Temperature Uniformity Analysis of a Multi-Well Vap or Chamber Heat Spreader

In this study, temperature uniformity and heating r ate of heat spreaders with multi-well are simulated an analyzed by CFD software under natural convection c ondition. The heat spreader (112mm in length; 75mm in width and 17.2 mm in thickness) includes 96 holes w ith a diameter of 5mm and a depth of 10mm. Firstly, multi-well heat spreaders made of aluminum, copper, silver, and vapor chamber are simulated and compar ed, when dual and six heat sources are applied at a hea ting power of 1200W. Secondly, with six heat source s at heating power of 188, 300, 600, and 1200W, the heat ing rate of heat spreaders are studied. The results showed that temperature uniformity in six heat sources mod e was better than dual sources mode. Vapor chamber heat spreader has the better temperature uniformity both in six sources and dual sources mode due to a high er thermal conductivity, followed by silver, copper an d aluminum heat spreader. Aluminum and silver heat spreader show the higher heating rate, followed by copper heat spreader, vapor chamber heat spreader d ue to a larger heat capacity, heat up the slowest. Furtherm ore, with the heating power increasing, the heating rate of heat spreader is increasing, but also reduces the t emperature uniformity.


INTRODUCTION
The polymerase chain reaction, PCR, was invented by K. Mullis, and includes three basic reactions, denature, annealing, and extension [1], all of which have corresponding temperatures, range of temperatures, periods of reaction, and temperature uniformity. As these reactions absolutely influence the final products [2], it is important to reduce the period of reaction and raise temperature uniformity. Many domestic and foreign researches are based on micro chips, which use MEMS technology or micro-tunnel polymerase chain reaction biochips [2~5]. Even though, the situation of a reduced area raises temperature uniformity to ± 0.5°C, the cost is high and the situation is not available for mass production. In this research, the size of the multi-well heat spreader is four times that of a micro chip and utilizes the temperature uniformity of a vapor chamber heat spreader, which allows simultaneous operations, in order to meet the needs of PCR.
A Vapor Chamber is a closed hollow object that is full of working fluid, with an inner vacuum pump. The purpose of vacuum pumping is to reduce the boiling point of the working fluid, which makes it easier to achieve the phase transition that allows heat to spread rapidly [6~9]. Thermacore, Inc. simulated copper fins, which they compared with a vapor chamber combined with copper fins [10]. The results show that copper fins have the obvious phenomena of centralizing the heat sources, which can easily generate a situation of uneven temperature; in contrast, a vapor chamber with copper fins has even temperature distribution. Currently, vapor chamber heat spreaders apply electronic cooling, which meet the high requirements of even temperatures in biomedical technology.
This research applies a basic simulation and analysis with copper, aluminum, silver, and vapor chamber heat spreaders. First, we change the number of heat sources, with a fixed heating power of 1200W, and simulate temperature distribution where the heating centre of dual and six heating sources on a multi-well heat spreader is from room temperature to 90°C. This study uses six heat sources to operate simulations at different heating speeds of 188, 300, 600, and 1200W, observes the period of reaction and speed of warming, and discusses the a multi-well vapor chamber heat spreader in the conclusion. Figure 1 shows a simplified model of the test equipment, which includes a multi-well vapor chamber heat spreader, heat sources, and cooling fins, which is an exact size according to actual measurements. As this study only simulates the situation of warming in the machine, we simplified the model and ignored fans, nozzle shaped fins, and fan cover.  Figure 2 is composed of a vapor chamber heat spreader (thickness 4mm), with 96 holes (diameter of the holes is 5mm and depth is 10mm). 2. Heat sources: the area of heat sources is 30×30mm. Based on simplified modeling, the heat sources is 2D, and assumes that heat generation is even. 3. Cooling fins (250×200×73mm): the thickness of the substrate is 13mm, the fins are nozzle shaped, the thickness of the substrate is 2mm, and the bottom is 1mm, as seen in Figure 3. In addition, the fins have 17 hollow cylinders, with a diameter of 13mm, and are located in the area with the multi-well heat spreader to allow the multi-well heat spreader, heat sources, and cooling fins to fully cooperate; as the actual nozzle fins are difficult to model, the simulation has simplified fins, with the single size of 1.5mm.

Exact Formula
Mass-conservation equation where ρ denotes density, u, v, and w are velocity components, p denotes pressure, µ denotes the viscosity coefficient, g denotes gravity, and h denotes enthalpy.
In the natural convection, we used a ( where ρ 0 is the density of the fluid, which is an identical value; T 0 is the temperature of operation.

Convergence Test
This article sets the convergence of momentum and energy at 10 -1, 10 -2, and 10 -3 in order to maintain the solution in a steady state, and the solution of 10 -2 is close to 10 -3 , and in both of the two situations, energy can weaken to 10 -7 ; therefore, this research set the convergence of momentum at 10 -2 , and the convergence of energy at 10 -7 .

The relaxation factor
As this article intends to resolve the process of transient heating in natural convection, to make the process easier, we set the relaxation factor at 0.7, and the momentum relaxation factor at 0.1, in order to complete the solution. It symbolizes that the difference of pressure from one iteration to the next will be limited under 70%, and the change of momentum will be limited under 10%.

Comparisons of experiments
The simulated test equipment, under heating powers of 188w and 288w, and with dual or six heating sources, are compared for temperature distribution and time, with results as shown in The simulation results, as shown in Figures  6 to 13, compare the different material temperature differences, and find that when under six heat sources, the temperature difference is smaller than in dual heat sources, as shown in Figure 14. Furthermore, the temperature uniformity is proportional to the material thermal conductivity coefficient. Thus, temperature uniformity could be arranged as vapor chamber, silver, copper, and aluminum.  Figure 14 The comparison of the temperature differential under dual and six heat sources at a heating power of 1200W Figure 15 shows that the simulation of the vapor chamber heat spreader requires a warming period from room temperature to 90°C when testing several heating powers of 188, 300, 600, and 1200W. temperature is regarded as an important parameter to influence the temperature of the heat source; therefore, the warming line is a curve. If the heating power goes lower, the steady temperature could be lower than 90°C. Prior to increasing the heating power, room temperature has no influence on the temperature of the heat source, and the line of warming tends to be a linear. Table 3 shows the detailed information, including the warming speed of several of kinds of heat spreaders with temperature uniformity. According to the four heating speeds shown in Table 3, there are different warming speeds, with different ingredients warming from room temperature to 90°C. When the temperature in the centre of the heat spreader reaches 90°C, it captures the distribution of the temperature in the heat spreader. This study calculates the difference between the high and low temperatures (∆T), as shown in Figure 16, which shows different temperature uniformity and warming speeds at 188, 300, 600, and 1200W, with different ingredients in the heat spreader. Figure 16 compares silver, aluminum, and copper vapor chambers have the best uniformity; however, the warming speed is also the slowest. In addition, the copper has the second best uniformity, with a faster warming speed. The warming speed in the reaction of PCR is regarded as the faster, the better, while temperature uniformity is regarded as the lower, the better; therefore, the ratio of the temperature uniformity and the warming speed is the smaller, the better. Figure 17 presents the relationships between heat spreaders of various materials and temperature uniformity, the ratio of the warming speed, and the heating power, and shows that the ratio of a vapor chamber heat spreader's uniformity and the warming speed is lower than any other material heat spreaders. The results suggest that a vapor chamber heat spreader is the most suitable for application in the reaction of PCR. Figure 17 The ratio of the temperature uniformity and heating rate with different watts and different materials t ∆Ti ∂

Aluminum
Copper Silver Vapor Chamber (°C/s)

CONCLUSION
In this study, the temperature uniformity and heating rates of heat spreaders with multi-wells were simulated and analyzed by ANSYS-Icepak software under natural convection conditions. We selected four materials for the multi-well heat spreader, including copper, aluminum, silver, and vapor chambers, as well as dual and six heating sources, at heating powers of 188, 300, 600, and 1200W, in order to simulate this research.
The simulation found that, when at lower heating powers, the surrounding temperature would have great effect, thus, the temperature rise in a curve line. Otherwise, when at higher heating powers, the effection by the surrounding temperature is very small, so the temperature was straight up.
According to the results, when under six heating sources, temperature uniformity would better than with dual sources. In addition, comparisons of temperature uniformity show that, a vapor chamber is better than silver, silver is better than copper, and copper is better than aluminum. Therefore, a multi-well vapor chamber heat spreader has better temperature uniformity than other materials.