Effect of Fin Orientation and Forced Convection on the Performance of Metal Foam Fins using a μ-CT Scan Based 3 D CFD Model

Metal foams are very attractive materials for thermal and electronic packaging applications due to their improved heat transfer capabilities. Their improved heat transfer effective properties are due to the relatively large contact area they possess because of their cell structure. This comes at the expense of the pressure drop. This work presents a methodology based on μ-CT scan to develop a realistic metal foam 3D model. The model is validated with experiments and used to study the behavior of the metal foam as a fin in terms of the temperature variation within the fin as well as the effect of the airflow velocity and fin orientation to the pressure drop. Results showed two major observations. First, this methodology could be used to identify a velocity value at which the fin orientation becomes obsolete and has no effect on the temperature variation. Second, the pressure drop alone could not be used to assess the fin, but also the fin orientation has to be taken into account to examine the total pressure drop.


Introduction
Open cell metal foams have been getting more attention recently in heat transfer and heat recovery applications.Due to their geometrical nature, the open cells increase the surface area in contact with any cooling fluid, leading to a more rapid temperature drop in any electrical or mechanical component.Two major drawbacks used to hinder the use of metallic foams, their manufacturability, and the pressure drop associate with their use.Recent advances in 3D printing, casting, and other techniques have helped in overcoming any issues related to manufacturing the desired foam shape for an application.The problem with the pressure drop cannot be avoided nor solved, but a more detailed analysis and understanding is needed to identify if the amount of pressure drop is considered relatively high or not.
In addition to their large surface area, metal foams have higher effective heat transfer properties because of the randomness in the cell structure.Therefore, it is sometimes difficult to identify a best configuration for a metal foam in a thermal or electronic packaging application without testing the model first.Experiments are useful but mostly for effective properties rather than a detailed assessment of the metal foam component.Therefore, the use of computational means has been a lot in the literature to assess the mechanical and thermal behavior of metallic metal foams [1][2][3][4].
A common approach in the literature is to model the metal foam using its effective properties without the need to have the actual geometrical representation.This approach overcomes the issues that comes with the difficulty in having a realistic 3D model but gives results in terms of the effective performance instead of a detailed analysis.Odabaee and Hooman [5] studied the effect of various parameters such as free stream velocity, metal foam thickness, metal foam porosity, etc. on the heat and fluid flow in metal foam heat exchangers.The numerical model used in their work modeled the metal foam as an isotropic homogenous porous media.Bayomy et al. [3,6] used effective metal foam properties to simulate the metal foam behavior and investigate the heat transfer characteristics in a metal foam heat sink.The approach is useful to study the behavior of the metal foam based heat sink design, but one has to pay attention to the calculation of the effective properties, as the accuracy of the model will depend on it.
A more involved approach is to develop geometrical construction of the metal foam open cells.This approach would allow a more detailed analysis of the fluid flow within the foam and would give results that are more detailed.Kopanidis et al. [1] constructed a 3D geometrical model for few metal foam open cells.The cells were used to generate a larger foam sample using symmetry.Finally, a random part of the large foam sample was cut out to produce a more random metal foam cell structure.The model was used to study the fluid flow characteristics of metal foams.A similar approach was used by Peng et al. [7] by using a body centred structure to construct a single cell.The unit cell model was used to compute the effective thermal conductivity and analyse the heat transfer at the gas-solid interface.This approach of the 3D geometrical construction is based on the Lord Kelvin's model and is not practical for performance analysis of thermal applications.
The most appropriate approach for detailed analysis of metal foams and metal foam components is the use of μ-CT scan to develop a realistic 3D representation.Della Torre et al. [8] used μ-CT scan to study the micro-structure of the foam.Mathematical calculations based on the CT scan model were compared with numerical computations of an ideal geometry.The models were used to study the fluid flow and the pressure drop.Ranut et al. [2,9] used μ-CT scan to develop a 3D metal foam geometry that was used to study the flow and thermal behavior using CFD analysis at the pore level.A detailed analysis on the effect of fluid flow Reynolds number on the heat transfer coefficient was presented.The model was useful in providing detailed analysis of the metal foam and its thermal behavior.
A similar μ-CT scan model was developed by Al-Athel et al. [4,10] and used to study the thermo-mechanical behavior of metal foam heat sinks.The model used was validated against experiments and used to calculate the heat transfer coefficient under free and forced convection.It is of importance to note that the foam geometry used was bigger than a unit cell, which is required to capture the number of pores per inch (PPI).This has an advantage of being able to look at the cell level to extract any needed data, in addition to studying the thermal behavior of the heat sink component as a whole.
In this work, the metal foam model developed in [4,10] is used to study the temperature variations and pressure drop in metal foam fins using computational fluid dynamics (CFD) analysis.In the literature, there exists a lot of work on metal foams using CFD and most of it can be  Specific heat (J/Kg.K) 895 A major advantage of temperature distribution results in Figure 5Figure 7 is that the CT scan model is detailed and can be used to extract the special temperature distribution at any point instead of having average values in effective models.Another observation can be clearly seen by comparing the temperature field in Figure 5,Figure 6, and Figure 7.In the case of airflow with 90 o fin orientation, the temperature values are almost uniform along every cross section, whereas for 0 o , and to some degree at 45 o , there is a special temperature gradient at both horizontal and vertical axes.These two observations provided by the μ-CT scan model can be very useful for designers of heat sinks, heat exchangers, and other applications that require the use of a heat transfer cooling system.Two major design parameters could be looked at for example, the efficiency or effectiveness of the fin, and the thermal resistance.The effectiveness of a fin in a heat sink could be defined as [12]: where R c is the heat sink capacity, T b is the base temperature, T fin is the fin temperature at the top, and T amb is the ambient temperature.The thermal resistance is defined as [13]: where Q is the total dissipated power.As can be seen from Eq. ( 1) and ( 2), the temperature data is important in calculating such parameters.The advantage of having a detailed model is the ability to utilize the temperature field data available to optimize the size and shape of the fin to minimize the thermal resistance and increase the efficiency.The analysis provided here does not require the computatio provides in analysis, it the 90 o giv on of the h nsight on t t can be seen ves the least

Temp
The metal look into t velocity.F airflow vel comes to t becomes c design poin of the fin o   means that efficiency of the metal foam fin is not the same for the whole fin.This could lead to more optimized designs of the fin cross section that would give the fin a uniform efficiency.
The analysis also showed that, depending on the size of the metal foam fin, the effect of the fin orientation on the temperature variation within the fin becomes negligible at high velocities.Actually, this appears to happen at a fixed velocity value for all cases.
The pressure drop was calculated per unit length and analyzed as a function of the airflow velocity and fin orientation.It is of high importance to not only look at the pressure drop values, but to examine the fin orientation associated with it.For example, a fin orientation of 0 o appears to have the least pressure drop per unit length for low to intermediate velocities.That being said, the 0 o orientation is the case where the airflow has to pass through more metal foam as compared with 45 o and 90 o m therefore making it the worst case for total pressure drop.
The methodology provided in this study extends on previous work presented in the literature that utilized μ-CT scan to develop a realistic metal foam model.The model presented in this work is of relatively large size and has 2.5x the minimum length required to capture the real behavior. Figu

Figure 7
Figure 7 T Temperature Figure 9 to Figure 8 orientation higher airf temperatur observation not the dis the horizon

Figure 10
Figure 10 P

Table 1
Metal foam fin CFD set of simulations.

Table 2
Material properties of 6101 aluminum alloy.