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Hydrodynamics and heat transfer in film flows along solid surfaces are analyzed by numerical simulation. The current version of the Kolmogorov-Prandtl turbulence model is used to obtain a compact mathematical description focused on engineering applications in power engineering and other heat technologies. Film flows with recirculation are studied as special modes of condensing (or evaporative) devices of power plants. Other possible applications are the problems of evaporative cooling, problems of hydraulic roughness of technical surfaces, technologies of thin-film materials and – in the field of large linear scales - modeling of some natural catastrophic phenomena, such as mudflows. The mathematical description is presented as a system of three ordinary first-order nonlinear differential equations - for distributions of turbulent energy, turbulent energy flux density, flow velocity. The phenomena of laminar – turbulent transition and special modes of “flooding” of the flow are diagnosed. Temperature distributions are calculated and heat fluxes are determined. The Reynolds number of the film and the Stanton number are presented as functions of two dimensionless determining parameters specifying the film thickness and the ratio of the friction stresses at the boundaries.