A One-Dimensional Model of Hydrodynamics and Heat Transfer in a Film Flow on a Permeable Surface

The problem of friction and heat transfer in a laminar, transition, or turbulent flow along solid permeable surfaces has been solved using a numerical simulation technique. To derive a compact mathematical description intended for engineering applications in the power industry and other thermal processes, a modern version of the Kolmogorov–Prandtl model with one differential equation (namely, the turbulent kinetic energy conservation equation) was employed. The mathematical model is represented by a system of first-order nonlinear ordinary differential equations for the distributions of flow velocity, friction stress, temperature, turbulent energy, and turbulent energy flux density across the film thickness. The problem of singularity of the mathematical description on a solid wall is discussed. The integral hydrodynamic and thermal characteristics of film flows currently receiving a lot of interest, such as the film Reynolds number and the Stanton number, were obtained. Functional correlations among dimensionless parameters that are relevant for engineering applications, including those for special regimes of film flows with recirculation and mass crossflow on permeable surfaces of structural materials, have been established. The film Reynolds and Stanton numbers are defined as functions of dimensionless parameters at which the relative values of the film thickness, acting forces, and mass crossflow are specified. The obtained correlations can be used in the design and optimization of condensation and steam-generating facilities in the power industry, for elaboration of evaporative coolers for high-stress structural elements in gas turbine and rocket equipment, simulation of hydraulic roughness, and in thin-film materials technologies.