes of the temperature in each pair are equal. In Fig. 4, the instantaneous velocity is plotted for reference. Due to symmetry, only one half of the test section was subjected to further measurements, which reduced the load on the limited data acquisition system, without loss of information. If only the maximum error in the wall temperature (±1.1 C) is considered, the periodic behavior of the wall temperature presented in Fig. 4 is not significant, since it lies within this error margin. However, based on the physics of oscillating flow and heat transfer, there is good reason to think that the periodic behavior is real, partly because it seems to be uniform and well ordered. If the maximum random error in the temperature readings was really present, no such ordered periodic behavior would show. 3.2. Instantaneous wall temperature The variation of wall temperature with time for the three locations on one half of the test section is plotted in Fig. 5. The nondimensional displacement Ao for this figure is 1.5; part (a) is for the low frequency, while part (b) is for the high frequency. The periodic behavior is obvious, especially for the locations 0.04 and 1.62 diameters from the entrance. The amplitude of the wall temperature is higher at 1.62 diameters since this location is inside the foam, while location 0.04 diameters is practically at the entrance of the foam. It should be noted that there is no oscillation of the wall temperature at the middle point of the test section (z/D ¼ 3.20) due to symmetry. The wall temperature oscillation is in phase with velocity for both low and high frequencies, indicating that thermal inertia for these flow frequencies does not play a significant role. € For 3-mm packed spheres, Pamuk and Ozdemir [4] reported a
Fig. 3. Wall temperature for Ao ¼ 2.2, Reu ¼ 1873, q00 ¼ 8866 W/m2.
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Fig. 4. Periodic behavior of wall temperature for Ao ¼ 2.2, Reu ¼ 1873, q00 ¼ 8866 W/m2.
phase shift or p radians between the velocity and wall temperature. This may be due to difference in porosity and thermal conductivity € of the steel spheres of Pamuk and Ozdemir [4] and the highlyporous open-cell aluminum foam of the current study. Significant phase shifts were also reported in the study of Pathak et al. [5] for heat transfer due to oscillating helium flow in a 75%-porous medium composed of square cylinders. There were no statements or evidence of the presence of a phase shift between velocity and wall temperature in the oscillating heat transfer studies due to air flow in metal and graphite foams [10e12,14]. Increasing the frequency, at the same displacement, is seen to cause a decrease in the wall temperature at the middle point of the test section, and an increase in the wall temperature close to the entrance. The higher frequency also reduces the amplitude of the wall temperature, which suggests that increasing the frequency leads to a more uniform wall temperature. At the low kinetic
Reynolds number, the wall temperature lies within the band 55e74 C, approximately, Fig. 5(a); while for high kinetic Reynolds number, this band narrows and ranges from 60 to 71 C, Fig. 5(b). These trends can be explained by considering the fact that increasing frequency amounts to higher fluid mean velocity [17], which enhances convection between the solid ligaments of the foam and the fluid; this in turn invites more heat transfer from the heated wall to the ligaments by conduction. The net effect is a decrease in the wall temperature at the center. The increase in the wall temperature close to the entrance at the higher frequency is due to a general increase in the bulk temperature in this region due to enhanced axial conduction. As the non-dimensional fluid displacement increases to 1.9 and 2.2, the same trends are present in the wall temperature, Figs. 6 and 7. However, the wall temperature in all locations is generally lower, indicating better rates of heat transfer for longer fluid
Fig. 5. Instantaneous wall temperature as a function of time for fluid displacement Ao ¼ 1.5: (a) for Reu ¼ 1873, (b) for Reu ¼ 5619.
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Fig. 6. Instantaneous wall temperature as a function of time for fluid displacement Ao ¼ 1.9: (a) for Reu ¼ 1873, (b) for Reu ¼ 5619.
Fig. 7. Instantaneous wall temperature as a function of time for fluid displacement Ao ¼ 2.2: (a) for Reu ¼ 1873, (b) for Reu ¼ 5619.
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displacements. For example, the wall temperature band for Ao ¼ 1.9 and Reu ¼ 1873 is 53e65 C, Fig. 6(a). For the maximum displacement Ao ¼ 2.2 and for Reu ¼ 5619, the wall temperature band is 51e58 C, approximately. The enhanced heat transfer is caused by the elongation of the two thermal entrance regions of the test section caused by increasing fluid displacement. Also for longer displacements, the fluid sweeps longer distances inside the test section and it removes more heat from the wall and eventually delivers this heat to the coolers. It can be stated here that one should not only consider the maximum error in the temperature readings (±1.1 C). The wellordered periodic behavior of the instantaneous wall temperature presented in Figs. 5e7 strongly suggests that this behavior is both real and consistent with the physics of oscillating flow and heat transfer. 3.3. Cycle-averaged wall temperature Fig. 8 shows the cycle-averaged wall temperature along the test section for the three displacements and two frequencies. The average wall temperature gradually increases as the distance from the entrance increases, and it reaches a maximum at the middle of the test section. This behavior is due to the presence of two thermal entry regions at both ends of the test section due to reversing flow direction in each oscillation. It is well known that heat transfer is maximum in the thermal entry region and it decreases as the distance from the inlet increases. This trend is similar to what was € presented in Pamuk and Ozdemir [4] for oscillating water flow in packed spheres (1 and 3 mm), Leong and Jin [10] for oscillating air
55
flow in 40-ppi aluminum foam in a rectangular channel, Leong and Jin [11] for oscillating air flow in 10-, 20- and 40-ppi aluminum foam in a rectangular channel, Leong and Jin [12] for oscillating air flow in 90%-porous 20-ppi aluminum and 60-ppi copper foams, and in Fu et al. [14] for oscillating flow of air in 40-ppi aluminum and 45-ppi graphite foams. In general, the wall temperature is seen to decrease as the displacement increases for both frequencies, which is consistent with [2,10,12]. This may be explained by the presence of a longer penetration zone of fresh fluid when the displacement is long. This fresh fluid can absorb more heat from the heated wall. Leong and Jin [11] tested only one displacement; and no statements were made by Fu et al. [14] regarding these effects. For the low frequency, there is a small difference between displacements 1.2 and 2.2, as seen is Fig. 8(a). The effect of displacement is more pronounced at the higher frequency, as shown in Fig. 8(b). And, the wall temperature is generally lower for the high frequency, which is the same observation made earlier. Higher frequency means higher mean flow velocity, which enhances convection (or reduces the thermal resistance) inside metal foam leading to a lower wall temperature. The combination of long displacement, Ao ¼ 2.2, and high frequency, Reu ¼ 5619, produces the lowest and most uniform wall temperature, as seen in Fig. 8(b). The interpretations of the behavior of the cycle-averaged wall temperature as presented in Fig. 8 are generally valid even when the maximum error in temperature (±1.1 C) is taken into account. The difference between the curves for various flow displacements is larger than the error in temperature, except perhaps for the curves representing displacements 1.9 and 2.2 for the lower frequency shown in Fig. 8(a). 3.4. Length-averaged wall temperature Fig. 9 is a plot of the wall temperature averaged over the length of the foam tube. The influence of both displacement and frequency can be ascertained quickly from this figure. Again, it can be stated that the longer the flow displacement and the higher the flow frequency, the lower the average wall temperature, with the influence of displacement being more pronounced at the higher frequency. The same trends were reported in other studies [4,10e12,14].
Fig. 8. Cycle-averaged wall temperature for (a) Reu ¼ 1873, (b) Reu ¼ 5619.
Fig. 9. Length-averaged wall temperature at low and high frequencies.
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One should bear in mind the maximum error in the wall temperature (±1.1 C). Considering this error, the length-averaged wall temperatures for the lower kinetic Reynolds number for fluid displacements 1.9 and 2.2 are practically the same. For all other cases, the temperatures spacing is well above the temperature measuring error, and thus the statements made above regarding the trends in the length-averaged wall temperature are well supported. 3.5. Temperature uniformity To assess wall temperature variations, Leong and Jin [12] and Fu et al. [14] defined the temperature uniformity index Iuni as
Iuni ¼
Tmax Tmin Tmax
(9)
where Tmax and Tmin are the wall maximum and minimum temperatures in K, respectively. A comparison of temperature uniformity for steady and oscillating flows is provided in Fig. 10. For this plot Reynolds number ReD was calculated as
ReD ¼
rUD m
(10)
where U is the average flow velocity for steady-state flow and is the time-averaged maximum velocity for oscillating flow:
U¼
2umax p
of length to hydraulic diameter of the pipe L/D [22]. If the channel is filled with a porous medium, other parameters are added to the list. For example Kim et al. [23] added Darcy number, the ratio of the effective thermal conductivity of the porous medium to that of the fluid keff/kf and the ratio of the effective heat capacity of the porous medium to that of the fluid ðrcp Þeff =3rcp . Habibi et al. [8] added the porosity of the porous medium 3. In the current study, only one fluid was used to oscillate in a single porous medium. In other words, the thermophysical properties and their ratios were fixed; similarly, the geometrical parameters of the test specimen were not varied. The two parameters that were varied were only the dimensionless displacement amplitude Ao and the kinetic Reynolds number Reu. These two parameters are most commonly used in probing and treating oscillating heat transfer data, e.g., Byun et al. [7], Leong and Jin [10,13], Pathak et al. [5] and Zhao and Cheng [22]. As such the current results will be interpreted based on these two key parameters, and their effects on flow and heat transfer. In oscillating-flow literature, e.g. Refs. [10,14], the local cycleaveraged Nusselt number is according to Eq. (7) above. This number decays in what seems to be an exponential fashion as the distance from the entrance increases, as shown in Fig. 11. It reaches a minimum at the middle point of the test section. These trends are valid for all fluid displacements and for the low and high frequencies. The presence of the thermal entrance region is responsible for the higher Nusselt number close to the inlet.
(11)
This is similar to what was employed by Fu et al. [14]. Fig. 10 is a plot of the temperature-uniformity index for steadystate and oscillating flows. Unfortunately, the steady-state and oscillating heat transfer data were not obtained at the same Reynolds numbers due to experimental limitations; as such no definite statements could be made. Leong and Jin [12] and Fu et al. [14] showed that the index is generally lower for oscillating flow indicating more uniform temperature, as compared to steady state heat transfer. Uniform surface temperature is desirable in electronic cooling to mitigate hot spots. 3.6. Cycle-averaged Nusselt number Heat transfer phenomenon due to oscillating flow in an open channel is described by the following similarity parameters: the dimensionless displacement amplitude Ao, the kinetic Reynolds number Reu (or Womersley number), Prandtl number and the ratio
Fig. 10. Temperature uniformity for steady and oscillating flows.
Fig. 11. Cycle-averaged Nusselt number for (a) Reu ¼ 1873, (b) Reu ¼ 5619.
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Longer fluid displacements seem to generally produce higher Nusselt numbers. The curves for displacements 1.5, 1.9 and 2.2 at the low kinetic Reynolds number of 1873 have some overlaps, especially close to the entrance of test section, Fig. 11(a). Considering the uncertainty in this Nusselt number (14.7%), one is unable to make any assertions. However, it is noticed that the effect of displacement is more severe when the frequency is high, Fig. 11(b). The highest Nusselt number is realized at the longest displacement and highest frequency, which is consistent with observations made earlier. The thermal entrance region for oscillating flow with large displacement amplitude is longer than that for the case with small amplitude. This means that higher heat transfer rates (higher Nusselt number) are obtained for larger displacement amplitude. As to the effect of frequency, higher frequency implies higher mean fluid velocity, which enhances the convection part of heat transfer, which is reflected in higher Nusselt numbers. The so-called annular effect simply means that the axial velocity near the wall is higher than the centerline velocity (with an inflection point in the velocity profile near the wall) [22]. Dai and Yang [9] indicated that there was annular effect in the temperature profile for oscillating flow in porous media, with this effect being more pronounced at higher kinetic Reynolds numbers. This basically signifies higher fluid temperatures close to the wall compared to the core region, and hence more heat transfer from the wall region to the core. The trends presented here are similar to what was presented for oscillating air flow in metal and graphite foam [10e14]. For oscillating water flow in packed steel spheres (1 and 3 mm), Pamuk and € Ozdemir [4] showed that the cycle-averaged Nusselt number increased along the porous medium for long displacements, and it decreased for short fluid displacements. These trends may be attributed to the large difference in porosity between the foam (around 90%) and packed spheres (36.9% and 39.1%). Another difference is in the thermal conductivity between aluminum foam and steel packed spheres. This is in addition to the vast difference in internal structure of the two porous media. € Pamuk and Ozdemir [24] experimentally showed that the transverse dispersion thermal conductivity increased linearly with the product AoReu for heat transfer due to oscillating water flow in steel balls. This added conductivity is responsible for heat transfer from the wall region to the core of the flow. Because transverse dispersion is directly proportional to AoReu, more heat transfer is expected for longer fluid displacements and higher frequency. This is consistent with the current results presented in Fig. 11.
57
Fig. 12. Length-averaged Nusselt number for current study and Leong and Jin [10].
only four foam cells, approximately. This indicates that there might have been considerable size effects in the results of [11]. Size effects in metal foam have been discussed in Refs. [25,26]. 4. Conclusion Characteristics of heat transfer due to oscillating water flow in commercial open-cell metal foam were experimentally acquired and presented for three flow displacements and two frequencies. The following statements can be made: For the frequencies encountered in this study, the wall temperature was in phase with flow velocity. Higher fluid displacements generally lowered the wall temperature and produced more uniformity in the wall temperature. The combination of long displacement, and high frequency produced the lowest and most uniform wall temperature. For the higher flow frequency case, the cycle-averaged Nusselt number was higher for higher flow displacement amplitude. This trend was not clear in the lower flow frequency case as Nusselt number curves for various flow displacement amplitudes overlapped and were not distinguishable considering the experimental uncertainty. To clearly establish the effect of frequency, more experiments are needed.
3.7. Comparison to Leong and Jin [11] Fig. 12 compares the results of the current study to those of Leong and Jin [11] who studied oscillating heat transfer in metal foam due to air flow. To have the most meaningful comparison, only the case for 20-ppi foam form [11] is used. The length-averaged Nusselt number for oscillating air flow of [11] is higher than that for oscillating water flow of the current study. A careful look at the study presented in Ref. [10] reveals significant differences between [11] and the current study: a) The foam channel of [11] was heated on one side only (heat sink arrangement). b) The non-dimensional displacement Ao employed in Ref. [10] was 4.08 (calculated based on the hydraulic diameter), while the maximum Ao for the current study was 2.2. The flow displacement has a strong effect on heat transfer, as was shown above in connection with Figs. 9 and 11(b). c) The height of the channel of [10] was only 10 mm. For commercial open-cell 20-ppi aluminum foam, this height contained
Acknowledgment This work was supported by the Scientific & Technological _ Research Council of Turkey (TUBITAK) under program 2221: 1059B211404522, for which the authors are very thankful. References [1] N. Dukhan (Ed.), Metal Foam: Fundamentals and Applications, DESTech, Lancaster, PA, 2013, p. xiv. € Bag € cı, M. Ozdemir, lu, Experimental fully[2] N. Dukhan, O. L.A. Kavurmacıog
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developed thermal convection for non-Darcy water flow in metal foam, J. Therm. Eng. 2 (2) (2016) 677e682. A.A. Lambert, S. Cuevas, J.A. del Rio, Enhanced heat transfer using oscillatory flows in solar collectors, Sol. Energy 80 (2006) 1296e1302. € M.T. Pamuk, M. Ozdemir, Heat transfer in porous media of steel balls under oscillating flow, Exp. Therm. Fluid Sci. 42 (2012) 79e92. M.G. Pathak, T.I. Mulcahy, S.M. Ghiaasian, Conjugate heat transfer during oscillatory laminar flow in porous media, Int. J. Heat Mass Transf. 66 (2013) 23e30. M. Sozen, K. Vafai, Analysis of oscillating flow compressible flow through a packed bed, Int. J. Heat Fluid Flow 12 (1990) 130e136.
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