The microtube heat transfer and fluid flow of dielectric fluids.

Lelea, Dorin ; Cioabla, Adrian ; Laza, Ioan 等

1. INTRODUCTION

Micro Thermal Systems (MTS) (Nishio, 2003), defined as the systems in which the key size has a length scale of a micrometer, could attain the high heat transfer coefficients. For instance, they are used as the cooling devices for LSI chips. On the other hand [mu]--TAS (Micro Total Chemical Analyzing System), MEMS (Micro Electric--Mechanical Systems) or bio --chips are some of the examples of MTS. The research reports in this field, concerning the thermal and hydrodynamic results, are mostly oriented to the water as a working fluid. However in defense electronics applications, like radars, lasers or avionics the dielectric fluids are used due to a sensibility of the operating conditions.

(Morini, 2004) has also presented the review on a single phase microchannel heat transfer, indicated some of the reasons for a large dispersion of the experimental results. Both gas and liquid flows have been considered.

In the recent years, (Lelea et al., 2004), have made the experimental research on microtube heat transfer and fluid flow with inner diameters between 100 and 500 pm for laminar regime of the water flow. These results have shown the good agreement with the conventional theories even for the entrance region of the tube.

(Lee et al., 2005) have investigated the laminar fluid flow of the water through the multichannel configuration of the rectangular cross-section with a hydraulic diameter from 318 to 903 pm. Their experimental and numerical results shown that, classical continuum theory can be applied for microchannels, considered in their study. On the other hand, the entrance and boundary effects have to be carefully analyzed in the case of theoretical approach.

The outcome of the research reports mentioned above, is that special attention has to be paid to macroscale phenomena that are amplified at the microscale. For example, due to a high heat transfer rate, the temperature variable fluid properties have to be considered. (Lelea, 2005) has investigated the influence of the temperature dependent fluid viscosity on Po number. On the other hand, the small diameter and large length of the tube can result in viscous heating even in the case of liquid flow, as presented in (Koo & Kleinstreuer, 2004).

Most of the research results have the water as the working fluids. Due to the sensibility of some specific electronic devices, water might not be a suitable fluid, so the dielectric fluids must be used. In the present research the dielectric fluid Novec-7600 is used for calculations.

2. NUMERICAL DETAILS

In order to discuss the axial conduction influence, the velocity and temperature distributions were numerically solved taking into account the temperature variation of the fluid properties, procedure described in (Lelea et al., 2004).

The computational domain is presented in Fig. 1, as follows: The fluid flow domain defined at r = 0, [R.sub.i] and z = 0, L; The temperature field domain defined at r= 0, [R.sub.o] and z=0, L.

The outer portion of the tube has two parts, the heated and insulated part. So, as shown in Fig. 2, the respective insulated part was included in the numerical domain. The following set of partial differential equations is used to describe the phenomena, taking into account the variable thermophysical properties of the dielectric fluid. Continuity equation, momentum and energy equations are as follows:

[partial derivative]([rho](T)x u)/[partial derivative]z + 1/4 [partial derivative](r * [rho](T) x v)/[partial derivative]r = 0 (1)

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII]. (2)

[1/r [partial derivative]/[partial derivative]r(k(T) x r [partial derivative]T/[partial derivative]r) + [partial derivative]/[partial derivative]z(k(T)[partial derivative]T/[partial derivative]z)] (3)

At the inlet of the tube, the uniform velocity and temperature field is considered, while at the exit the temperature gradient is equal to zero. The boundary conditions are

z = 0, 0 < r < [R.sub.o] : u = [u.sub.0], T = [T.sub.w] = [T.sub.0] (4)

0 < z < [L.sub.tot] :r = 0, [partial derivative]u/[partial derivative]r = 0, v = 0 r = [R.sub.i], u = v = 0 (5)

The Joule heating of the tube wall can be expressed either by the uniform heat generation through the tube wall or by the uniform heat flux imposed on the outer surface of the wall. For the latter case, the boundary condition is defined as,

[FIGURE 1 OMITTED]

R = [R.sub.o] : [q.sub.o] = [k.sub.s] [partial derivative]T/[partial derivative]r (for the heated portion of the tube) (6)

[k.sub.s] [partial derivative]T/[partial derivative]r = 0 (for the insulated portion of the tube) (7)

where [q.sub.o] is the heat flux based on the outer heat transfer area of the tube wall.

Z = [L.sub.tot] 0 < r < [R.sub.o]: [partial derivative]T/[partial derivative]z = 0 (8)

where qo is the heat flux based on the outer heat transfer area of the tube wall.

R = [R.sub.I] : [T.sub.S][absolute value of Ri+ = [T.sub.f]]Ri- (9)

[k.sub.s][([partial derivative][T.sub.s]/[partial derivative]r).sub.Ri+] = [k.sub.f][([partial derivative][T.sub.f]/[partial derivative]r).sub.Ri-] (10)

The fluid properties of the Novec-7600 were considered as temperature dependent with following equations (3M Engineering fluids, 2008): Dynamic viscosity, density, thermal conductivity and specific heat are:

[mu](t) = (1587.5-1.755 x t) x [10.sup.-6] * e 464.403382/t+133 2.881482 (11)

[rho](t) = 1587.5-1.755 x t (12)

k(t) = 0.078-0.0003 x t (13)

[c.sub.p](t) = 3.1631 x t+1240.2 (14)

The partial differential equations (1)-(3) together with boundary conditions, are solved using the finite volume method described in (Patankar, 1980). First, the parabolic flow field condition is considered and the velocity field is solved. The temperature field, as a conjugate heat transfer problem, was then solved as the elliptic problem using the obtained velocity field. As a consequence of the temperature dependent fluid properties, iterative procedure is needed to obtain the convergence of the fluid properties (viscosity, thermal conductivity, density and specific heat capacity) through the successive solution of the flow and temperature field. Further details regarding the numerical code are presented in (Lelea, 2007).

3. RESULTS AND CONCLUSIONS

The microtube conjugate heat transfer analysis was made for two values of the wall thickness [D.sub.i]/[D.sub.o] = 125.4/300 /an and silicon substrate (k = 198 W/m K). In order to investigate the axial conduction behavior in the tube wall, the low Re range was considered Re < 800. The input heat transfer rate was constant for all the runs [Q.sub.0] = 0.75 W.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

The following outcomes might be emphasize from the results presented in the Figs. 2 and 3:

Due to the poor fluid properties of the Novec-7600 the wall and bulk temperatures are higher for both cases. For u=0.5 m/s and Novec-7600 [T.sub.w,max]=94 [degrees]C and [DELTA]T=17 [degrees]C and for water [T.sub.wmax]=67 [degrees]C and [DELTA]T=3 [degrees]C. If u=6 m/s and Novec-7600 [T.sub.wmax]=43 [degrees]C and [DELTA]T=13[degrees]C while for the water [T.sub.wmax]=29[degrees]C and [DELTA]T=2[degrees]C.

Despite the large temperature difference and higher maximum wall temperature, microchannel heat transfer might be a good candidate for heat dispersion of dielectric fluids.

4. ACKNOWLEDGEMENTS

This work has been financially supported by the Romanian National University Research Council (CNCSIS) and Ministry of Education and Research of Romania, grant nr. 670/2009.

5. REFERENCES

Nishio, S. (2003). Single-Phase Laminar Flow Heat Transfer and Two-Phase Osscilating Flow, Proceedings of 1st International Conference on Microchannels and Minichannels, pp. 25-38, 0791836673, ASME, Rochester USA.

Morini, GL. (2004). Single-phase convective heat transfer in microchannels: a review of experimental results. Int Journal of Thermal Science, Vol. 43, (January, 2004) (631651), 1290-0729

Lelea, D.; Nishio, S.; Takano, K. (2004). The experimental research on microtube heat transfer and fluid flow of distilled water. International Journal of Heat Mass Transfer, Vol. 47, (April, 2004) (2817-2830), 0017-9310

Lee, PS.; Garimella, SV.; Liu, D. (2005). Investigation of heat transfer in rectangular microchannels. International Journal of Heat Mass Transfer, Vol. 48, (1688-1704), 0017-9310

Lelea, D. (2005). Some considerations on frictional losses evaluation of a water flow in microtubes. jnt Commun Heat Mass Transfer, Vol. 32, No. 7, (August, 2005) (964-973), 0735-1933

Koo, J.; Kleinstreuer, C. (2004) Viscous dissipation effects in microtubes and microchannels. International Journal of Heat Mass Transfer, Vol. 47, (July 2004) (3159-3169), 0017-9310

Patankar, SV. (1980). Numerical Heat Transfer and Fluid Flow, McGraw Hill, 0-89116-522-3, New York

Lelea, D. (2007). The conjugate heat transfer of the partially heated microchannels, Heat and Mass Transfer, Vol. 44 (January, 2007) (33--41), ISSN

*** (2008) www.3M.com/electronics--3M[TM] Novec[TM] 7600 Engineered Fluid, 3M Electronics Markets Materials Division, Accessed on: 2009-05-15