The micro-tube heat transfer and fluid flow of aqueous solutions with ethylene glycol.

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

1. INTRODUCTION

The thermal management of the electronic devices and power sources became the challenging issue in the last decade because of both, miniaturization and heat transfer rate increasing. The various cooling solutions have been proposed using both the single and two-phase heat transfer.

Micro Thermal Systems (MTS), 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 (Lelea, 2009).

Koo et al, studied the effects of viscous dissipation on the temperature field and also on the friction factor using dimensional analysis and experimentally validated computer simulations for three different working fluids (water, methanol and iso-propanol) in micro-tubes and micro-channels. The variation of temperature with the Reynolds number was studied for rectangular channels and there was made a comparison between the experimental data and the computational results (Koo, 2004).

Celata et al, analyzed the issue of scaling effects that cause influential effects when channel geometry is reduced below a certain limit. The results were connected with the role of viscous heating in micro-channel flows, it's occurrence in the Navier Stokes equations and also there was made an experimental validation for verifying it's presence in practice. The experimental results were compared with the values existing in literature for compliance (Celata, 2006).

Hooman et al, analyzed theoretically the role of viscous dissipation on forced convection, with temperature-dependent viscosity and thermal conductivity, through microchannels and micropipes, under isoflux wall boundary condition. The analytical results can be used for macrochannels where continuum assumption, and hence, no-slip condition is still valid (Hooman, 2009; Hooman, 2010).

Tunc and Bayazitoglu investigated the convective heat transfer for steady laminar hydrodynamically developed flow in microtubes with temperature jump at the wall and viscous heating conditions. It was concluded that Nusselt number takes higher values for cooling and lower for heating (Tunc, 2001).

2. SIMULATION PART AND DISCUSSION

2.1 Establishing the relations for Nu, Po, Re criteria and Br number

The thermal properties of Ethylene Glycol are presented below:

Because Ethylene Glycol is an aqueous solution, the general form for thermal conductivity and specific heat is :

k = [c.sub.p] = A + B x T + C x [T.sup.2]

Where : T, K, temperature

A, B, C, coefficients with given values (***)

The following set of partial differential equations is used to describe the studied phenomena, considering the variable thermo-physical properties of the fluid and viscous dissipation:

Continuity equation:

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

Momentum equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (2)

Energy equation:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (3)

Where the viscous dissipation term is defined as:

[MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (4)

The heat transfer coefficient

h = q/[t.sub.w] - [t.sub.b] (5)

The Brinkman number for constant wall heat flux is defined as:

Br = [u.sup.2.sub.m] x [mu]/q x [D.sub.i] (6)

Where:

[c.sub.p], J/kg K, specific heat

D, m, tube diameter

h, W/[m.sup.2] K, heat transfer coefficient

k, W/mK, thermal conductivity

Nu, Nusselt number

Po, Poiseuille constant

R, m, tube radius

Re, Reynolds number

T, K, temperature

u, v, m/s, velocity components

x, z, spatial coordinates

Greek symbols

[mu], Pa s, viscosity

[rho], kg/[m.sup.3], density

The partial differential equations (1)-(4) 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).

2.2 Pressure drop and heat transfer coefficient variation

There were analyzed the pressure drop and variation for the heat transfer coefficient for three different concentrations of aqueous solutions of Ethylene Glycol (30%, 40% and 50%), considering heating and cooling regimes for a value of 0.5 for the Brinkman number (+0.5 for heating regime and -0.5 for cooling regime).

The obtained results are presented in Figures 1 and 2.

[FIGURE 1 OMITTED]

[FIGURE 2 OMITTED]

3. CONCLUSIONS

The numerical model for heat and fluid flow through the pipes, considering the viscous heating of the fluid. The aqueous solutions of Ethylene Glycol (30%, 40% and 50%) were considered as the working fluid. The Brinkman number is used to estimate the viscous dissipation effect with Br = 0.5 (both for heating and cooling. The following conclusions are outlined:

* Both the heat transfer coefficient and pressure drops are influenced by the viscous heating

* Different behaviours of the covered parameters are observed for heating or cooling of the tube wall.

* In the case of heat transfer coefficient the boundary layer evolution of the heat transfer coefficient is observed regardless the Ethylene Glycol Vol% in water

* The Ethylene Glycol Vol% in water slightly influences the heat transfer coefficient during the heating case

* Contrary to heating, during the cooling case the heat transfer coefficient is decreasing as the Vol% is increasing

4. ACKNOWLEDGMENT

This work was supported by CNCSIS -UEFISCSU, project number 670 PNII--IDEI 938/2008.

5. REFERENCES

Celata, G.P.; Morini, G.L.; Marconi, V.; McPhail, S.J. & Zummo, G. (2006). Using viscous heating to determine the friction factor in microchannels--An experimental validation, Experimental thermal and fluid science, Volume 30, pp. 725-731, ISSN: 0894-1777

Hooman, K. & Ejlali, A. (2010). Effects of viscous heating, fluid property variation, velocity slip, and temperature jump on convection through parallel plate and circular microchannels, International Communications in Heat and Mass Transfer, Volume 37, pp. 34-38 ISSN: 0735-1933

Hooman, K.; Hooman, F. & Famouri, M. (2009). Scaling effects for flow in micro-channels: Variable property, viscous heating, velocity slip, and temperature jump, International Communications in Heat and Mass Transfer, Volume 36 pp. 192-196, ISSN: 0735-1933

Koo, J. & Kleinstreuer, C. (2004). Viscous dissipation effects in microtubes and microchannels, International Journal of Heat Mass Transfer, Volume 47, pp. 3159-3169, ISSN: 0017-9310

Lelea, D.; Cioabla, A.E.; Laza, I. & Mihon L. (2009). The Nu Number Behavior on Micro-tube Heat Transfer and Fluid Flow of Dielectric Fluid, The Open Thermodynamics Journal, Issue 3, pp. 38-41, ISSN: 1874-396X

Lelea, D. (2007). The conjugate heat transfer of the partially heated microchannels, Heat and Mass Transfer, Vol. 44 (January, 2007) (33-41), ISSN 0947-7411

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

Tunc, G. & Bayazitoglu, Y. (2001). Heat transfer in microtubes with viscous dissipation, International Journal of Heat and Mass Transfer, Volume 44, pp. 2395-2403, ISSN: 0017-9310 http://www.meglobal.biz/media/product_guides/MEGlobal_MEG.pdf