– Volume 20 ( 2014 ) No . 1 76 HEAT TRANSFER THROUGH MINI AND MICRO CIRCULAR CHANNELS OF CPU ’ S COOLING SYSTEMS

The cooling systems of the CPU have in their competence mini and microchannels whose performances at intensifying the thermal transfer have been discovered and proved. It is justified the interest in studying the shape of these components, their possibilities of manufacture, the phenomena that occur in channels of small dimensions and processes of heat transfer. The current article aims to realize a brief presentation of mini and micro-channels situated inside the cooling system of the CPU, while in the second part is proposed a calculation model for heat transfer in circular mini and micro-channels. In the case of the analyzed channel, it is realized the modeling of the process of heat exchange in micro-channels. The used model is validated by comparison with numeric results obtained by authors in specialized literature.


INTRODUCTION
The high level of performances of the central processing unit (CPU) has been made possible only by adopting technical solutions designed to ensure the dissipation of the generated heat.The tendency of minimizing electronic components and, implicitly, the CPUs, has led to the manufacture of a broad area of efficient cooling systems whose composition includes mini, micro and nano-channels traversed by different sorts of cooling agents.
The research in this area of expertise has verified the applicability of the theory for heat and mass transfer for every type of micro-channel (with dimensions between 10-200 µm).There have been conceived calculation models of the parameters, [1][2][3], and there have been performed experimental determinations for confirming the results.The data has been validated by comparison with results obtained by other authors.

CONSIDERATIONS REGARDING MINI AND MICRO-CHANNELS IN CPU'S COOLING SYSTEMS
The discovery of the performances gained by using micro-channels in the field of microelectronics and other areas of expertise has led to intense research of heat transfer in mini, micro and nano-channels in parallel with the evolution of the manufacturing technologies.
The manufacturing micro-techniques are conventional technologies and modern methods that can produce channels with dimensions of about a hundred microns, having different geometric shapes.From micromechanics, there are used for producing micro and nano-channels: doping, lithography, and corrosion using plasma, micro-modeling.Today, there is variety of specialized processes such as (with electron beam processing, selective laser sintering, engraving techniques), which do not posses dimensional limit in the manufacturing process of the channels, for heat transfer applications.Despite all the difficulties regarding the manufacture of the micro-channels, one of the advantages is their big surface with regard to their volume at small dimensions.As a result, there are important consequences on surface forces and a coefficient of heat transfer that becomes increasingly higher.

CALCULATION MODEL OF HEAT TRANSFER THROUGH CIRCULAR MICRO-CHANNELS
In order to analyze heat transfer, we consider air flow through a circular micro-channel, described in Figure 1, with an interior diameter 2r = 1.2 m and length l = 3 mm.It is applied the calculation model realized in [1], taking into account simplifying hypothesis such as: coarse walls with constant thermal-flux, constant wall temperature T = 368 K, properties of the fluid remain unmodified with time, fluid is compressible and the mass flow rate is of hydrodynamic type.The pressures at entrance and exit, considered in the calculations, are presented in Table 1 as follows.We presume that the VSS model of collision, proposed by Koura andMatsumoto (1991, 1992), in [1], describes with precision the collision of the molecules.The chosen model is applied in Mathcad for the following values [1], viscosity coefficient of air = 0.77; the exponent for VSS model is = 1.36; the dynamic viscosity in standard conditions 0 = 171.910x 10 -7 Pa•s; molecular mass M = 28.9710x 10 -3 kg/kmol and specific gas constant R = 9.907 x 10 3 J/kgK.
The dynamic viscosity at temperature T, (T) = 20.488x 10 -6 Pa•s, is calculated using the law of variation: The mean free path at entrance/exit is obtained from the expression: in which the coefficient k 2VSS for the VSS model is k 2VSS = 1.034 and k 2HS = 1.277 for the HS model, calculated using relations (3,4), from [1]: The variation of the parameter VSS and HS with regard to the entrance pressure p intlet is represented in Figure 2. where = p i / p o is the ratio between the entrance and exit pressure, is the "accommodation coefficient" and Kn o is the "exit Knudsen number".

CONCLUSIONS
The obtained results represented in Figure 4 for three values of show that the mass flow rate at entrance has values of the same order of magnitude.The shape of the graphs for circular channels is approximately the same as for the rectangular ones (from [1]).This fact indicates that the same manner of variation applies to the two shapes of micro-channels analyzed.
The representation of the variation of Nusselt number depending on admission pressure -Figure 5 -shows an increase of Nusselt number, together with the value of pressure, which shows that the heat exchange by convection is intensified at the same time as the rise in flux.
The obtained results for air flux through circular channels have the same order of magnitude as the ones obtained for rectangular channels in [1][2][3][4].Moreover, the shape of the graphics is identical with the one obtained by other authors [1,3].In conclusion, the proposed and applied mathematical model is validated.

Fig. 3 .
Fig. 3. Variation Kn -p inlet .Variation of the mass flow depending on , values calculated for air, is shown in the graph from Figure 4.It can be observed a mass flow rate increase according to the rise in entrance pressure.Moreover, there are identified lower values of the mass flow rate for lower values of .The Nusselt number is determined using the relation below[1]:

Table 1 .
Entrance pressure p i and exit pressure p o .