这个设计是通过Ansys实现，如需代码可私聊。
An Optimized Passive Fin-Plate Cooling System Design for Electronic Chip
Abstract
This research designs a cooling system for electronic chip aiming at cooling the hot chip efficiently and effectively with an acceptable cost. In order to find the optimized parameters for this cooling system, a series of groups with the combination of different total mass of fins, different numbers of fins and the thickness of each fin are modeled and simulated in Ansys. Then an optimization is processed to find the possible solutions to reduce the total cost or to continue reducing the temperature.
Key Words
Passive cooling system, Ansys simulation, parameters of copper fins, optimization.
I. Introduction
This project aims at designing a passive cooling system to control the temperature of a chip which constantly generate heat. Due to joule heating, electronic chips are often heated, and proper release of the heat is necessary to protect the chips. This chip can be modeled as a thin plate. In favor of good heat conductivity performance, a copper plate is used to cover the chip, on the top surface of which fins are installed with the same material to better spread out the heat in an effective way. The entire system is symmetric and hence only a quarter of the domain needs to be modeled as shown in Fig.1. The conditions can be shown below:
a) The dimensions of the plate are 10cm×10cm×1cm;
b) The dimensions of the chip are 5cm×5cm×4mm.
c) The hot chip generates a constant heat flux of q ̇=0.2 W⁄cm^2 into the plate.
d) The temperature of ambient air, that is, air located about more than 50cm away from the plate, is 25^o C.
e) The convective heat transfer between solid and air is modeled as q ̇=h_c (T_s-T_air) with a constant convective transfer coefficient of h_c is (1.0 W)⁄(m2∙(_o)C ).
f) The thermal conductivities of copper and air are (400 W)⁄(m∙(^o)C ) and 2.4 W⁄(m∙(^o)C ) respectively.
g) The maximum height of the fins allowed is 10cm.
The design objective is to make the chip as cool as possible while keeping the cost as low as possible. In the meantime, the design has to be practical.
Fig.1 a quarter of the domain needs to be modeled (front view)
II. Conceptual Design and Rationale
In the design, the plate-fin structure is utilized for its excellent performance in heat conduction and transforming the heat into surroundings. The plate totally covers the chip which generates a constant heat flux. In the modelling, we did not draw the chip but determined the heat received on the inner faces. The entire system is symmetric so only a quarter is modeled. Firstly, we determine the basic geometrical parameters. We model 1/4 of the plate and chip, which is 5cm×5cm×1cm and 2.5cm×2.5cm×4mm separately, as shown in Fig.2(a). Because air 50cm away can be regarded as 25^o C (boundary condition)( as shown in Fig.6©) and there is no air flow in the space for it is a passive cooling system, so we simplify the air as a solid box and the volume discussed is 50cm×50cm×50cm, which is also 1/4 of total volume of air, as shown in Fig.2(b). We put the 1/4 cooling system at the corner of the air box where is connected with bottom face and 2 symmetry planes, as shown in Fig.3.
Fig.2 modeling of the system
Fig.3 a quarter of the domain is modeled
III. Detailed design
After series of experiments and simulations, we find the optimized solution for the passive cooling system. The height of fins is 10cm to better transform heat into air. Besides the required structure for the plate, we modify the total thickness and number of fins, and fins are placed uniformly so that the distance between two neighbor fins are automatically determined after the first two parameters are set. The simulation is divided into 4 groups of different total thickness of fins which are 10mm, 20mm, 30mm and 40mm. In each group, the number of fins is 10, 20, 30, 40 for each design of the cooling system. For example, if the total thickness of fins is 10mm and there are 10 fins on the plate, then the thickness for one fin is 1mm and the distance between two neighbor fins is 1cm. After simulation for each plan, the best one can be identified which is expected to have the lowest temperature. Actually, the optimized design is that the number of fins is 50 and the thickness of each one is 0.4mm with a 2mm uniform gap.
Plus, in order to reduce the total utilized mass of used copper to reduce cost, slot structure and reducing the height of fins are considered in section VI. However, in the simulation, the cooling performance is found to be weaker. The material used for the whole cooling system is copper, for its excellent performance of heat conduct. The table is shown below to better explain the detailed design.
Table.1 Features to be considered
IV. FEM analysis
Ansys is the method used for the FEM analysis. Considering the balance between the calculating capacity of the computer, the simulation time and the quality of meshing, tetrahedron mesh is used, as shown in Fig.4. After each possible mesh solution is established, element quality and skewness are checked. If the mesh quality is relatively poor and other improvement technique will be applicated such as reducing the mesh size, using refinement, or adding more restrictive conditions, as shown in Fig.5.
Fig.4 Tetrahedron mesh
Fig.5 Before and after improvement
According to the feature of heat transform, the heat flux across the symmetry plane is q ̇=0 W⁄cm^2 . We ignore the heat flux across the bottom face, so it is 0 too, as shown in Fig.6(a). The shared faces of air and fins/plates is passed with a convective heat, as shown in Fig.6(b). The heat in the air and the entity of plate and fins is conductive heat with different rate given in the introduce. The heat flux generated by the chip on the inside faces is designed as Fig.6(d).
Fig.6 the Loading condition for the simulation
As is discussed in section III, the simulation is organized by a series of change of the total thickness of fins and the number of fins, the table below show the highest temperatures for each design. Also, a convergence is conducted for each simulation to ensure the accuracy of the result.
Table.2 Simulation result
In order to show the result more directly, figure below shows the comparison for each group. It is obvious that with the increasing of the number of fins, the cooling capacity grows noticeably. Actually, the thickness of fins plays flew role in controlling temperature. The best one in the experiments is that the thickness of one fin is 0.5mm while the number is 40, and it is the option in the design because we give first priority of cooling capacity as the assessing criterion. Admittedly, if less copper is expected to be used with acceptable temperature rise for the preference of decreasing cost, the thickness of fin can be reduced from 0.5mm to 0.25mm for example, and the temperature only increases 〖0.127〗^o C.
Fig.7 Simulation result
V. Performance analysis
According to internet search, it is around $50 per 1kg for copper. The density is of copper is 8.9g/cm3. Because the thickness of fin is 0.5mm, the height and the length are 10cm and the number is 40 so the total volume of fins is 200cm3, therefore the mass is 1.78kg and the cost is $89. If the thickness of fin is reduced to 0.25mm, the cost will drop to $44.5.
VI. Optimization
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Reduce the Height of Fins
The factors which influences the cooling capacity is the number, thickness, shape and height of fins and in the former tests the number and thickness have been investigated. Though it is thought that with the increasing of shared surface between fins and air it can cool better, as the design has already reached the highest limitation of height, the effect of reducing height is expected to be found. If reducing height would not impact the cooling performance greatly, it can optimize in this way to reduce cost. The table below compares the temperature of height 10cm and 7.5cm. It is obvious that reducing height will dramatically weaken the cooling capacity so that the height will not be decreased.
Table.3 Comparison of height -
Increase the Number of Fins
According to the conclusion in section IV, it is easy to raise an improvement plan of increasing the number of fins. So, an extra optimization is done to check the effect of further increasing the fin number. The result shows that the temperature is reduced as expected. The conclusion in section IV can be improved that further increasing the number of fins can help to strengthen the cooling capacity. An extra comparison is done to show the performance when the thickness is 0.20mm. The temperature is slightly higher than the former one. If the small difference is ignored, the design can be this one for its less utilization of copper.
Table.4 Comparison of fin number -
Add Slot
Besides the features which would perhaps influence how the system works, the shape of the fin-plate structure is then considered. A slot is adding in the middle of the fin, as shown in Fig.8. The result can be found in Table.5. After a slot is added, the cooling capacity is reduced. Therefore, this feature is not adopted as well, for each slot, it can save $1.28, which can be considerable with large manufacture though.
Fig.8 Slot
Table.5 Comparison of slot
VII. Summary
A passive cooling system is designed according to the change of total volume and number of fins, and then the uniform gap between fins and the thickness of one fin can be naturally identified. The surrounding is modified as a 50cm×50cm×50cm air cubic which is regarded as a solid block. The heat inside the copper material or air is conductive while on the interface of fins is convective heat. The primary principle for the design is to find the option which can preserve a lowest temperature and then the cost as well as aesthetics. According to the Ansys simulation above, the chosen thickness of one fin is 0.4mm, the number of fins is 50 and the height is 10cm. Finally, optimization is boosted to find better design. According to the result, if ignoring slight loss of cooling capacity, the thickness of fins can be further decreased to 0.20mm and the cost of material will be the half. Fig.9 below shows the structure of the cooling system.
Fig.9 The passive cooling system
