This paper presents a numerical investigation in which thermal performance characteristics of pin fin heat sinks enhanced with phase-change materials (PCMs) designed for cooling of electronic devices are studied. The paraffin RT44 HC is poured into the aluminum pin fin heat sink container, which is chosen for its high thermal conductivity. The effects of different geometrical parameters, including number, thickness and height of fins, on performance are analyzed. Different aspects for heat transfer calculation, including the volume expansion in phase transition as well as natural convection in a fluid zone, are considered in the study. In order to validate the numerical model, previous experimental data and the present results are compared, and an acceptable agreement between these two is observed. Results show that increasing the number, thickness and height of fins leads to a significant decrease in the base temperature as well as operating time of the heat sink.

Because of the fast development of modern technology and miniaturization of electronic packaging, new electronic devices generate a large amount of heat, which threatens their performance and efficiency. Therefore, thermal management of effective cooling systems has become one of the most important considerations in design of different pieces of electronic equipment. Considering the effects of temperature on the performance of electronic devices, an effective thermal design should be able to keep the working temperature of devices below their allowable maximum temperature during the entirety of normal operation.

There are common techniques, including air cooling, liquid cooling, piezoelectric pump and heat pipes, to remove high heat flux effectively from heat-generating electronic devices. Thermal energy storage, as a cooling method for electronic applications, is one of the techniques that have been widely researched in recent years. The thermal properties of some phase-change materials (PCMs), including melting- and solidification-related specifications, are listed by Abhat (1983). High latent heat of fusion, the capability of being a heat source at a constant temperature, and chemical stability are three of the favorite properties of PCMs. However these materials have the undesirable property of low thermal conductivity, which brings about a serious challenge in design application of PCM-based electronic cooling systems. In order to overcome this drawback, different techniques of enhancement have been proposed, including fins (Eftekhar et al., 1984; Henze and Humphrey, 1981), metal matrices (Ettouni et al., 2006) and nanoparticles (Ranjbar et al., 2011; Hosseini et al., 2013).

Several previous papers have studied the advantages of PCM utilization in
electronic cooling systems. As reported by Pal and Joshi (2001), use of a
PCM-based heat sink is an effective method for cooling of electronic
devices. Kandasamy et al. (2007) in a combined experimental and numerical
work studied the effects of various parameters such as power input level and
the system configuration on PCM melting rate. Results showed that the
geometrical shape of the package does not have a significant effect on the
performance, while the input power influences the melting rate noticeably.
Akhilesh et al. (2005) directed a numerical investigation to develop a
thermal design procedure that maximizes the operating time of a composite
heat sink which is made up of an elemental heat sink, PCM
and high-conductivity base material. Hosseinizadeh et al. (2011) reported a
parametric study on a plate fin PCM-based heat sink and found that
increasing the number of fins and their height results in a considerable
increase in overall thermal performance, whereas increasing the fins'
thickness only brings about a slight improvement. Baby and Balaji (2012)
compared the heat transfer performance of a plate fin heat sink with that of
a pin fin heat sink in an experimental study. Their results showed that the
pin fin heat sink exhibits a longer operation duration for electronic
devices in comparison with similar plate fin heat sinks. Baby and Balaji
(2013) experimentally developed an artificial neural network–genetic hybrid
algorithm to determine the optimum configuration of a PCM-based pin fin heat
sink in which the critical time is maximized. Shatikian et al. (2008)
recommended a correlation among Nusselt, Stefan and Fourier
numbers for a constant heat flux system. In their simulation, a complete
formulation was endeavored which considers convection in the fluid zone
and volume expansion of the PCM during phase transition. Nayak et al. (2006)
studied a numerical model for PCM-based heat sinks with some different types
of thermal conductivity enhancer (TCE) distribution. Their results showed that the use of TCE leads to a
lower chip temperature. They also concluded that the convection in the
melted PCM improves the temperature uniformity by increasing the effective
heat transfer coefficient. Saha et al. (2010) presented a numerical
investigation on melting of

The present work evaluates the melting process of the PCM in the presence of pin-fin-type thermal conductivity enhancers (TCEs) for electronics cooling applications. The main purpose of this article is to investigate different effective parameters on the heat sink base temperature and melt fraction. The studied geometric parameters are the number of fins (for three values), fin thickness (for three values) and fin height (for two values).

The schematic diagram of the PCM-based pin fin heat sink is shown in Fig. 1.
The heat sink is made of aluminum with a different number of fins as well as different fin
thicknesses, fin heights and base thicknesses. The dimensions of heat
sink base are 70 mm

Example of a PCM-based pin fin heat sink:

Numerical cases explored in this work.

Properties of materials employed in the present study.

In order to simulate the melting process of the PCM, the enthalpy–porosity
approach (Brent et al., 1988) is employed, wherein the porosity in each cell
is set equal to the liquid fraction in that cell. In order to allow the PCM
expansion during melting, the enclosure is filled to only 90 % of the fin
height and the remaining volume is occupied by air. Numerical approaches,
previously applied by other authors to heat sinks enhanced with plate fins
(Shatikian et al., 2005; Kandasamy et al., 2007), considered a similar
assumption to the expansion. A “volume-of-fluid” (VOF) model is used to
solve the PCM–air system in which a moving internal interface is considered
and interpenetration of the two fluids is disregarded (Hirts and Nichols,
1981). In this model, if the

For the aluminum base and fins, only a conduction mechanism is considered.
Accordingly, the energy equation is

In all simulations the initial temperature of the whole system is

Schematic of the computational domain.

Fin thickness and inter-fin distance for different fin numbers.

The boundary conditions applied to the computational domain, in Fig. 2,
are(a) heat flux to the bottom,

(b) symmetry boundary conditions at all enclosing sides,

(c) adiabatic boundary condition at fins' tip,

The SIMPLE algorithm within a 3-D in-house code (Rahimi et al., 2012)
developed by authors was utilized for pressure–velocity coupling. The QUICK
differencing scheme was adopted for solving the momentum and energy
equations, whereas the PRESTO scheme was used for the pressure correction
equation. The effects of time step and grid size on the solution were
carefully examined in preliminary simulations. Therefore, the time step in
the simulations is set to 0.005 s. Different grid sizes are used in the
simulations, varying from 9500 to 34 000 cells for the fin height of 15 mm,
15 500 to 56 000 cells for the height of 25 mm, and 18 500 to 74 000 cells for the
height of 35 mm. It is noticeable that, for the same fin height, the population of denser
fins requires a larger number of grid cells. The convergence is
checked at each time step, with the convergence criterion of

Comparison of base temperature profile between the present work and Hosseinizadeh et al. (2011).

In this section, the results of the parametric study are presented and discussed. The analysis involves the PCM melt fractions and the base temperatures as functions of time, which is intended to explain the effect of the geometry variation on the thermal performance of the heat sink.

Figures 4 and 5 present the melt fraction and base temperature as functions of time for different number of fins at various fin heights. As expected, for both fin heights of 15 and 25 mm, the total melting time of the PCM decreases as the number of fins increases, as shown in Fig. 4a and b. This is due to the fact that the PCM volume decreases as the number of fins rises. The lesser volume of the PCM leads to a latent heat potential reduction and thus a shorter melting period.

Melt fraction evolution with time for different numbers of
fins:

Base temperature evolution with time for different numbers
of fins:

The effect of the number of fins is examined by checking the base temperature profiles in Fig. 5. It can be seen that the curves have similar forms and trends for both fin heights of 15 and 25 mm. Because of the extra surface, 100 fins provide more heat storage capacity compared to 25 fins, so a lower base temperature is observed for a greater number of fins, i.e., a 100-fin unit has a lower base temperature compared to units with 49 and 25 fins. It should be noted that although the base temperature decreases as the number of fins increases (which is significantly effective in electronics cooling systems), the latent heat period (which maintains the base temperature within a specified and almost constant range) decreases. For instance, in Fig. 5b, the latent heat period for heat sinks with 25, 49 and 100 fins is about 392, 310 and 138 s, respectively. As mentioned earlier, this is due to the decrease in the latent heat capacity of the system while the number of fins increases.

Melt fraction evolution with time for different fin
thicknesses:

Figure 6 shows the melt fraction versus time for different pin fin
thicknesses. As can be seen, the total melting time of PCM decreases as fin thickness increases. As mentioned, this is because the smaller
PCM volume provides a lower latent heat absorption capacity. Second, the
initiation of the PCM melting occurs later as the fins become thicker. This behavior
was first observed by Hosseinizadeh et al. (2011) for PCM-based plate fin heat
sinks. Their results showed that this property is related to the mode of
heat transfer in the PCM, and heat is mainly transferred by conduction. According to
Fourier's law

Figure 7 compares the base temperature profiles for various fin thicknesses. It can be seen that, with increasing fin thickness, the base temperature decreases considerably during the latent heat period. For instance, case 1 exhibits a lower temperature than cases 2 and 3 by about 8 and 10 K respectively.

Base temperature evolution with time for different fin
thicknesses:

Melt fraction distribution for 49 fins and various fin thicknesses.

From Fig. 7, it can be observed that fast growth of the base temperature causes a peak in the profiles of thinner fins. In other words, due to the low heat capacity of the thinner fins, the base temperature rises rapidly at the early stages of melting. As the effect of natural convection increases, the flow circulation results in a local decrease in base temperature. But for thicker fins, due to the high heat capacity of the system, heat is distributed uniformly and thus the base temperature curves are flattened. We can see that various fin thicknesses in Fig. 7b have smoother profiles compared to those in Fig. 7a. For example, the 4 mm thick fin of 15 mm fin height (case 2) includes the peak, but no peak is observed for that of 25 mm fin height (case 7).

Figure 8 shows plan view of the melt front evaluation with time for different
fin thicknesses at half-height of the fin. As can be seen, in all cases the
melting process starts at the four sidewalls of the fins. Over time, more
of the PCM melts, and at final stages of melting processes, the liquid regions
formed around the fins connect to each other. Temperature contours
corresponding to Fig. 8 are given in Fig. 9. It is worth mentioning
that, before 250 s, the thicker fin (

Temperature evolution for 49 fins and various fin thicknesses.

Temperature evolution and velocity fields:

Melt fraction evolution with time for different fin
heights:

Base temperature evolution with time for different fin
heights:

As previously mentioned, the present work considers the effect of natural convection in the liquid PCM. Figure 10 deals with this subject for the wide case, case 6, and the narrow case, case 9. The right- and left-hand slices show the temperature evolution and velocity fields, respectively. As can be seen, in case 6, which contains a thick layer of PCM, the flow is trivial at a melt fraction of 0.1 but it becomes powerful at a melt fraction of 0.6. However, in case 9, which has a relatively thinner layer of PCM, the velocity field is weak even at a melt fraction of 0.6. This figure implies that the natural convection in the molten PCM depends on both the melt fraction and the geometrical characteristics of the heat sink. It should be noted that the strongest flow field is observed in the air region due to the lower density of air compared to that of liquid PCM. Figure 10 also shows that the use of thick fins causes a more uniform temperature distribution in the system.

Figure 11 shows the melt fraction versus time for two fin heights. As expected, the total melting time increases with increasing fin height, e.g., from 371 to 565 s for cases 1 and 6. This is because of the large amount of PCM in the enclosure designed for the higher fins of the heat sinks. This observation is contrary to the results obtained by Hosseinizadeh et al. (2011) for plate fin heat sinks. This is due to the fact that, in their study, the height of the heat sink and consequently the amount of PCM content is assumed fixed, whereas in this study the heights of the heat sink and the fins are equal to each other. Therefore the PCM content increases as the fin height increases.

Figure 12 presents the temperature evaluation for the cases in Fig. 11. From this figure it can be seen that, for longer fins, the temperature growth is slower than that of the shorter fins, and thus the average temperatures of the heat sink are less. Furthermore, the latent heat period of the system in which the base temperature remains almost constant increases.

The use of PCMs in electronics cooling systems has been of increasing interest to researchers in recent years. Increasing the number of fins leads to a lower melting time. This is because of the fact that, by increasing the number of fins, the heat storage capacity of the system increases while the PCM volume decreases.

The total melting time of the PCM reduces when initiation of the PCM melting processes is delayed due to increased fin thickness. Finally, taller fins result in a lower melting time and lower base temperature. It can be concluded that increasing the number of fins as well as the fin thickness and height results in a lower base temperature, which means a lower chip temperature. Edited by: A. Barari Reviewed by: two anonymous referees