Improving the Cooling Efficiency of Heat Sinks through the Use of Different Types of Phase Change Materials

Abstract

As the temperature of electronic devices increases, their failure rate increases. That is why electrical devices should be cooled. One of the promising cooling techniques is using Phase Change Materials (PCMs). A new passive temperature management technique, that involves the direct placement of PCMs on the chip, has been explored and developed. PCMs are potential temperature regulators that can store thermal energy and release it during melting and freezing respectively. PCM-based heat sinks can efficiently store the heat dissipated from the electronic components to delay the peak temperature of the electronic devices as much as possible and then release the stored energy during the off period. This paper compares the temperature distribution on a heat sink with and without PCM with different magnitudes of heat flux. Also, two different PCMs with different densities, namely salt-hydrate and wax, have been investigated in cooling electronic devices.

1. Introduction

Modern life is deeply interconnected with electronic equipment, from toys and appliances to high-power computers. The recent increase in processing demands has forced manufacturers to increase the performance and functionality of integrated circuit chips and to minimize their size leading to high power dissipation through smaller packages. This has made thermal management a critical aspect of successful processor system designs and finding new cooling techniques has subsequently become much more valuable. Moreover, the failure rate of electronic systems increases exponentially with temperature. The operation of electronics produces the leakage power and degrades the reliability of integrated circuits. To avoid such problems, integrated circuit packages must be designed to remove any predicted excessive heat [1].

In order to reduce the temperature of chips and consequently avoid any potential failure, active and passive cooling techniques are used. In many applications, standard cooling methods are insufficient for the heat load produced during continuous operation over long periods due to some limitations such as limited thermal conductivity of air for convection and copper for conduction and small spaces decreasing the performance. In this work, a thermal management technique for chips using Phase Change Materials (PCMs) is proposed. PCMs can absorb the heat dissipated by the chip and release it back later benefiting from its thermo physical properties. PCM-based heat sinks can effectively store the dissipated heat from the components to delay the peak temperature of the electronic device. Generally, the global maximum allowable temperature of various chips ranges from 85 °C to 120 °C [2]. Among the advantages of PCMs is that the latent heat capacity per unit volume can be very high; the capacity to absorb heat is called latent heat capacity. In addition, the temperature remains relatively constant, and only a small volume change occurs during the phase change.

PCMs are successfully used as heat-storing materials for different applications such as air conditioning [3], thermal reservoir [4], thermal management of photovoltaic panels [5], and electric chips cooling [6,7]. It may be possible to use a large scale PCM-based system to cool large-scale systems. PCMs fall into four main categories [8]: water-based, salt hydrates, paraffin, and vegetable-based.

Paraffin waxes have suitable thermo-physical properties such as higher heat of fusion, lower corrosion rates to metals and negligible sub-cooling with no phase segregation. Such characteristics allow paraffin to withstand multiple thermal cycles with no substantial change in their thermo-physical properties. Paraffin waxes as PCMs do possess the disadvantage of a lower thermal conductivity, higher volume expansion during melting-freezing up to 15 and a lower density [9].

The most attractive characteristics of salt hydrates are their higher latent heat of fusion, higher thermal conductivity, negligible volume change during phase transition, and lower cost. The main problems with salt hydrates as temperature regulators are their lower thermal stability, chemical instability and sub-cooling below the solidification temperature. Sub-cooling is suppressed by addition of thickening agents and nucleating agent such as borax [10]. However, high-density borax may settle down when added into PCM, which may require further investigation to solve this problem.

It should be noted that PCMs need to re-solidify after being molten, that is, they need to dissipate the heat gained to the surroundings while the device is off [11]. Therefore, such cooling systems are only applicable to devices that have rest periods and not to those with continuous operation.

2. Modeling

2.1. Domain

A numerical study was done on the heat sink, with and without PCM and using two different types of PCM. The problem was modeled and solved using Ansys fluent simulation platform. The heat sink was modeled and placed in a fluid domain, with one inlet and one outlet as shown in Figure 1. The solution was updated every 0.01 s with 40 iterations per time step. The heat sink was studied under three different heat fluxes of 1250, 2500, and 5000 $\left(\mathrm{W}/{\mathrm{m}}^2\right)$ at 24 °C ambient temperature. Taking into account the area of the heat sink, these heat fluxes correspond to 0.5, 1, and 2 W. The same study was repeated with PCM embedded into the heat sink.

Due to the fact that the heat sink is exposed to free convection, that is there is no air flow, the inlet and the outlet of the fluid domain were assumed to be symmetric. Moreover, due to isotropy, half of the domain and the heat sink was enough to be studied as shown in Figure 2.

The domain was divided into 1,200,000 hexahedral elements as shown in Figure 3. Then, after adding the PCM, the number of elements increased to 1,350,000 elements.

The heat generated by the electronic chip is transferred through the heat sink by conduction, and then the heat is carried out by the surrounding air by convection (natural convection is considered in our study) and radiation. Usually, a heat spreader is used to ensure the distribution of the heat all over the whole base of the sink and to overcome the size difference between the electronic chip and the heat sink.

2.2. Governing Equations

2.2.1. Heat Transfer

Heat transfer is the exchange of thermal energy between physical systems. It’s the transfer of heat from higher to lower temperature surfaces, and it’s highly affected by the medium surrounding the system. The three types of heat transfer are encountered by the heat sink: conduction, convection and radiation as shown in Figure 4.

• Conduction: is the transfer of energy from the more energetic to the less energetic particles of the same substance or between two substances in contact due to the interaction between particles. In this case, conduction occurs from the chip to the heat sink [12].

  $$q^{″}=-K·\nabla T$$

  (1)

  where;
  • $q^{″}$ is the heat transfer rate $\left(\mathrm{W}/{\mathrm{m}}^2\right)$;
  • $K$ is the thermal conductivity $\left(\mathrm{W}/\mathrm{m}·\mathrm{K}\right)$.

    $$\overrightarrow{\nabla }T=\left(\frac{\partial T}{\partial x}\overrightarrow{i}+\frac{\partial T}{\partial y}\overrightarrow{j}+\frac{\partial T}{\partial z}\overrightarrow{k}\right)$$
• Convection: is the transfer of energy between the surface of an object and a fluid in motion when both are at different temperatures [12].

  $$q^{″}=-h\left(T_s-T_{\infty }\right)$$

  (2)

  where;
  • $h$ is the convective heat transfer coefficient $\left(\mathrm{W}/{\mathrm{m}}^2·\mathrm{K}\right)$;
  • $T_s$ is the surface temperature (K);
  • $T_{\infty }$ is the fluid temperature (K).
• Radiation: Thermal radiation is the energy emitted by matter that is at non-zero absolute temperature. The energy of the radiation field is transported by electromagnetic waves [12].

  $$q^{″}=J-G$$

  (3)

  where;
  • J is the radiosity, the rate at which radiation leaves a surface per unit area $\left(\mathrm{W}/{\mathrm{m}}^2\right)$;
  • G is the irradiation, the rate at which radiation is incident upon a surface per unit area $\left(\mathrm{W}/{\mathrm{m}}^2\right)$.

    $$J=E+\rho G$$

    (4)
  where;
  • E is the emissive power, the rate at which radiation is emitted from a surface per unit area $\left(\mathrm{W}/{\mathrm{m}}^2\right)$;
  • $\rho$ is the reflectivity, the fraction of the irradiation on a surface that is reflected.

2.2.2. Phase Change Materials

The absorption of energy by PCM causes its transformation from solid to liquid, and the release of energy by PCM causes its transformation from liquid to solid.

The liquid fraction (β) of PCM represents the amount of liquid present at an instant with respect to the total amount of PCM [13].

$$\mathsf{\beta }=\frac{T-T_{sol}}{T_{liq}-T_{sol}}$$

(5)

where, T_sol and T_liq represent the solidus and liquidus temperatures of the PCM respectively.

The liquid fraction is zero for fully solid, one for fully liquid, and is between zero and one for temperatures between the solidus and liquidus states.

Assuming that the thermo-physical properties of PCM are independent of temperature, the three dimensional energy equations is written as follows:

$$\frac{\partial }{\partial t}\left(\rho C_{p}T\right)=\frac{\partial }{\partial x}\left(K\frac{\partial T}{\partial x}\right)+\frac{\partial }{\partial y}\left(K\frac{\partial T}{\partial y}\right)+\frac{\partial }{\partial z}\left(K\frac{\partial T}{\partial z}\right)+S_h$$

(6)

where, $\rho$ is the density $\left(\mathrm{kg}/{\mathrm{m}}^3\right)$ and $C_p$ is the specific heat at constant pressure $\left(\mathrm{J}/\mathrm{kg}·\mathrm{K}\right)$, $S_h$ is the source term. The enthalpy of the material is computed as the sum of the sensible enthalpy, h, and the latent heat, $∆$H, such that:

$$H=h+∆H$$

(7)

$$h=h_{ref}+{{\displaystyle \int }}_{T_{ref}}^T{C}_{p}dT$$

(8)

with

• $h_{ref}$, reference enthalpy (J/kg);
• $T_{ref}$, reference temperature (K).

$$∆H=\mathsf{\beta }L$$

(9)

where, L is the latent heat of fusion of the material in J/kg.

The energy equation of solidification/melting can be written as:

$$\frac{\partial }{\partial t}\left(\rho H\right)+\nabla ·\left(\rho \overrightarrow{v}H\right)=\nabla ·\left(K\nabla T\right)+S_h$$

(10)

where $\overrightarrow{v}$ is the fluid velocity vector in (m/s).

3. PCM Selection

The time duration for the PCM heat storage varies depending on the PCM’s thermos-physical properties thus making the choice of an optimum PCM crucial.

One of the most important thermos-physical properties for selecting PCM to cool electronic devices is the melting temperature. The selected PCM must have a solidus temperature above the ambient temperature and a liquids temperature below the steady state temperature of the heat sink. Also, the density plays an important role in choosing an optimum PCM. Because we are usually limited in the volume of the heat sink, a PCM with high density lead to a larger mass transfer from solid to liquid and vice versa.

In the current study we choose the salt hydrate and wax as PCMs to be studied, benefit from that they have approximately the same latent heat of fusion and same heat capacity but different densities and thermal conductivities. So, the effect of density and thermal conductivity can be investigated.

Table 1. Thermo-physical properties of the Phase Change Materials (PCMs) [9].

Materials	Salt Hydrate	Wax
Thermal conductivity $\left(\mathrm{W}/\mathrm{m}·\mathrm{K}\right)$	0.6	0.15
Specific heat capacity $\left(\mathrm{kJ}/\mathrm{kg}·\mathrm{K}\right)$	2	2.2
Density $\left(\mathrm{kg}/{\mathrm{m}}^3\right)$	1500	820
Viscosity $\left(\mathrm{kg}/\mathrm{m}·\mathrm{s}\right)$	0.00184	0.00068
Solidus temperature $(℃)$	27	30
liquidus temperature $(℃)$	32	40
Latent heat of fusion $\left(\mathrm{kJ}/\mathrm{kg}\right)$	200	190

lists the thermo-physical properties of the PCMs used.

4. Results

Simulation as well as experimental studies were performed on the heat sink, with and without PCM.

4.1. Numerical Results

The first simulation was done without PCM with a heat flux of 1250 (W/m²), Figure 5 shows the temperature versus time graph, the temperature increases from the ambient temperature (297 K) to the steady state temperature (325 K). At the beginning, the temperature increases significantly, then its rate starts to decrease with time, this result was expected, since when the surface temperature of heat sink increases, the temperature difference with ambient $T_s-T_{\infty }$ increases so that the heat rejected by convection and radiation increases with time and becomes closer to heat generated by the chip until reaching steady state 1250 W/m² after 10 min as shown in Figure 5. Eventually, the generated heat is equal to heat being rejected.

As mentioned earlier the heat sink was studied under three different heat fluxes 1250, 2500, and 5000 (W/m²). Figure 6 shows the different profiles of temperature of the heat sink under these three fluxes selected for this study.

As one might predict, the steady state temperature increases with the increase of the heat flux, and that was shown clearly in Figure 6, the steady state temperature becomes 347 and 380 K for 2500 and 5000 W/m², respectively, instead of 325 K for 1250 (W/m²).

At the end of the simulation, and after reaching the steady state, the temperature profile of the heat sink under 1250 W/m² is of the form shown in Figure 7. The temperature reaches its maximum value at the center of the heat sink, and it decreases gradually when moving away from the center and up to the top of the fins where convection has the main influence.

Now, instead of the air filling the gaps between the fins, PCM is modeled using Ansys and placed between the fins up till the tips. Throughout the phase change of the PCM, the volume is considered constant, and melted PCM doesn’t slip out of the heat sink.

In order to investigate the effect of the PCM on the transient variation of the sink temperature, the variation of the sink temperature with and without PCM are plotted on the same graph as shown in Figure 8. The PCM used in this simulation is the Sodium Sulfate deca-hydrate.

Figure 8 shows clearly, that at the beginning, the temperature of the heat sink with and without PCM increases in the same manner, until reaching the melting temperature of the PCM. At this point, the salt maintains its temperature while the temperature of the heat sink (without PCM) continues increasing until reaching the steady state temperature (325 K).

The time taken by the heat sink with PCM to reach the steady state temperature increased from 600 to 2500 s. So, during the melting process, the PCM delays the peak temperature of the sink by absorbing the energy generated by the electronic chip in operation.

In order to compare between the Salt hydrate and Wax, the simulation results of the temperature profiles of the heat sink under the three heat fluxes are depicted in Figure 9.

As shown in Figure 9a, we can clearly notice that at the beginning, the two graphs have the same variation, until reaching the melting temperature for the salt hydrate (300 K) which is less than that of wax (303 K) that’s why salt hydrate starts to melt first. At this point, the PCM starts to absorb energy until reaching the liquidus temperature for each PCM (305 K for salt and 313 K for wax) which indicates that the PCM is completely melted then the temperature continues to increase until reaching the steady state temperature which is equal to 325 K.

The time needed to reach steady state is 1700 s (for wax) and 2500 s for salt hydrate.

The same observation can be drawn from Figure 9b,c, Due to the fact that the density of the salt hydrate is much larger than the density of the wax, the mass of the salt hydrate is greater than the mass of the wax (mass = density × Volume).

Note that the two PCMs used in this test have approximately the same heat capacity and the same latent heat of fusion. Also, the melting time of the two PCMs is approximately the same (the time from solidus to liquidus status) despite the difference of the mass used, thus is due to the difference in the densities and the difference in term of thermal conductivity. Wax has a smaller thermal conductivity than salt so it can absorb smaller amount of heat by conduction and can consequently melt slowly.

As shown in Figure 10a, the time needed to reach the steady state temperature decreases to 1200 s and 1000 s when increasing the heat flux to 2500 and 5000 W/m² respectively instead of 1700 s for 1250 W/m². That is due to the fact that when increasing the heat generated, more heat can be absorbed by the PCM so the time needed to melt the PCM decreases which in turn decreases the time needed to reach steady state. The same can be observed in Figure 10b.

From Figure 11, we can see that there is a difference between the temperature profile of the sink and the PCM during the mushy region and this is due to the fact that PCM usually has a specific capacity to absorb latent heat and this capacity decreases when liquid fraction increases. So, during the mushy region, the heat sink gives energy to the PCM until the PCM is fully melted. After that the temperature of the PCM increases rapidly to coincide with the sink temperature.

4.2. Experimental Validation

A heater (Peltier plate) is connected to a DC Power supply to heat up the heat sink. The instantaneous temperature variation of the sink is measured using thermocouples of T type which are connected to a heat transfer service unit and to a data logger to display and save the results on a dedicated computer. The resistance of the Peltier plate is 0.4 Ω, so a current of 1.12 A was generated by the power supply in order to dissipate a heat flux of 0.5 W (the power of electrical resistor is equal to the product of the voltage and the current) which corresponds to a total heat flux of 1250 W/m².

For the PCM experiment, salt hydrate is added to the heat sink in liquid form to ensure that the air gap is minimized when the PCM is melted and the thermal expansion of PCM won’t cause damage to the heat sink.

To simplify the comparison, at the same heat generation and approximately same boundary condition, the result of the experiment and the simulation were plotted in Figure 12. One can clearly notice that the two curves (experimental and simulation) have approximately the same variation (the same steady state temperature at the same time).

The result of the experiment for the heat sink with PCM is represented on the same graph with the simulation data (Figure 13).

Figure 13 shows that the experimental and numerical results have approximately the same path with some differences because of a few experimental setup difficulties.

The discrepancies from computed are due to a non-reliable device with the data shown in the board being slightly different than the saved data and, more importantly, the difficulty in conducting the experiment with the conditions that match the simulation set up like the heater used (Peltier plate). These factors cause the curves to diverge.

5. Discussion

After performing multiple simulations and experiments, some conclusions can be outlined. An increase in the heat flux, leads to an increase in the steady state temperature. PCM contributes in delaying the peak temperature by absorbing the heat, which leads to better long term performance of the intermittent uses of the chip. Variety of choices exists when choosing the appropriate PCM to be used in the application, but the decision is taken depending on five main properties: Heat capacity, Latent heat of fusion, melting temperature, density, and thermal conductivity. Here, the main aspects were density and thermal conductivity. With the increase of the density, obviously the mass will change with the same volume, leading to the delay of the steady state temperature, and by increasing the thermal conductivity, the PCM will absorb more energy and will melt faster during the heating process. From the results, it’s clearly noticed that the salt hydrate has a better performance in delaying the peak temperature than the wax. Moreover, the heat flux and the meting time of the PCM are inversely related. Finally, the simulation results and the experimental results were in good agreement regardless of some discrepancies due to the difficulty in conducting the experiment with the conditions that match the simulation set up like the heater used (Peltier plate) and difficulty to enclose the domain to get the same boundary conditions.

6. Conclusions

This paper aims to simulate the heat distribution over a heat sink using Ansys fluent simulation tool to serve the goal of investigating and studying the effect of integrating phase change materials into the heat sink in order to improve the cooling performance and consequently increase the efficiency of electronic chips. It also investigates the importance of the density and thermal conductivity and how it affects the peak time. Moreover, experiments were performed in order to verify the obtained simulation results. PCMs are usually used in application where electronic devices have rest periods; this will allow PCMs to re-solidify.

With the use of a relatively small amount of PCM, the time needed to reach the peak temperature was delayed by more than 25 min for a low heat generation (0.5 W). This is an interesting feature for mobiles phones where their usage is often limited to a few minutes and the heat generated is considerably low compare to other application.