Analytical analysis of fluid flow and heat transfer through microchannels.

Khan, Mohd Nadeem ; Islam, Mohd ; Hasan, M.M. 等

Introduction

The development of micro-fluidics devices has been particularly striking during the past 10 years. Today, the research on MEMS (Micro-Electro-Mechanical Systems) is exploring different applications, which involve the dynamics of fluids, and the single and two-phase forced convective heat transfer. An interesting aspect of fluid dynamics through micro-channels is lied to the transition from laminar to turbulent regime. Some studies indicate that the transition from laminar to turbulent flow in micro-scale passages takes place at "critical" Reynolds number ranging from 300 to 2000. In particular, the experimental data of Wu and Little1 on trapezoidal glass and silicon micro-channels, indicated that for Re<1000 the flow is laminar, for 1000<Re<3000 the flow drops into the transition region and for Re>3000 the flow is fully turbulent. Choi et al.2, analyzing microtubes with an hydraulic diameter of 53 ?m and 81.2 ?m, indicated that the transition to turbulent flow occurs at Re=2000. They found that this value decreases for micro-channels having an hydraulic diameter smaller (Re=500 for Dh=9.7 [micro]m and 6.9 [micro]m). The experimental analysis of metallic micro-channels conducted by Peng et al.3-4 indicated that the critical Reynolds values for the flow regimes through rectangular micro-channels could be less than the values found by Wu and Little; Peng and Peterson5 indicated that the Re[member of][200- 700] range represents the upper bond for laminar flow transition to turbulence. In particular, Peng and Peterson gave Re<400 for laminar flow, 400<Re<1000 for the transition region and Re>1000 for fully turbulent flow. Harms et al.6 found that for deep rectangular micro-channels having an aspect ratio of 0.244 the critical Reynolds number is about 1500.

Literature Review

Tuckerman and Pease first suggest that the use of microchannels for high heat flux removal, their study was conducted for water flowing through laminar conditions through microchannels machined in a silicon wafer. Heat flux as high as 790 W/[cm.sup.2] were achieved with the chip temperature maintain below 110[degrees]C. Peng et al. [2,3] experimentally investigated the flow and heat transfer characteristics of water flowing through rectangular stainless steel microchannels with hydraulic diameters of 133-367 [micro]m at channel aspect ratio of 033-1. Their fluid flow results were found to deviate from the value predicated by the classical correlations and the onset of transition was observed to occur at Reynolds numbers from 200 to 700. These results were contradicted by the experiments of Xu et al. [4] who considered liquid flow in 30-344 [micro]m (hydraulic diameter) channels at Reynolds number of 20-4000. Their results show that characteristics of flow in microchannels agree with conventional behavior predicated by Navier-Strokes equation. They suggest that the deviations from classical behavior reported in early studies may have resulted from the errors in the measurement of microchannel dimensions, rather than any microscale effects.

Lui and Garimella [5] showed that conventional correlations offer reliable predications for the Laminar flow characteristics in the rectangular microchannels over a hydraulic diameter range of 244-974 [micro]m. Judy et al. [6] made extensive pressure drop measurement for Reynolds numbers of 8-2300 in 15-150 [micro]m diameter microtubes and two different cross-section geometries. They conclude that if any non-Navier-Strokes flow phenomena existed their influence was masked experimental uncertainty.

Harms et al. [7] studied conventional heat transfer of water in rectangular microchannels of 251 [micro]m width and 1000 [micro]m depth. In the laminar region of Reynolds number investigated, the measured local Nusselt numbers agreed with classical developing flow theory. Qu and Mudawar [8] performed experimental and numerical investigations of pressure drop and heat transfer characteristics of singlephase laminar flow in 231 [micro]m and 713 [micro]m channels. Good agreement was found between the measurement and numerical predications, validating the use of conventional Navier-Strokes equation for microchannels.

Adams et al. [9] investigated the single-phase force convection of water in the circular microchannels of diameter 760 [micro]m and 1090 [micro]m. Their experimental Nusselt numbers were significantly higher than those predicated by traditional large- channels correlations. Adams et al. [10] extend this work to non-circular microchannels of large hydraulic diameters, greater than 1130 [micro]m. All their data for the large diameters were well predicated by the Gnielinski [11] correlation, leading them to suggest a hydraulic diameter of approximately 1200 [micro]m as the lower limit for the applicability of standard turbulent single- phase Nusselt type correlations to non-circular channels.

Numerical Analysis

This section covers the analysis of Reynolds number with the variation of hydraulic diameter and flow rate of air through microchannel. The hydraulic diameter of microchannel varies from 150 [micro]m to 500 [micro]m and the flow rate varies from 0.5 liters per hr. to 4 liters per hr. The results as shown in graph 1 and graph 2 indicates that as the hydraulic diameter increases, Reynolds number decreases and this rate of decreases of Reynolds number with increases of flow rate increases. Also for the particular value hydraulic diameter and flow rate, the value of Reynolds number increases as the temperature of airflow through the channels decreases.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

The experimental Nusselt numbers are generally higher in the turbulent region than predictions from correlations. Some well-developed summaries of experimental results for heat transfer in the microchannels found in the literature are available in number of publications. Wu and Little [14] tested rectangular microchannels and found that the Nusselt number varied with Reynolds number in the laminar regime. This is one of the first studies that predicted a higher Nusselt number for microchannels when compared to microscale equations. Choi et al. [15] also suggested from their experiments with microchannels that the Nusselt number did in fact depend on the Reynolds number in laminar microchannel flow. They also found that the turbulent regime Nusselt number is higher than expected from the DittusBoelter equation. Rahman and Gui [16] found Nusselt number to be higher in the laminar regime and low in the turbulent regime as compared to theory. The Hausen correlation for Nusselt number for thermally developing laminar (constant wall temperature) flow is applicable for Re<2200 and the expression is

Nu = 3.66 + 0.19[(Re.D.Pr./L).sup.0.8]/1 + 0.117[(Re.Pr.D/L).sup.0.467] (1)

Equation (i) indicates that Nusselt number is the direct function of Reynolds number and Pradtl number (Pr). Graphs 1 & 2 shows that Reynolds number is the function of flow rate of air and hydraulic diameter of microchannels, so Nusselt number indirectly affected by flow rate and hydraulics diameter of microchannels. Pradtl number is the function of temperature and its value varies with temperature. Graphs 3 and graph 4 shows the results of Nusselt number with the variation of Reynolds number and hydraulic diameter.

[FIGURE 3 OMITTED]

[FIGURE 4 OMITTED]

The surfaces are very close to each other as shown in figure 3 and its very difficult to analyze the results therefore each surface is shifted to -0.1 units with respected to previous one with reference to the graph for Nusselt number for air flow rate when the air temperature is 20[degrees]C as shown in figure 4. At the fixed hydraulic diameter and Reynolds number the Nusselt number attain its maximum value when the air is minimum temperature. There are four surfaces stand for different air temperature and in each case the condition for maximum value of Nusselt number is that the hydraulic diameter and Reynolds number is maximum. In this case Nusselt number attain its maximum value when the hydraulic diameter is 500 [micro]m , Reynolds is 225.3 and air temperature is 20[degrees]C.

Results & Discussion

From the figure 3 and 4 it is clear that the Nusselt number is the function of Reynolds number and with increase of Reynolds number, Nusselt number also increases. The heat transfer coefficient (h) is the function of Nusselt number, thermal conductivity of fluid (k) and the hydraulic diameter (D). The concept behind microchannels leads itself to the definition of Nusselt number (Nu), which is related to heat transfer coefficient (h)

h = K.Nu/D

If the flow is laminar and fully developed because of small hydraulic diameter, and the Nusselt number is constant, assuming the classical channel flow, the small D of the microchannels in the denominator should enhanced the heat transfer coefficient significantly. The thermal conductivity of fluid is the function of its operating temperature and in the above case the value of thermal conductivity of air at different operating temperature is different therefore the value of K is different for different temperature. Keeping in mind, graphs are plotted between heat transfer coefficient Vs diameter of microchannels and flow rate of air through the microchannels as shown in figure 5.

Figure 5 shows at the fixed value of hydraulic diameter and flow rate of air through microchannel, the heat transfer coefficient (h) attain its maximum value when the air is at maximum temperature instead of this that the value of Nusselt number under the same condition have its minimum value. If the temperature of air is fixed then heat transfer coefficient attain its maximum value when the flow rate of air is maximum and the hydraulic diameter of microchannel is minimum. In all the heat transfer coefficient attain its max. value when the air at 50[degrees]C flowing at maximum flow rate through microchannel having the maximum hydraulic diameter.

[FIGURE 5 OMITTED]

[FIGURE 6 OMITTED]

Conclusion

From the above analysis it is quite comfortable to say that in order to enhance the heat transfer through microchannel the following conditions are exist simultaneously.

(a) The flow having low Reynolds number.

(b) The hydraulic diameter of the microchannel is minimum.

(c) The operating temperature of air flowing through the microchannel is maximum.

This means that flow must follow the above conditions in order to enhance the heat transfer coefficient as shown in figure 6. In actual case it is very difficult to predicate under which conditions heat transfer coefficient is maximum because many factors like temperature gradient, pressure gradient, surface roughness, boundary condition etc are involve.

References

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[17] Rahman, M.M. and Gui, F., Experimental measurements of fluid flow and heat transfer in microchannel cooling passages in a chip substrate, Proceedings of the ASME International Electronics Packaging Conference in Binghamton, NY, USA, ASME publications, 1993,Vol. 4-2, p. 685-692.

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Mohd Nadeem Khan (1), Mohd Islam (2) and M.M. Hasan (2)

(1) Assistant Professor Department of Mechanical Engineering Krishna Institute of Engineering and Technology, Ghaziabad (India) E-Mail: khankiet@kiet.edu

(2) Professor Department of Mechanical Engineering Jamia Millia Islamia, New Delhi (India) E-Mail: muzaffar_jmi@yahoo.com