## 2 Experimental Setup  
An experimental setup is currently being designed at CEA Cadarache. This setup involves a specific test section that will allow (i) a direct visualization of the boiling flow using the same technique as the one used by [PERSON] [4] (shadowgraphy), but also (ii) a characterization of the temperature field from the wet side of the heated plate, similar to [PERSON]'s work [6]. Nevertheless, in order to account for the representativeness of the heating surface, we considered a metallic plate (stainless steel) instead of metallic coating as [PERSON] proposed [6], i.e., a plate whose thickness needs to be determined. Figures 3 and 4 depict a schematic of the future test section and its measurement systems. Three sapphire windows will allow direct visualization of the bubbles created along the heated plate, which will be soldered on a fourth sapphire window to retain the fluid pressure. The metallic plate will be heated by the direct Joule effect. The temperature of the heated plate will be measured on its external face (dry side \(T_{dry}\)) using an infra-red camera and the temperature of the wet side of the plate \(T_{wet}\) will be deduced from the dry temperature by solving the heat diffusion equation within the plate (see Figure 5). The wet temperature may be useful to analyze the data collected by shadowgraphy through the sapphire windows. Indeed, as mentioned before, due to the thermal gradients in the vicinity of the heated wall ([4,8]), pictures obtained by shadowgraphy can be distorted, making the identification of the bubble detachment time, as a consequence the bubble lift-off diameter, difficult. It is believed that thermal imaging will be helpful as the bubble detachment should correspond to a local variation of the temperature field on the wet side of the heated plate. As an illustration, one can cite the recent work of [PERSON] and [PERSON] [9], who calculated the temperature profile as a function of time under a nucleation site. Figure 6 describes the prototypical behavior of the wall temperature beneath a nucleation site as a function of time. Figure 4: Operating measurement principles. Figure 5: Schematic diagram of IR thermography measurements and thermal conductive problem. Figure 3: The 3D schematic of the future test section. The heated element is drawn in red: The heated length L \(\approx 5\times 10^{-1}\) m, heated width l \(\approx 1\times 10^{-2}\) m, and thickness of the metallic plate are to be determined. One can observe two distinct stages. First, while the bubble is still attached to its nucleation site and is growing, the temperature decreases because of the vaporization. Then, the bubble detaches from the heated wall at \(t_{g}\) (called the growing time), and the temperature increases until a new bubble begins to grow on the nucleation site. \(t_{w}\) is called the waiting time. Thermal imaging may help us to identify the time when the bubble effectively detaches from the wall (\(t_{g}\)). Determining the plate thickness should then result in a compromise. On the one hand, the thickness should be large enough to ensure good representativeness of the heating surface and boiling; on the other hand, the thickness should be thin enough to allow for accurate determining of the temperature on the wet side of the heating plate. Figure 5 depicts the problem to be solved. As a preliminary step, assuming that the plate thickness will be much lower than the other characteristic dimensions of the heater, a one-dimensional approach will be considered. By solving the diffusion equation within the plate for a given set of boundary conditions, it is possible to determine the wet temperature \(T_{wet}\). In the experimental configuration, all of the measurements will be performed on the external side. So the boundary conditions will be expressed on the same face (dry side of the plate). The associated heat conduction problem is then an inverse problem where the major characteristic is an ill-posed problem (from a mathematical point of view).