Topology Optimization for Natural Convection Cooling Geometry

Foundational Work (Alexandersen, Sigmund, Aage, 2016)

“Large scale three-dimensional topology optimisation of heat sinks cooled by natural convection.” International Journal of Heat and Mass Transfer, Vol. 100, pp. 876-891.

Method

• Density-based topology optimization
• Steady-state incompressible Navier-Stokes coupled to thermal convection-diffusion
• Boussinesq approximation for buoyancy
• 20-330 million state degrees of freedom
• Grashof numbers between 10³ and 10⁶ (laminar flow)
• Parallel computational framework

Key Discovery

The number of branches in optimized 3D designs increases with increasing Grashof numbers — opposite to 2D results. This means larger-scale thermal convection systems naturally develop more complex branching architectures. The obtained topologies show that “carefully tailored and complex geometries may improve cooling behaviour considerably compared to simple heat fin geometries.”

Nature-Inspired Geometries

Optimized high-conductive material distributions resemble natural tree-structures, with primary branches extending toward the furthest corners of the domain. Increasing seed locations from 1 to 4 improved thermal performance by up to 20% for a 5% volumetric constraint. Nature-inspired fractal/branching geometries emerge spontaneously from the algorithms.

Scaling Toward Architecture

”Poor Man’s” Approach (Pollini et al., 2020)

Follow-up reduced computational cost to 5-20% of full Navier-Stokes, making desktop-scale 3D topology optimization of natural convection feasible. Removes a key barrier to scaling up.

Generative Cooling Channels (Liu, 2026)

Generative algorithms coupled with physics-based thermal models using “constrained reaction-diffusion process” generate novel channel topologies. Achieved >5°C reduction in average temperature and >35°C reduction in maximum temperature vs. parallel channel baselines. Demonstrates the method works for cooling channels at intermediate scale.

The Building-Scale Gap

What Exists at Building Scale

• Parametric/evolutionary optimization: Genetic algorithms optimize predefined building parameters (window ratios, orientation, wall thickness). Achieves 23-28% energy reductions (Yang 2025 survey).
• TABS pipe network optimization: He et al. (2023) used genetic algorithms on pipe network topology in high-rise TABS. 11.21% energy cost reduction. But optimizes graph connectivity (which pipes go where), not physical channel geometry.
• CFD simulation: Evaluates given designs but doesn’t generate new geometries.

What Does NOT Exist

Nobody has applied density-based or level-set topology optimization — the methods that produce branching/tree cooling channel geometries at component scale — to:

• Building ventilation channels
• Facade cooling geometries
• Architectural passive cooling forms

This is a genuine research frontier where the computational methods exist, the building-scale need exists, but the connection has not been made.

Connection to Fuller

Topology optimization that generates optimal cooling geometry from scratch — maximum thermal performance with minimum material — is the computational realization of Fuller’s ephemeralization principle. The algorithms converge on nature-inspired branching patterns, echoing Fuller’s conviction that nature’s coordinate system holds the key to optimal design.