Geodesic
Determination of the heat flux density in the region of the contact line during evaporation of a liquid into a bubble
Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 95-111

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The article describes a method for determining the heat flux density on the surface of a thin foil that is inaccessible for thermal imaging measurements according to thermal imaging data from the other side of the foil available for measurements. Mathematically, the problem is reduced to solving the Cauchy problem for an elliptic equation, which is ill-posed. The problem is solved using noise smoothing in the initial temperature field and the correct limit on the number of expansion terms in the Fourier series. According to the measurement results, the heat flux density reaches its maximum in the area of the contact line and amounts to 4200 W/m$^2$.
Keywords: ill-posed problem, Cauchy problem, heat equation, heat flux density, contact line. 
@article{SJIM_2023_26_3_a7,
     author = {N. E. Sibiryakov and D. Yu. Kochkin and O. A. Kabov and A. L. Karchevsky},
     title = {Determination of the heat flux density in the region of the contact line during evaporation of a liquid into a bubble},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {95--111},
     publisher = {mathdoc},
     volume = {26},
     number = {3},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a7/}
}
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N. E. Sibiryakov; D. Yu. Kochkin; O. A. Kabov; A. L. Karchevsky. Determination of the heat flux density in the region of the contact line during evaporation of a liquid into a bubble. Sibirskij žurnal industrialʹnoj matematiki, Tome 26 (2023) no. 3, pp. 95-111. http://geodesic.mathdoc.fr/item/SJIM_2023_26_3_a7/