Constructal design under discontinuities: Emergence and stability of flow architectures under irreversible constraints
Year: 2026
Type: article
Abstract: Constructal Law states that a finite-size flow system that persists in time must evolve its configuration to provide progressively easier access to the currents flowing through it. Classical Constructal theory typically derives hierarchical flow architectures by minimizing resistance under finite-size constraints. Yet many real transport systems operate under irreversible limits that generate regime switching and discontinuities in the governing transport laws, conditions for which smooth variational formulations are inadequate.This paper develops a dynamical realization of Constructal Law using nonsmooth differential inclusions. The evolving flow architecture is modeled as the state of a Filippov system defined on a compact, forward-invariant admissible set of configurations. Irreversible transport constraints generate switching manifolds across which the architectural vector field becomes discontinuous. A resistance dissipation inequality formalizes the principle of ”progressively easier access” as a nonsmooth Lyapunov condition, while a uniform contraction assumption provides verifiable spectral bounds for regime-wise Jacobians.Under these conditions, we prove global exponential convergence of all admissible trajectories toward a unique invariant architecture. Finite size, irreversibility, and resistance dissipation therefore imply the existence, uniqueness, and stability of persistent flow configurations without requiring static optimization.As an application, the classical area-to-point transport hierarchy of Bejan–Bădescu–De Vos is embedded in this framework. The optimal assembly ratios appear as switching manifolds, and the classical Constructal scaling relations emerge as sliding invariant sets of the Filippov inclusion. Under contraction, their intersection forms the unique globally attracting architecture. Constructal hierarchy is therefore characterized as a stability property of dissipative, regime-dependent transport dynamics.
Authors: Pascal Stiefenhofer, Cafer Deniz
Institution: Newcastle University
Language: English
Subfield: Mechanical Engineering
Field: Engineering
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,560
OpenAlex ID: W7171071083