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Available online xxx Keywords: Evaporated sessile drop Contact line Local heat flux Cauchy problem for elleptic equation a b s t r a c tThe study deals with the heat and mass transfer process near the dynamic three-phase liquidgas-solid contact line. The evaporating sessile water droplets on a horizontal heated constantan foil are studied experimentally. The temperature of the bottom foil surface is measured by an infrared scanner. To measure the heat flux density for the inaccessible part of the boundary by temperature measurements obtained for the accessible part, the well-known heated thin foil technique is applied. In contrast to the usual approach, the heat conductivity along the foil is taken into account. To determine the heat flux value in the boundary region, inaccessible for measurements, the problem of temperature field distribution in the foil is solved. From the point of mathematics, it is classified as the Cauchy problem for the elliptic equation. According to calculation results, the maximum heat flux density occurs in the region of the contact line and it surpasses the average heat flux from the entire foil surface by the factor of 5 − 7. The average heat flux density in the wetted zone exceeds the average heat flux density from the entire foil surface by the factor of 3 − 5. This is explained by heat inflow from the foil periphery to the droplet due to the relatively high heat conductivity coefficient of foil material, and high evaporation rate in the contact line zone.