Interest of data Analysis in Transient Convective Heat Transfer and From Transient to Chaotic Behaviour in Convective Flows

J. Padet & F. Arinc

During the Symposium, two workshops were held. These were: "Interest of Data Analysis in Transient Convective Heat Transfer", and "From Transient to Chaotic Behaviour in Convective Flows. The first workshop was held following the lecture presented by Colette Padet. The second one concluded the meeting and was introduced by Roger Martin who presented an experimental investigation realized with a mixed convection flow of water in a horizontal pipe heated on a part of its length. In this experiment, irregular fluctuations of temperature occur on the pipe wall, which are due to chaotic structures appearing inside the flow. The ensuing discussions and the ideas expressed by A. Bejan, B.L. Bhatt, L. Estel, H. Herwig, R. Martin, J.K. Nieuwenhuizen, C. Padet, J. Padet, I. Pop, J.B. Saulnier, and A. Ungut are presented here.

During the discussions following the first workhop, all agreed that there is a strong need for reliable and physically clear (and as easy to handle as possible) packages of data analysis. For instance, in many practical applications, one may seek to identify a marginal effect in a complex transient phenomenon: usually, the trend that people is looking for is hidden within noise and other unrelated effects.

The comment on the idea of being able to extract information about the mean behaviour (B. Bhatt) was that it has relevance also to the two-phase flow phenomena. The stochastic fluctuations, inherent to any two-phase flow, interact with the system dominated time dependent phenomena as in externally imposed transients in the study of transient response characteristics.

Separation of scales is identified as another important problem, for instance, in turbulent unsteady flows. It was expressed that scales and trends are also needed in two-phase flows in order to improve the modeling of movements for the dilute phase. Nevertheless, a preliminary scale analysis gives a basic benefit since it places theory ahead of experiment. But, separation of scales based on data analysis is useful too for verification of a theory as well as for giving basic information when it is missing. So, the method proposed by Colette Padet and Jean-Marie Roche could be useful in such problems, and is complementary to the wavelet analysis approach which provides a similar information in the frequency domain. It would be interesting to extend the method to the two-dimensional analysis where there is a similar need.

As far as the second topic is concerned, dissipative or chaotic structures in fluids are generally investigated with stationary boundary conditions. But, it appears from the papers by S. Kakaš, R. Martin, A.A. Merrikh and L. Estel, that they can be generated, modified, or destroyed by time-dependent boundary conditions. Moreover, the question is strongly linked to the problem of scales and consequently to data analysis. For example, on the onset of Benard convection (or in other transient conditions) where convection can be associated with a comparison of time scales, the system opts for the shorter communication time across the fluid layer. Why should it be 'in a hurry!?

Another important question is to improve the precision of the relation of unstable and chaotic behaviours. All these problems offer a large field for further investigations.

It was noticed at last that multidisciplinary approaches, as illustrated by the meeting of data analysis and transient convective heat transfer, can be very fruitful and must be encouraged, despite the fact that publications on these topics are more difficult because they are often considered by the reviewers as "not enough mathematical" or "not enough physical papers". They serve at least one purpose which is an increased understanding of the fundamental phenomena or mechanisms.

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