The mathematical modeling of transport of Reynolds shear stress, sub layers of turbulence fluid flow and viscous incompressible fluid flow would be the subject of this thesis. A generalized wall function proposed Shih et al (1999), it accounts the effect of pressure gradients on the flow near the wall. Theory shows that the effect of pressure gradients on the flow in the inertial sub layer is very significant and the standard wall function should be replaced by a generalized wall function.

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... the theory is also valid for boundary layer flows toward separation, the generalized wall function may be applied to complex turbulent flows with acceleration, deceleration and separation. This paper would try to introduce about Reynolds number, viscosity, parameters of turbulence fluid flows and also sub boundary layer of turbulence. This thesis would be ends with a comprehensive lists of boundary conditions associated with the Navier –stokes equation.