Published on: 2026-07-09
Source: Peter the Great St. Petersburg Polytechnic University –
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A team of scientists from Russia and Belarus conducted a joint computational and experimental study of free-convective heat transfer in air cooling units consisting of bundles of horizontal finned tubes. The researchers evaluated how the spacing between the tubes and edge effects influence the structure of the air flow and the intensity of heat removal in a mode where cooling occurs without fans — solely due to the natural rise of heated air. The results supported by a grant Russian Science Foundation, studies that will potentially improve the efficiency of heat exchangers at the design stage, have been published in a high-impact international journal Applied Thermal Engineering.
Air cooling devices surround us everywhere — from large industrial installations and power plants to household appliances. Their task is to remove excess heat from the heated medium and transfer it to the surrounding air. Most often, the cooled medium passes through pipes with external fins: many thin plates multiply the surface area from which heat is removed, similar to the ribs on a car or motorcycle radiator. Usually, the pipes are blown with air forcibly using fans. This is the most productive, but also the most uneconomical mode: it requires electricity, creates noise, and needs constant monitoring to avoid emergency situations. In passive cooling mode, no forced fan draft is required; natural convection occurs because heated air is lighter than cold air and rises upwards. This mode is silent, environmentally friendly, and consumes almost no energy, but at the same time has a lower heat transfer intensity.
The effectiveness of passive cooling is directly influenced by the geometry of the surface: how closely the tubes are arranged in the bundle, the fin spacing, and how the bundle is oriented relative to the direction of gravity. To find the optimal shape of the cooling surface, scientists from Peter the Great St. Petersburg Polytechnic University and the A.V. Lykov Institute of Heat and Mass Transfer of the National Academy of Sciences of Belarus conducted a joint computational-experimental study of free convection and heat exchange in air cooling apparatus. For the three-dimensional computational model of a single-row bundle of six finned tubes, the full equations of motion and heat transfer for the air were solved, which allowed them to “look” inside the bundle in a way that is extremely difficult to achieve in a real experiment.
It was found that an unsteady thermal plume forms above a densely packed bundle: large-scale fluctuations of the airflow develop, causing the heat removal to vary over time within 20% of the average. Scientists calculated the necessary and sufficient distance between the cooling system pipes, at which the thermal plume forms locally above each pipe, and a further increase in distance does not affect the overall cooling efficiency. Moreover, boundary effects were evaluated. It turned out that with a tight packing of the bundle, the difference in heat removal from different pipes can exceed 20%.
In industry, heat exchangers often have to switch to natural convection mode — for example, when the main forcing equipment fails — and it is important here to know in advance how to achieve maximum efficiency from passive cooling, — explains the project leader, Candidate of Physical and Mathematical Sciences, Associate Professor at SPbPU Marina Zasimova. — In essence, we are creating a digital twin of the heat exchanger: numerical simulation allows us to see the details of the flow and heat transfer that are almost impossible to measure directly. Our research shows that under certain conditions, simple geometric modifications can increase heat removal by more than 30% — which means the economic efficiency of the device grows by about the same amount.
Another important methodological outcome of the work is the justification that for such problems, one cannot be limited to the classic Boussinesq approximation, which is widely used in modeling natural convection. With large temperature differences between the pipe surface and the surrounding air, this approximation introduces significant errors; therefore, it is correct to consider the air here as a compressible gas with variable physical properties. The validity of the model is confirmed by comparison with experimental data from Belarusian colleagues.
The published article is just one of the results of a large-scale international project supported by a grant from the Russian Science Foundation No. 24-49-10003 within the framework of the joint competition of the RSF and the Belarusian Republican Foundation for Fundamental Research (BRFFI). The project is dedicated to creating the scientific foundations for designing energy-efficient air-cooled heat exchangers operating under dominant free convection effects and unites two strong research teams.
The computational part is conducted by the hydrodynamics laboratory of the Physical-Mechanical Institute of SPbPU: the scientific director of the laboratory is Professor, Doctor of Physical and Mathematical Sciences Evgeny Smirnov, a well-known specialist in the field of fluid, gas, and plasma mechanics; the application of machine learning methods is handled by Associate Professor, Candidate of Physical and Mathematical Sciences Alexey Abramov. The experimental part is carried out by a group of young researchers from Minsk under the leadership of Candidate of Technical Sciences Galina Marshalova, head of the Department of Energy Saving, Hydraulics, and Heat Engineering at the Belarusian State Technological University, and research associate at the A. V. Lykov Institute of Heat and Mass Transfer of the National Academy of Sciences of Belarus. According to the researchers, it is precisely such close collaboration between computational scientists and experimentalists that became the key to success: this is a rare opportunity to obtain reliable, thoroughly documented empirical data for the validation of numerical models.
Multivariate calculations that allowed obtaining several thousand solutions for various sets of defining parameters were carried out using the resources of the Polytechnic Supercomputing Center. The accumulated data formed the basis of a separate branch of the project: using machine learning methods, the team is searching for universal relationships linking heat transfer intensity with the operational and geometric parameters of the apparatus. For free convection regimes, such universal formulas still do not exist, and their search is one of the fundamental tasks of the project.
The results of the work are regularly tested at all-Russian and international conferences. Recently, the project performers presented three reports at the 18th Minsk International Forum on Heat and Mass Transfer — one of the largest specialized scientific events. Also, the project leader Marina Zasimova delivered a report at the Tomsk International Energy Forum and plans to present the results at the large-scale heat and mass transfer conference IHTC (International Heat Transfer Conference), which is held every four years and will take place this year in Rio de Janeiro (Brazil).
Ahead for the team is a new stage: the search for unconventional ways to intensify heat exchange in passive devices, including through targeted destabilization of flow and the addition of vortex generators that create secondary flows near heat transfer surfaces.
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