Numerical study of fluid flow and heat transfer in microchannel cooling passages
Introduction
The application of microchannel heat sinks is drawing increasing attentions as one of the most promising high-efficiency heat exchange technologies in, e.g., the cooling of electronic devices, automotive heat exchangers, laser process equipments, and aerospace technology, etc. Microchannel flow and heat transfer has become an quite active thermal and fluid research field since the early work of Tuckerman and Pease [1], and Wu and Little [2], [3]. Intensive investigations were performed experimentally and theoretically in the following decades [4], [5], [6], [7], [8], [9], [10], which were categorized into various topics and elaborately summarized in the comprehensive review of Sobhan and Garimella [11]. The friction factor and heat transfer coefficient were the most concerned parameters in the literature, whose derivation from classical theory and the dependency on the channel diameter were not conclusive due to the different or even contradictory suggestions provided by different investigators [12].
Besides the reasonable suspect on the quality of measured data, several possible explanations were provided for the derivations from classical theory, or so-called microscale effects. Some attributed the derivations to wall roughness, since the same absolute surface roughness has enlarged effect on small diameter channels than on large ones, as in the work of Kandlikar et al. [13]. Some introduced the electric double-layer (EDL) effect, as in Yang et al. [14], and in Ng and co-worker [15], [16], as a body force term in the momentum equation to obtain the Nusselt number and friction factor for an aqueous solution of low ionic concentration and a wall surface of high zeta potential. However, it was also noted that for the conditions used in the evaluation of the model, EDL effects should not be important for pressure drop or heat transfer in channels larger than 40 μm.
Flow development of hydraulic and thermal boundary layers is considered important in microchannel convections, which are often characterized by laminar flow. Fedorov and Viskanta [17] reported a substantial developing flow effect in the channels from their three-dimensional numerical simulations. Similar conclusion was drawn in the numerical investigation of Qu and Mudawar [18]. Their most recent work [19], collaborated with other authors, conducted experimental and computational studies on flow development and pressure drop for adiabatic single-phase water flow in a single 222 μm wide, 694 μm deep, and 12 cm long rectangular microchannel at Reynolds numbers ranging from 196 to 2215. The velocity field was measured using a microparticle image velocimetry system. Pronounced flow field evidence was provided for the strong entrance effect from their experiments and numerical simulations. Gamrat et al. [20] performed both two- and three-dimensional numerical analysis of microchannel convection, considering the thermal entrance effects and conjugate heat transfer of fluid and solid wall. The results of their numerical simulation confirmed, together with those mentioned above, that the continuum model of conventional mass, Navier–Stokes and energy equations are of adequate accuracy in representing the microchannel flow and heat transfer characteristics.
As mentioned above, constant thermophysical properties were usually used in the analyses of previous work. They could not fully reveal the characteristics of fluid flow and heat transfer in the conditions of high heat flux and low Reynolds number flow, implying large variation of liquid properties, which is always encountered in the applications of microchannels. For water in the temperature range from 0 to 100 °C, μ varies by 84% (decrease), k by 21% (increase), ρ by 4% (decrease) and cp by 1% (non-monotonic). [21]. The relatively large variations of μ and k indicate that the two properties should be treated as functions of temperature. As a result, the energy equation is no longer independent of the momentum equation in the conservative model, drawing significant difficulty in the theoretical analysis. The property-ratio method [22] was introduced and was popularly employed to the correction of Nusselt number for convection in convectional tubes, which fails to provide reasonable prediction for large heat flux. Mahulikar and Herwig [23] established a continuum-based model for laminar convections, incorporating temperature dependence of fluid viscosity and thermal conductivity. The solution of the model relied on mature computational fluid dynamics technology and showed applicability for a large range of heat flux, indicating its suitable usage in microchannel convections. In their most recent work [24], detailed effects of temperature-dependent properties were provided on the fully developed laminar microconvection in circular tubes.
Non-uniform heating conditions are another important feature in the practical operation of microchannel devices in terms of both space and time scales. It was usually assumed, however, uniform thermal boundary in the previous studies, as either isothermal or uniform heat flux condition. The non-uniformity of thermal boundary conditions should remarkably alter the temperature distribution of the fluid, and additionally alter the flow field through the variation of μ and k.
The present work numerically investigated the two-dimensional low Reynolds number convection of water in microchannel with the combination of locally heated wall boundary condition and temperature-dependent viscosity and thermal conductivity of liquid water. Heat transfer performance was evaluated by comparing with constant–property solutions. The effect of thermal development and property variation was discussed through detailed analysis of local momentum and heat transport.
Section snippets
Fundamental considerations
The model is derived from continuum-based conservation equations of mass, momentum and energy [25], with the following several basic assumptions:
- (1)
Steady laminar flow.
- (2)
Incompressible Newtonian fluid.
- (3)
Constant specific heat of the fluid.
- (4)
Thermal conductivity and viscosity are the single variable functions of temperature.
- (5)
Negligible effect of gravity and other forms of body forces.
The resulting governing equations are:
Continuity equationMomentum equationEnergy
Numerical method and validation
The governing equations with boundary conditions were solved by the commercial CFD code, CFX5. The equations were discretized by means of a fully implicit second order finite volume method with modified upwind advection scheme. In this work, the grid points used in the x and z directions were selected to be 600 and 70, respectively, with carefully distributed density near central heated region. To obtain better accuracy in the numerical computations, coarse and fine grid systems were considered
Results and discussion
For all tested cases in this work, the channel width, D, was 100 μm, and inlet temperature, T0 = 20 °C. The Reynolds number, ReD and heat flux were varied to examine the effects of property variation within the temperature range of liquid water. For the convenience of comparison with other researches, the heat flux was non-dimensionalized as the following form:which ranged from 0.057 to 0.855 in the present study.
Conclusion
Numerical investigation was conducted in an effort to perform an in-depth analysis for microchannel convections. Localized non-successive high heat flux boundary condition is frequently encountered in practical applications of microchannel heat exchangers, which results in steep temperature rise and dramatic property variation of working liquid in both flow and cross-flow directions. By considering liquid water of μ- and k-variation with temperature, two-dimensional convection in a D = 100 μm
Acknowledgements
This investigation is currently supported by National Natural Science Foundation of China (Contract No. 90505012). The first author would like to appreciate Professor W.M. Yan for supporting his visit and research at Huafan University in Taipei.
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