An HP-Adaptive Finite Element Model for Heat Transfer within Partitioned Enclosures

Document Type



Purpose – The purpose of this paper is to describe the development and employment of an hp-adaptive finite element method (FEM) algorithm for solving heat transfer problems in partitioned enclosures, which has attracted the attention of both experimental and theoretical researchers in recent years.

Design/methodology/approach – In the hp-adaptive FEM algorithm presented here, both the element size and the shape function order are dynamically controlled by an a posteriori error estimator based on the L2 norm; a three-step adaptation strategy is used with a projection algorithm for the flow solver.

Findings – Simulation results are obtained for 2D and 3D natural convection within partitioned enclosures. Results show refined and enriched elements that develop near the partition edges and side walls of the enclosure, as expected. The heat transfer between the heated and cooled side walls is reduced in the presence of a partial partition.

Research limitations/implications – The Rayleigh numbers were set to 105 in the 2D case and 103 in the 3D case. Efforts are underway to apply the hp-adaptive algorithm to partitioned enclosures at much higher Rayleigh numbers, including comparison with available experimental data.

Practical implications – Heat transfer within partitioned enclosures occurs in many engineering situations: heat transfer across thermo pane windows, solar collectors, fire spread and energy transfer in rooms and buildings, cooling of nuclear reactors and heat exchanger design.

Originality/value – The hp-adaptive FEM algorithm is one of the best mesh-based algorithms for improving solution quality, whilst maintaining computational efficiency. The method shows considerable promise in solving a wide range of heat transfer problems including fluid flow.


Aerodynamics and Fluid Mechanics | Applied Mathematics | Heat Transfer, Combustion | Mechanical Engineering | Theory and Algorithms


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