Contents
ThermoElectric Rayleigh-Bénard Instability
Scientific Context
The situation where a fluid is contained between two plates and heated from below has been extensively studied in the literature from more than a century. The Rayleigh-Bénard convection (RBC) has shown to be an adequate system for analysing features of fundamental interest, like e.g. turbulence patches, Eckhaus transition, phase diagram or more general dynamical systems behaviour.
Boundary Conditions & Feedback effects
In the classical approach, boundary conditions are generally considered to be ideal Dirichlet or Neumann, with fixed temperatures for both heat exchangers or a fixed temperature at the top and a fixed heat flux at the bottom. In other words, feedback effects from the working fluids are always considered to be negligible. However as expected, one can observe that local temperature i s increasing where the fluid is rising and decreases where the fluid is falling. It has also been shown (Belmonte 1993 PRL) that half of the total temperature difference occurs at the vicinity of the boundary layer and reconnects to the temperature of the bulk, which is almost constant. Consequently the temperature of the heat exchanger cannot be considered independent of time and space. The wall temperatures (i.e. at the wall conditions) are indeed function of the Dirichlet temperature, which is imposed far from the wall, and of the heat flux generated by RBC. Hence, RBC on its own is a good model to explore the general feedback effect of a system by exploring the spatio-temporal modulations of the wall temperature. Moreover, in the presence of charged particles in the bulk of the fluid, the coupling effect of a temperature difference is a voltage difference, namely the thermoelectric effect. One can also expect that the temperature difference, which leads to the RBC, and the modulations due to the feedback, can also generate a dynamical (spatio-temporal) voltage difference. Consequently, we shall examine a modified situation and consider a closed loop in a single system (feedback effects) with coupling between a dynamical flow (including heat and mass transfer) and a potential variation.
Work-in-progress
We would like to examine the three facets of the considered situation. Namely,
i) the experimental set-up, that involves to capture possibly very small temperature differences close to the wall;
ii) the direct simulation of the whole system (including a Conjugate Heat Transfer approach to the solid-fluid thermal exchange and a model for charged particles multi-component flow);
iii) the design of a reduced simplified semi-analytical toy model, able to mimic the main features of the behavior.
Participants
Eric Herbert, Yves D'Angelo, Christophe Goupil.