Numerical simulation of conjugate heat transfer in electronic cooling and analysis based on field synergy principle
Introduction
With the miniaturization of electronic devices and increasing process speed, the high heat flux is often encountered in the electronic industry, which leads to the large temperature rise. According to the survey by the US Air Force [1], more than fifty percents of all electronics failures are related to the temperature. Furthermore, for every 2 °C temperature rise, the reliability of a silicon chip will be decreased by about 10% [2]. Hence, it is crucial to find efficient solution of heat removal from the high flux devices.
Due to the low efficiency of natural convection, forced convection is widely adopted in the electronic cooling. Incropera [3] early provided a comprehensive review on electronic equipment cooling with forced convection. Later Yeh [4] and Sathe and Sammakia [5] reviewed the recent technologies in thermal control and management of electronic equipments. Recently Leung et al. [6] studied the influence of heat source size and their separation between two parallel plates on the local Nusselt number distribution, mean Nusselt number of each block and overall Nusselt number. Furthermore, Young and Vafai [7] investigated the influence of more parameters on the Nusselt numbers, such as heat source height, width, spacing and number, along with the block thermal conductivity, fluid flow rate and heating method.
Besides the influence of conventional geometric parameters, the influence of heat source distribution was also addressed by several researchers. To achieve better thermal performance, by virtue of constructal theory da Silva [8] suggested that the heat sources should be distributed non-uniformly with the smallest distance near the inlet boundary. Liu and Thien [9] also found similar phenomenon and pointed out that the center-to-center distances between two adjacent chips should follow the golden mean (1.618). Chen et al. [10] proved this result by experiment and stated that if the geometric ratio is increased beyond 2.0, the thermal performance begins to decrease.
In the electronic devices the solid region usually occupies a large portion of the whole volume, and the conductive heat transfer in the solid and convection heat transfer in the fluid coexist, therefore neither the temperature nor the heat flux at the solid–fluid interfaces can be prescribed as a priori, and available empirical correlations can not be used directly for thermal design and analysis. Amon [11] indicated that such conjugate heat transfer can significantly affect the temperature distribution. Ramadhyani et al. [12] and Sugavanam et al. [13] also reported that through the heat conduction in the substrate, the heat transfer can be enhanced due to the extended surface effect. Hung and Fu [14] and Hung [15] proposed a conceptual design by modifying the attached substrate with openings, and they claimed that by allowing the fluid flow between the upper and lower channels, the flow stagnation between two adjacent obstacles is diminished, hence the cooling capacity of the array of blocks can be enhanced.
Once substrate is arranged with the openings, it will become the ‘isolated island’ problem, which means that solid region is located in the interior and not attached to any wall of the investigated domain, which will increase the difficulty in numerical simulation. Yang and Tao [16], [17] and Wang et al. [18] studied this kind of problem both through numerical simulation and flow visualization, and their numerical results agree quite well with the experimental data. However, most of investigation is focused on the problems with simple geometries on staggered grid. In this paper, the fluid flow and heat transfer with complex isolated solid region is tried to be solved on the collocated grid with the newly proposed CLEARER algorithm [19], and special treatment is given on the solid region in the fluid.
From the literature review above, it can be seen that most of previous investigation is focused on the parametric study. By varying one of the influencing parameters while keeping the others unchanged, the resultant friction and thermal performance are obtained. While in this paper, these problems are revisited from a novel viewpoint of the field synergy principle, which can explain the above problem from the essence.
This principle was firstly proposed by Guo and his co-workers [20], [21] in 1998 in parabolic convective flow. Later Tao et al. [22] extended it to the elliptic flow when the fluid Peclet number is not too low. The basic idea of the principle is that the heat transfer enhancement is related not only to the velocity field and temperature field, but also to the synergy between them. This paper examines the effects of openings on the substrate, the heat source height and the heat source distribution on the overall thermal performance and the result is explained from the viewpoint of field synergy principle.
Section snippets
Physical model and mathematical formulation
The model is simplified from the practical electronic cooling problem, as shown in Fig. 1. Four heat sources made of copper with thermal conductivity 398 W/(m K) are of constant heat flux, and are attached to the substrate, which is made of Teflon with thermal conductivity 0.35 W/(m K). In order to improve the thermal performance, according to Hung’s idea [14], [15] the substrate between the adjacent heat sources is slotted. To lower the temperature of the heat sources, the cooling air is forced to
Results and discussion
In the electronic cooling, the maximum temperature has great significance to electronic components; hence in the definition of heat transfer coefficient, the maximum temperature is adopted as follows:To evaluate the synergy between the velocity field and temperature field based on the field synergy principle, the local synergy angle is defined in Eqs. (12), (13) is the average synergy angle in the full field.
The
Conclusion
In this paper, the conjugate heat transfer in electronic cooling is investigated on collocated grid with CLEARER algorithm, and special attention is given to the treatment of the isolated solid region for both velocity and temperature. The influence of three geometric parameters on the thermal performance are numerically investigated and analyzed with the field synergy principle, the major conclusion are summarized as follows:
- 1.
The openings on the substrate in the channel can lower the maximum
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