Development and verification of a mathematical model of three-dimensional laminar flow of viscous incompressible liquid and conjugate heat transfer applied to microchannel heat exchangers

Аuthors

Razvalyaev S. V.^*, Boldyrev A. V.

1,2Naberezhnye Chelny Institute of Kazan Federal University, Kazan, Russia, Republic of Tatarstan

*e-mail: Ssergei.1991@mail.ru

Abstract

Microchannel technology has gained widespread adoption in microelectronic cooling systems. Today's electronic chips emit heat fluxes on the order of 100 W/cm². With advances in microprocessor technology, heat fluxes at equipment “hot spots” are approaching 1000 W/cm² [1]. Traditional cooling methods using a combination of heat pipes and fans provide approximately 200 W/cm², which is clearly insufficient [2]. The performance of electronic systems significantly decreases when temperature thresholds are exceeded. Furthermore, it has been found that accumulation of excess temperatures within devices leads to degradation of material properties used for device fabrication, such as structural integrity and chemical stability. These factors contribute to reduced service life of equipment.
Therefore, microchannel heat exchangers with flow channel dimensions less than 1 mm are gaining increasing popularity [3–5].
To improve microchannel heat exchangers, besides costly experimental methods, three-dimensional numerical simulation of hydrodynamics and heat transfer can be employed using specialized software packages provided that the mathematical model is adequate.
Thus, this article focuses on verifying a mathematical model of three-dimensional laminar flow of viscous incompressible fluid and conjugate heat transfer applied to microchannel heat exchangers, as well as investigating the influence of some geometric parameters of these devices on thermohydraulic efficiency.
The article presents verification of a mathematical model of three-dimensional laminar flow of viscous incompressible fluid and conjugate heat transfer applicable to microchannel heat exchangers, along with investigation into how certain geometric parameters affect their thermohydraulic efficiency. A heat exchanger design consisting of ten parallel microchannels with cross-sectional width of 0,1 mm and height of 0,2 mm was considered. Experimental data presented in the paper were compared with mode-ling results:
– For hydraulic friction multiplied by Reynolds number (fapp×Re), maximum deviation was 12 % at Re = 150, while minimum deviation was 1 % at Re = 450;
– For Nusselt number (Nu), maximum deviation was 11 % at Re = 650, whereas minimum deviation was 1 % at Re = 550.
Based on the verified mathematical model of three-dimensional laminar flow of viscous incompressible fluid and conjugate heat transfer, an analysis was conducted on the impact of several geometric parameters of microchannel heat exchangers on thermohydraulic efficiency.
It was confirmed that numerical simulations based on the mathematical model of three-dimensional laminar flow of viscous incompressible fluid and conjugate heat transfer could be utilized for qualitative assessment of various geometric and operational parameters' effects on hydraulic resistance and Nusselt number of microchannel heat exchangers. This information, in turn, may facilitate subsequent optimization of the design of these heat exchange apparatuses.

Keywords:

numerical modeling, verification of a mathematical model, microchannel heat exchanger, Reynolds number, Nusselt number

References

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