On the problem of determining the separation point of the laminar boundary layer by the example of the Howart–Tani flow

A new approach is proposed how to calculate the laminar boundary layer in slow flows. It is based on describing the velocity profile using a polynomial of indefinite degree and on introducing two additional coordinate-dependent parameters, one of which defines the separation of the boundary layer from a wall once this parameter reaches zero. The approach based on three integral relations and reducing the problem to the system of three ordinary differential equations was further developed. A numerical analysis performed for the Howart–Tani flow showed that the separation point of a laminar boundary layer is determined highly exactly using this approach. It was shown that introducing into consideration certain restrictions for the outer surface of a boundary layer allows one to find the problem solutions which would adequately define and fairly exactly determine the flow velocity distribution within this layer, and at any point up to the point of its separation. The proposed numerical-analytical calculation method based on three integral relations and two additional parameters and involving the definition of the flow velocity profile by a polynomial of indefinite degree can be extended to other slow flows past smooth two-dimensional surfaces.