Computational analysis of actively-cooled 3D woven microvascular composites using a stabilized interface-enriched generalized finite element method

The computational design of an actively-cooled 3D woven microvascular composite plate with sinusoidal and straight microchannels is presented. The design objectives include minimizing the maximum temperature of the composite, the microchannel volume fraction, and the pressure drop needed to circulate the coolant in the microchannels. We study the impact of a variety of parameters on the optimal design of a microvascular composite plate subjected to a uniform heat flux over its bottom surface. These parameters include the spacing, wavelength, and amplitude of the microchannels, the coolant type and flow rate, and the applied thermal loads. To facilitate the computational design process, a mesh-independent Interface-enriched Generalized Finite Element Method (IGFEM) is employed to evaluate the temperature field in the actively-cooled composite. The IGFEM solver also includes the streamline upwind Petrov-Galekin stabilization scheme to eliminate the spurious oscillations in the temperature field due to the convection-dominated heat transfer in the microchannels. This study reveals that the straight microchannels are often the optimal configuration. Design maps are presented to evaluate the required flow rate as a function of the applied thermal load and the plate dimensions.

[1]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: II. Beyond SUPG , 1986 .

[2]  T. Hughes.  Multiscale phenomena: Green's functions, the Dirichlet-to-Neumann formulation, subgrid scale models, bubbles and the origins of stabilized methods , 1995 .

[3]  T. Hughes,et al.  A new finite element formulation for computational fluid dynamics: V. Circumventing the Babuscka-Brezzi condition: A stable Petrov-Galerkin formulation of , 1986 .

[4]  M. Allen,et al.  Active cooling substrates for thermal management of microelectronics , 2005, IEEE Transactions on Components and Packaging Technologies.

[5]  S. Kim,et al.  Numerical optimization of the thermal performance of a microchannel heat sink , 2002 .

[6]  Leopoldo P. Franca,et al.  On a two‐level finite element method for the incompressible Navier–Stokes equations , 2000 .

[7]  M. Patterson,et al.  Experimental and Numerical Study of a Stacked Microchannel Heat Sink for Liquid Cooling of Microelectronic Devices , 2007 .

[8]  L. Franca,et al.  Stabilized Finite Element Methods , 1993 .

[9]  A. Huerta,et al.  Finite Element Methods for Flow Problems , 2003 .

[10]  J. Lewis,et al.  Self-healing materials with microvascular networks. , 2007, Nature materials.

[11]  Philippe H. Geubelle,et al.  A 3D interface-enriched generalized finite element method for weakly discontinuous problems with complex internal geometries , 2012 .

[12]  C. Seeton.  Viscosity–temperature correlation for liquids , 2006 .

[13]  I. Mudawar,et al.  Experimental and numerical study of pressure drop and heat transfer in a single-phase micro-channel heat sink , 2002 .

[14]  H. Rosenberg,et al.  The thermal conductivity of glass-fibre and carbon-fibre/epoxy composites from 2 to 80 k , 1982 .

[15]  Thomas J. R. Hughes,et al.  Finite element methods for first-order hyperbolic systems with particular emphasis on the compressible Euler equations , 1984 .

[16]  Thomas-Peter Fries,et al.  Review of Petrov-Galerkin Stabilization Approaches and an Extension to Meshfree MethodsA , 2004 .

[17]  C. Duarte,et al.  An interface-enriched generalized finite element method for problems with discontinuous gradient fields , 2010 .

[18]  D. Ouazar,et al.  Computational Hydraulics , 1983 .

[19]  Mahmood Yaghoubi,et al.  Influence of channel geometry on the performance of a counter flow microchannel heat exchanger , 2009 .

[20]  T. Hughes,et al.  Streamline upwind/Petrov-Galerkin formulations for convection dominated flows with particular emphasis on the incompressible Navier-Stokes equations , 1990 .

[21]  J. Z. Zhu,et al.  The finite element method , 1977 .

[22]  Piyush R. Thakre,et al.  Three‐Dimensional Microvascular Fiber‐Reinforced Composites , 2011, Advanced materials.

[23]  S. Martel,et al.  PCB-Integrated Heat Exchanger for Cooling Electronics Using Microchannels Fabricated With the Direct-Write Method , 2008, IEEE Transactions on Components and Packaging Technologies.

[24]  Yu. F. Maidanik,et al.  Miniature loop heat pipes for electronics cooling , 2003 .

[25]  Nancy R. Sottos,et al.  Polymer Microvascular Network Composites , 2010 .

[26]  J. A. Lewis.  Direct Ink Writing of 3D Functional Materials , 2006 .

[27]  C. Shu,et al.  Fluid flow and heat transfer in wavy microchannels , 2010 .

[28]  Philippe H. Geubelle,et al.  An interface‐enriched generalized FEM for problems with discontinuous gradient fields , 2012 .

[29]  Ya-Ling He,et al.  Numerical study of laminar heat transfer and pressure drop characteristics in a water-cooled minichannel heat sink , 2009 .

[30]  G. Whitesides,et al.  Generation of Solution and Surface Gradients Using Microfluidic Systems , 2000 .

[31]  Alessandro Russo,et al.  Applications of the pseudo residual-free bubbles to the stabilization of convection-diffusion problems , 1998 .

[32]  J. Lewis,et al.  Erratum: Chaotic mixing in three-dimensional microvascular networks fabricated by direct-write assembly (Nature Materials (2002) 2 (265-271)) , 2003 .

[33]  Eugenio Oñate,et al.  A stabilized finite element method for incompressible viscous flows using a finite increment calculus formulation , 2000 .

[34]  Arif Masud,et al.  A variational multiscale stabilized formulation for the incompressible Navier–Stokes equations , 2009 .

[35]  Martin F. Borthwick,et al.  Computational hydraulics , 2010, Hydraulics in Civil and Environmental Engineering.

[36]  Brian N. Johnson,et al.  An integrated nanoliter DNA analysis device. , 1998, Science.

[37]  Hong-Sen Kou,et al.  Optimum thermal performance of microchannel heat sink by adjusting channel width and height , 2008 .

[38]  F. Brezzi,et al.  A relationship between stabilized finite element methods and the Galerkin method with bubble functions , 1992 .

[39]  Yildiz Bayazitoglu,et al.  International Journal of Heat and Mass Transfer , 2013 .

[40]  G. Peterson,et al.  Experimental investigation of heat transfer in flat plates with rectangular microchannels , 1995 .

[41]  T. Hughes,et al.  Stabilized finite element methods. I: Application to the advective-diffusive model , 1992 .

[42]  O Orwar,et al.  Microfluidic device for combinatorial fusion of liposomes and cells. , 2001, Analytical chemistry.

[43]  J. Thome,et al.  Saturated critical heat flux in a multi-microchannel heat sink fed by a split flow system , 2010 .

[44]  J. Thome,et al.  State of the Art of High Heat Flux Cooling Technologies , 2007 .

[45]  M. Islam,et al.  Thermal Conductivity of Fiber Reinforced Composites by the FEM , 1999 .

[46]  J. Lewis,et al.  Chaotic mixing in three-dimensional microvascular networks fabricated by direct-write assembly , 2003, Nature materials.

[47]  Min-Soo Kim,et al.  Experimental study on microchannel heat sinks considering mass flow distribution with non-uniform heat flux conditions , 2010 .

[48]  Yaochu Jin,et al.  Optimization of micro heat exchanger: CFD, analytical approach and multi-objective evolutionary algorithms , 2006 .

[49]  Nancy R. Sottos,et al.  Computational Modeling and Design of Actively-Cooled Microvascular Materials , 2012 .

[50]  G. Yeoh,et al.  Three-dimensional modelling of fluid flow and heat transfer in micro-channels with synthetic jet , 2012 .

[51]  O. C. Zienkiewicz,et al.  The Finite Element Method: Its Basis and Fundamentals , 2005 .

[52]  Chiu Han-Chieh,et al.  The heat transfer characteristics of liquid cooling heatsink containing microchannels , 2011 .

[53]  Tian Jian Lu,et al.  Analysis of microchannel heat sinks for electronics cooling , 2002 .