Thermal analysis of a metal foam subject to jet impingement

Thermal analysis of a metal foam subject to jet impingement

International Communications in Heat and Mass Transfer 39 (2012) 960–965 Contents lists available at SciVerse ScienceDirect International Communicat...

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International Communications in Heat and Mass Transfer 39 (2012) 960–965

Contents lists available at SciVerse ScienceDirect

International Communications in Heat and Mass Transfer journal homepage: www.elsevier.com/locate/ichmt

Thermal analysis of a metal foam subject to jet impingement☆ Kok-Cheong Wong School of Mechanical, Manufacturing and Materials Engineering, University of Nottingham Malaysia campus, Jalan Broga, 43500 Semenyih, Selangor, Malaysia

a r t i c l e

i n f o

Available online 2 June 2012 Keywords: Jet impingement Metal foam Porous heat sink Infrared thermography imaging Temperature contour

a b s t r a c t The present study conducted a thermal analysis on a FeCrAlY foam subjected to jet impingement cooling in a horizontal channel. The temperature distribution of the metal foam is captured with infrared thermography imaging camera for different jet velocities (219.5 ≤ Pe ≤ 548.9). Two dimensional numerical studies have been conducted to obtain the temperature contour of the metal foam and compared to the thermographic images. The thermographic images show inconsistencies in temperature variation across the metal foam due to the porosity within the metal foam. The temperature contours of the metal foam obtained numerically are found to be similar to the thermographic images. The top portion of the metal foam directly impinged by the jet of low velocities shows lowest temperature, but the heat near the heated surface is transferred majorly through conduction. © 2012 Elsevier Ltd. All rights reserved.

1. Introduction Jet impingement is a cooling technique used for various systems that require cooling such as gas turbine blades and electronics components. Generally, heat transfer can be enhanced by extending heat transfer surface area with a heat sink. One of the heat sink with higher surface area is metal foam heat sink which is porous. The study of jet impingement on metallic foam heat sink has been extensively investigated, for example, the study of square pin-fin heat sink with impinging jet by Issa and Ortega [1], the study of cooling performance of a plate-fin heat sinks with a confined slot jet impingement by Lin et al. [2], and the heat transfer of metal foam heat sinks with a slot jet by Jeng and Tzeng [3]. Recently, the study of the heat transfer of porous heat sink/metal foam received considerable attention. Researchers found that metal foams are capable of enhancing the heat transfer rate [4-6]. Jeng and Tzeng [4] investigated numerically the jet impingement cooling of a metal foam heat sink and found that the use of the aluminum foam could give 2 to 3 times higher heat transfer performance relative to the case without the aluminum foam. Another study by Kim et al. [5] showed that an aluminum foam heat sink with low pore density is thermally 28% more efficient than a conventional parallel-plate heat sink of the same size. Jeng and Tzeng [6] investigated numerically the mixed convection in a lid-driven square enclosure filled with water-saturated aluminum foams. They found that, higher porosity of foam promotes enhancement of convective heat transfer, but lower porosity gives higher total heat transfer due to higher value of effective thermal conductivity. This shows the potential of heat transfer enhancement through metal foam heat sink. ☆ Communicated by W.J. Minkowycz. E-mail address: [email protected] 0735-1933/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.icheatmasstransfer.2012.05.021

Metal foam is a type of porous medium. The use of porous medium however not necessarily improves the heat transfer as compared to without porous medium [7]. De Lemos and Fishcher [7] considered a jet impingement cooling on a heated plate covered with and without a porous layer. They investigated the effect of porosity and thickness of the porous layer. Their results show that, for low porosity medium, the use of porous medium is always beneficial as compared to without porous medium regardless of the height of the porous medium. However, the high porosity medium with small thickness might give lower heat transfer rate as compared to without porous medium. Recently, several authors [8-10] conducted numerical studies of confined jet impingement cooling of a porous layer but in the mixed convection regime. The study by Saeid and Mohamad [8] reported that the average Nusselt number increases by either increasing the Rayleigh number, increasing the jet width when Péclet number is high, or by narrowing the distance between the jet and the heated surface. However, mixed convection may lead to minimum heat transfer rate. Minimum heat transfer rate is found occurring at some values of Péclet number due to the weak dispersed jet flow and interaction of buoyancy force which caused minimum flow rate through the heated surface. Another study by Wong and Saeid [9] investigated the jet impingement through porous medium under thermal non-equilibrium conditions in the mixed convection regime and shows similar trend with the study by Saeid and Mohamad [8]. Marafie et al. [10] have considered partially porous channel. They found that the heat transfer rate can be enhanced by decreasing both the channel height and porosity, and increasing the Richardson number and solid-to-fluid thermal conductivity ratio. Infrared thermography imaging method was used by many researchers to measure the surface temperature of solid objects especially heat exchanger or heat sink. An infrared thermography imaging

K.-C. Wong / International Communications in Heat and Mass Transfer 39 (2012) 960–965

Nomenclature c d g h H k L Nu Nu Pe s T Vo x, y X, Y

height of metal foam (Fig. 1), m half of the width of the jet (Fig. 1), m gravitational acceleration, ms − 2 distance from jet inlet to the bottom of porous medium, m, or heat transfer coefficient, Wm − 2 K − 1 dimensionless distance from jet inlet to the bottom of porous medium, H = h/L thermal conductivity, W/m K half of the heat source length (Fig. 1), m local Nusselt number, Eq. (1) average Nusselt number along the heat source, Eq. (1) Péclet number, Pe = V0L/αf distances from the end of heated portion to the end of domain (Fig. 1), m temperature, K jet velocity, ms − 1 Cartesian coordinates, m dimensionless distance, X ¼ xL, Y ¼ yL

Greek symbols c θθ non-dimensional temperature, θ ¼ TT−T h −T c 2 −1 α thermal diffusivity, m s

Subscript c f h s

cold wall fluid hot wall solid

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impingement cooling. The measurement accuracy is ±2% with a thermal sensitivity of 0.08 °C at 30 °C and a spatial resolution of 1.3 mrad. The thermography camera is placed in front of the FeCrAlY foam heat sink. The images obtained provide the temperature distribution of the metal foam. Calibration of the thermography imaging camera was conducted. For the calibration, thermocouples are placed at few locations of the metal foam and the temperatures were read from data logger. At the same time, the temperatures at these locations were also read from the thermal imaging camera. The emissivity factor was adjusted until the discrepancies between the temperature measured by data logger and the thermal imaging camera become minimal. Then the emissivity factor is considered the best value for the experiments. The value of emissivity factor obtained for FeCrAlY foam is 0.68. Eight pieces of K-type thermocouples were placed in the heat spreader equidistantly to measure the temperature of the heat spreader. The thermocouples were connected to a data logger. The thermocouples were calibrated at ice point and boiling point to check its accuracy. The maximum deviation is about ±0.5 °C. The maximum temperature non-uniformity across the heat spreader is found to be ±1.0 °C from the average value. The average temperature of these thermocouples gives the value of Th. Note that, the thermography imaging camera only captures the image of half of the FeCrAlY foam heat sink in order to focus on a smaller area to obtain a better image. The jet width (2d) and the heater length are 10 mm and 127 mm, respectively. The distance h (see Fig. 2) is 50.8 mm. The FeCrAlY foam is obtained from Porvair Advanced Materials [15]. It has pore density of 20 ppi and a height of 28 mm. The length of the FeCrAlY is the same as the length of the heater and heat spreader. Its permeability, coefficient of friction and effective thermal conductivities were determined by methods described in Refs. [16,17] and their values are 9.13 × 10 − 8 m 2, 0.22 and 0.531 W/m K respectively. The physical setup of the experiment is shown in Fig. 1.

3. Numerical procedures

system consists of a camera that connects to a PC or data storage system, equipped with a data processing software. With the infrared thermography imaging camera, Meinders and Hanjalic [11] investigated the heat transfer coefficient of an array of cubic objects in a tunnel flow, and Ay et al. [12] investigated the heat transfer of a platefinned-tube heat exchanger. The infrared thermography imaging method is non-intrusive and only can measure the surface temperature of a solid object. Li et al. [13] investigated the thermal performance of plate heat sinks with confined impinging jet by an infrared thermal imaging system FLIR (ThermaCAM SC500 camera). Research study related to the use of infrared thermal imaging method on porous medium or metal foam cannot be found. The objective of the present study is to study thermal response of a metal foam under the low velocity slot jet impingement in a horizontal channel using the infrared thermal imaging method and compare to the numerical result. The metal foam used for the investigation is a FeCrAlY foam.

2. Experimental setup The experimental setup used in the previous study [14] is used in the present study to investigate the thermal response of the air jet impinging onto heated metal foam (made of FeCrAlY) in a horizontal channel. The experiment setup is shown schematically in Fig. 1. In the present experiment study, the infrared thermography imaging system of FLIR Systems Model Thermovision A40 (Fig. 1b) was used to capture thermographic image of the metal foam during jet

The physical model of numerical study is shown in Fig. 2. Fluid superposed porous layer is modeled for the domain. The physical parameters in the present problem are the jet width 2d, the jet velocity Vo, the temperature difference (Th − Tc), the heat source length 2L and the distance from the jet inlet to the heat source h. Tc is the fluid temperature at the jet inlet whereas Th is the temperature of the heat source measured at the heat spreader. The metal foam is assumed to be homogeneous and isotropic. In the present study, the solid matrix of the porous medium is assumed to be in local thermal equilibrium with the fluid. The flow in the channel is assumed to be steady, laminar and incompressible. The thermophysical properties of fluid are evaluated based on a reference temperature of(Th + Tc)/2. The Boussinesq approximation is used for the relation of temperature-density variation. Two sets of governing equations are required to solve the two dimensional problem with fluid/porous interface; one for porous region, another for the clear fluid region. The codes, boundary conditions and numerical method used in the present study are the same with the previous study [14]. Therefore, all the governing equations for fluid region and the porous region for continuity, momentum and energy are the same as given in the Ref. [14]. The energy balance, grid test and also validation were also reported in the previous study [14]. The heat transfer performance is evaluated with the local Nusselt numbers along the heated surface and the average Nusselt numbers are defined respectively as:

NuL ¼

hL ¼ kf

  ∂θ − ; ∂Y Y¼0

1

NuL ¼ ∫0 NudX

ð1Þ

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Air inlet (fan) Expansion diffuser Straightener

Air chamber

Contraction diffuser Aluminum plate (Top plate)

Jet inlet Air oultet

h

FeCrAlY foam Wood (Bottom plate) Heat spreader (foil heater at bottom)

(a) Schematic diagram Fan

Expansion diffuser

Thermography camera

Contraction diffuser

Transformer DC power supply

Anemometer

Porous foam

(b) Experimental setup with infrared thermography imaging camera Fig. 1. Experimental setup.

4. Experimental results

distribution of thermographic images of the FeCrAlY foam is then compared to the numerical results. Four thermographic images for Pe = 219.5, Pe = 329.3, Pe = 439.1 and Pe = 548.9 were taken and shown in Fig. 3. It should be highlighted that the thermographic images are taken on the outer surface of the metal foam. The outer surface of the foam is bounded by the

Experiments investigating the flow patterns of different jet Péclet numbers (Pe = 219.5 to 548.9) have been carried out and presented in Ref. [14]. Experiments conducted in the present study are to capture the thermographic images of the metal foam. The temperature

y

2d Tc (isothermal) g

x

0

h

V 0 , Tc A

Tc (isothermal) B

Clear fluid region

0

x

c

C

x adiabatic

Th (isothermal) 2L

adiabatic s

Fig. 2. Physical model of numerical study.

K.-C. Wong / International Communications in Heat and Mass Transfer 39 (2012) 960–965 116.8°C

Pe = 291.5

963 116.4°C

29.7°C

29.2°C

Pe = 329.3

Uneven solid density 114.2°C

116.3°C

Pe = 439.1

Pe = 548.9

29.8°C

27.7°C

Fig. 3. Thermographic images of different Péclet numbers.

acrylic plate. In the experimental setup, the foam is fixed in the channel without touching the acrylic plates. There is a small gap to ensure no direct contact between the acrylic plate and metal foam. This would avoid high heat transmitting through conduction to the acrylic plate. Furthermore, the temperature of the heated foam is high (with the highest temperature exceeding 110 °C) and may cause acrylic plate to be softened and deformed. For the thermographic images shown in Fig. 3, some patches of color in the middle of the foam can be observed. These patches are due to uneven density of solid matrix near the surface of foam. The metal foam often contains this type of defects of uneven solid density on the foam surface, as can be found in other Ref. [16]. The current manufacturing process of foam does not produce uniform porosity [18]. This will affect the emissivity of the region with higher solid density, and therefore they are seen as some patches of different color. The metal foam consists of metal fibers and pores. It can be observed in the images in Fig. 3 that, the temperature variation across the metal foam is not consistent in which the images show bright spots are followed by darker spots. The variation of temperature across the foam is checked and found to be up and down due to the porous structures of the foam. Fig. 4 shows the dimensionless temperature profile across a horizontal line at about 2 mm below the top of the metal foam for Pe = 219.5, 329.3, 439.1, 548.9. The temperature profiles in Fig. 4 appear to be inconsistent for all the values of Pe. The system cannot detect the temperature of the air in the pore as it can only capture the temperature of a solid surface. The pores appear to be darker and give different emissivity. Therefore, the pore area will show lower temperature as compared to the metal fiber.

The peaks along the temperature profiles are likely to be the location where there are metal fibers. The metal fibers are very fine and surrounded by the pores. The emissivity of the fine metal fibers could be affected. The thermal imaging camera might be giving inaccurate temperature as there is a discontinuity in emissivity which caused the fluctuation of temperature as evident in Fig. 4. Therefore, the investigation with infrared thermography method on metal foam does not give accurate measurement and a gross comparison between the thermographic images and numerical results is carried out and discussed in the next section. Generally, it can be observed in Fig. 4 that, the temperature decreases as Pe increases, indicating higher jet velocity results in better cooling or lower temperature.

(a) Pe = 219.5 (Δθ = 0.05, NuL = 0.741) Thermal plume

0.6 0.4 0.2

0 0

0.5

1

1.5

2

2.5

3

3.5

4

2.5

3

3.5

4

2.5

3

3.5

4

2.5

3

3.5

4

(b) Pe = 329.3 (Δθ = 0.05, NuL = 0.772) 0.6 0.4 0.2

0 0

0.5

1

1.5

2

(c) Pe = 439.1 (Δθ = 0.05, NuL = 0.826) Pe =219.5, 329.3, 439.1, 548.9

0.6 0.4 0.2 0 0

0.5

1

1.5

2

(d) Pe = 548.9 (Δθ = 0.05, NuL = 0.883)

X

0.6 0.4 0.2 0 0

Fig. 4. Dimensionless temperature along a horizontal line at about 2 mm from the top of the metal foam for different values of Pe.

0.5

1

1.5

2

Fig. 5. Isotherms of numerical results for different Péclet numbers.

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K.-C. Wong / International Communications in Heat and Mass Transfer 39 (2012) 960–965

Jet impingement area

(a) Pe = 219.5

116.8°

4

4

0.4

3

0.2

2 1

0 -1

-0.8

-0.6

-0.4

-0.2

29.7°C

0

Uneven solid density

(b) Pe = 329.3

116.4°C

0.4

4

4

3

0.2

2 1

0 -1

-0.8

-0.6

-0.4

-0.2

29.2°C

0

(c) Pe = 439.1

116.3°C

0.4

5

4 4 3

0.2

2 1

0 -1

-0.8

-0.6

-0.4

-0.2

29.8°C

0

Jet impingement area

(d) Pe = 548.9

114.2°C

0.4

5

4

4

3

0.2

2 1

0 -1

-0.8

-0.6

-0.4

-0.2

27.7°C

0

Fig. 6. Temperature distribution of numerical results (left) with Δθ = 0.05 and thermographic images (right) for different Péclet numbers.

5. Numerical results Numerical results have been obtained based on the same experimental conditions. The results of the mean Nusselt number have been obtained and shown in Fig. 5. The results in Fig. 5 show that as jet Péclet number increases, the value of NuL increases as expected. Grid independence test has been conducted for two mesh sizes (51 × 126) and (101 × 251). The maximum discrepancy between the two mesh sizes is less than 3%. Therefore, the results are considered robust. The numerical results for the temperature contour are plotted in Fig. 5 which shows the temperature of the clear fluid layer and the porous layer (colored). A thermal plume can be seen in the fluid layer in Fig. 5a–d. The thermal plume in Fig. 5a for Pe = 219.5 is about 45° relative to horizontal surface. When Péclet number increases, the angle gradually decreases. Obviously the plume occurs due to mixed convective flow as presented in the Ref. [14]. The isotherms near the heat source are approximately parallel to the heated surface, indicating major heat transfer of conduction through the metal foam. The isotherms of the porous domain in Fig. 5 are enlarged and illustrated in left part of Fig. 6 for the purpose of comparison with the thermographic images. The thermographic images shown in Fig. 3 for increasing Péclet number are processed to show based on temperature range or color band which the changes in temperature distribution can be observed easier. The processed images are

shown in the right parts of Fig. 6. Note that the isotherms of numerical results presented in Fig. 6 only show the temperature contour of the porous domain/metal foam. This is for easy comparison with the thermographic images that shows the temperature field of left half of the metal foam. Some of the color bands are numbered as “1, 2, 3, 4, 5” as indicated in right part of Fig. 6. The higher the color band number, the lower the temperature. The effect of increasing jet Péclet number shown in Fig. 6 can be observed clearer near the jet impingement area indicated by the black arrow. As Péclet number increases from Pe = 219.5, Pe = 329.3, Pe = 439.1 to Pe = 548.9, the color band near the impingement area (indicated in Fig. 6) shows that the temperature becomes lower. This can be observed with the changes in the color band “4” and “5.” Color band “5” becomes thicker and wider as Péclet number increases. This signifies that higher jet velocity has caused more cooling at the top of the metal foam where the jet impinges on, which corresponds to the higher average Nusselt number for higher Péclet number. This is justified by the temperature profiles shown in Fig. 4. The isotherms of the simulation results (left of Fig. 6) also show that the temperature gradient increases slightly as Pe increases especially near the jet impingement area. The isotherm patterns of the simulation result (left of Fig. 6) are compared with the color bands pattern of the thermographic images (right of Fig. 6) for each Péclet number presented. To show clearer variation, the color bands are divided by dotted line as shown in Fig. 6c–d. The gross comparison shows similarity between the color

K.-C. Wong / International Communications in Heat and Mass Transfer 39 (2012) 960–965

bands patterns of thermographic images and the isotherm patterns of simulation. 6. Conclusion The work in the present study provided information of the thermal distribution of the metal foam under confined jet impingement acquired by infrared thermography imaging method. No previous work is found to conduct similar thermal analysis of metal foam with infrared thermography imaging, coupled with the numerical analysis of low velocity jet impinging on a fluid superposed porous layer. The results of the thermography show inconsistency in temperature across the metal foam due to the porous structure of the metal foam. The temperature distribution of the metal foam obtained using infrared thermal imaging system was compared to the numerical results. The gross comparison between the temperature contour of the numerical results and thermographic images shows similarity. The thermographic images show that increasing the jet velocity results in better thermal performance. The top portion of the metal foam which is nearest to the jet shows lowest temperature on the metal foam. References [1] J.S. Issa, A. Ortega, Experimental measurements of the flow and heat transfer of a square jet impinging on an array of square pin fins, ASME Journal of Electronic Packaging 128 (2006) 61–70. [2] T.W. Lin, M.C. Wu, L.K. Liu, C.J. Fang, Y.H. Hung, Cooling performance of using a confined slot jet impinging onto heated heat sinks, ASME Journal of Electronic Packaging 128 (2006) 82–91. [3] T.M. Jeng, S.C. Tzeng, Experimental study of forced convection in metallic porous block subject to a confined slot jet, International Journal of Thermal Sciences 46 (2007) 1242–1250.

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[4] T.M. Jeng, S.C. Tzeng, Numerical study of confined slot jet impinging on porous metallic foam heat sink, International Journal of Heat and Mass Transfer 48 (2005) 4685–4694. [5] S.Y. Kim, J.W. Paek, B.H. Kang, Thermal performance of aluminum-foam heat sinks by forced Air Cooling, IEEE Transactions on Components, Packaging, and Manufacturing Technology 26 (2003) 262–267. [6] T.M. Jeng, S.C. Tzeng, Heat transfer in a lid-driven enclosure filled with water-saturated aluminum foams, Numerical Heat Transfer Part A 54 (2008) 178–196. [7] M.J.S. de Lemos, C. Fischer, Thermal analysis of an impinging jet on a plate with and without a porous layer, Numerical Heat Transfer Part A 54 (2008) 1022–1041. [8] N.H. Saeid, A.A. Mohamad, Jet impingement cooling of a horizontal surface in a confined porous media: mixed convection regime, International Journal of Heat and Mass Transfer 49 (2006) 3906–3913. [9] K.C. Wong, N.H. Saeid, Numerical study of mixed convection on jet impingement cooling in a horizontal porous layer under local thermal non-equilibrium conditions, International Journal of Thermal Sciences 48 (2009) 860–870 14. [10] A. Marafie, K. Khanafer, B. Al-Azmi, K. Vafai, Non-Darcian effects on the mixed convection heat transfer in a metallic porous block with a confined slot jet, Numerical Heat Transfer Part A 54 (2008) 665–685. [11] E.R. Meinders, K. Hanjalic, Vortex structure and heat transfer in turbulent flow over a wall-mounted matrix of cubes, International Journal of Heat and Fluid Flow 20 (1999) 255–267. [12] H. Ay, J.Y. Jang, J.N. Yeh, Local heat transfer measurement of plate finned-tube heat exchangers by infrared thermography, International Journal of Heat and Mass Transfer 45 (2002) 4069–4078. [13] H.-Y. Li, S.-M. Chao, G.-L. Tsai, Thermal performance measurement of heat sinks with confined impinging jet by infrared thermography, International Journal of Heat and Mass Transfer 48 (2005) 5386–5394. [14] K.-C. Wong, N.H. Saeid, C.S. Tan, Visualization of mixed convective rolls of a slot jet in a fluid-superposed metallic porous foam heated from below, Numerical Heat Transfer Part A 56 (2009) 20–41. [15] www.porvairadvancedmaterials.com. [16] V.V. Calmidi, R.L. Mahajan, The effective thermal conductivity of high porosity fibrous metal foams, Journal of Heat Transfer 121 (1999) 466–471. [17] N. Dukhan, Correlation for the pressure drop for flow through metal foam, Experiments Fluids 41 (2006) 665–672 88. [18] L.J. Betchen, A.G. Straatman, An investigation of the effects of a linear porosity distribution on non-equilibrium heat transfer in high-conductivity graphitic foam, Numerical Heat Transfer Part A 58 (2010) 605–624.