A “poor man's approach” to topology optimization of cooling channels based on a Darcy flow model

Xi Zhao, Mingdong Zhou*, Ole Sigmund, Casper Schousboe Andreasen

*Corresponding author for this work

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A topology optimization methodology for optimizing cooling channels using an approximate but low-cost flow and heat transfer model is presented. The fluid flow is modeled using the Darcy model, which is a linear problem that can be solved very efficiently compared to the Navier–Stokes equations. The obtained fluid velocity is subsequently used in a stabilized convection–diffusion heat transfer model to calculate the temperature distribution. The governing equations are cast in a monolithic form such that both the solid and fluid can be modeled using a single equation set. The material properties: permeability, conductivity, density and specific heat capacity are interpolated using the Solid Isotropic Material with Penalization (SIMP) scheme. Manufacturable cooling-channel designs with clear topologies are obtained with the help of a pressure drop constraint and a geometric length-scale constraint. Several numerical examples demonstrate the applicability of this approach. Verification studies with a full turbulence model show that, although the equivalent model has limitations in yielding a perfect realistic velocity field, it generally provides well-performing cooling channel designs.

Original languageEnglish
JournalInternational Journal of Heat and Mass Transfer
Pages (from-to)1108-1123
Publication statusPublished - 2018


  • Convective heat transfer
  • Cooling channels
  • Darcy flow
  • Length-scale control
  • Topology optimization

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