Optimal Control of Heat Transfer Systems

Optimal control of heat transfer systems encompasses the formulation and solution of mathematical problems aimed at directing thermal processes toward desired objectives under physical and operational constraints. Such systems span a wide range of applications, from enhancing the efficiency of heat exchangers and managing temperature distributions in electronic devices to regulating thermal comfort in buildings and controlling phase‐change operations in advanced manufacturing. The underlying models are typically governed by partial differential equations representing conduction, convection and radiation, often coupled through buoyancy‐driven flows described by the Boussinesq approximation or more general fluid–thermal interactions. Control parameters may include boundary temperatures, heat fluxes or internal heat sources, and the optimisation criteria often balance energy consumption, temporal performance and safety margins. Methodological advances draw upon functional‐analytic proofs of existence and uniqueness for weak solutions, adjoint‐based derivations of optimality conditions and robust numerical algorithms such as finite element discretisation and iterative solvers. Emerging trends focus on real‐time implementation using model predictive control, data‐driven surrogate modelling for rapid decision making and the integration of sensor networks for adaptive control. The global significance of this research lies in its potential to reduce energy waste, improve system reliability and enable novel thermal technologies across engineering, environmental and biomedical domains.

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Optimal Control of Heat Transfer Systems publication trend

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Technical terms

Optimal control: A mathematical strategy for finding input functions or boundary values that minimise or maximise a chosen performance criterion subject to differential‐equation constraints.

Boussinesq approximation: A simplification of the Navier–Stokes and heat equations that treats density variations as negligible except where they appear in buoyancy terms.

Boundary condition: A specification of the solution’s behaviour on the domain boundary, commonly classified as Dirichlet (fixed value), Neumann (fixed flux) or Robin (linear combination).

Weak solution: A generalised solution concept in which differential equations are satisfied in an integral sense, allowing for less regularity in the solution functions.

Finite element method: A numerical technique for approximating solutions to boundary value problems by subdividing the domain into smaller, simple geometric elements and constructing piecewise polynomial trial functions.

References

1. Analysis and Computations of Optimal Control Problems for Boussinesq Equations. Fluids (2022).
2. The Heat Transfer Problem in a Non-Convex Body—A New Procedure for Constructing Solutions. Axioms (2023).
3. Inhomogeneous Boundary Value Problems for the Generalized Boussinesq Model of Mass Transfer. Mathematics (2024).