To study and develop wall-functions for modeling of near-wall turbulent flows, a linear model equation is introduced. This equation simulates major mathematical peculiarities of the low-Reynolds-number model including a near wall sub-layer and transition region. Dirichlet and Newman boundary-value problems are considered. The standard and analytical wall-functions are investigated on different properties including the mesh sensitivity of a solution. A Robin-type interpretation of wall-functions as boundary conditions is suggested. It is shown that solution of a problem is mesh independent and more accurate in this case. General type analytical and numerical wall-functions are developed on the basis of a boundary condition transfer. An effective numerical method of decomposition is suggested. The method can be used in application to either high-Reynolds-number models with the numerical wall-functions or low-Reynolds-number models directly. Although a model equation is considered, the formulas, methods and conclusions are valid and can be directly used for the Reynolds Averaged Navier-Stokes (RANS) equations.