Velocity and temperature similarity solutions of wedge flow laminar boundary layer with wall injection

The mathematical model of the wedge flow laminar boundary layer with wall injection boundary was established. Based on this model, the similarity solutions of dimensionless velocity and temperature distribution in the laminar boundary layer were obtained by solving the ordinary differential equations of the dimensionless stream function and dimensionless temperature. The ordinary differential equations were derived through similarity transformation from the partial differential equations describing the flow and heat transfer of wedge flow laminar boundary layer with wall injection. The curve fitting of dimensionless stream function derived takes into account the wall injection effect of cooling gas. The Runge-Kutta method was used to solve the ordinary differential equations of dimensionless stream function and dimensionless temperature in order to analyze the variations in the dimensionless velocity and temperature distributions in the wedge flow laminar boundary layer with wall injection with changes in wedge angle, blowing parameter, and cooling medium temperature. The results of the dimensionless velocity and temperature similarity solutions in the laminar boundary layer of wedge flows with wedge angles of 0°, 18° and 36° show that both the velocity boundary layer thickness and temperature boundary layer thickness of the laminar wedge flows with wall injection enlarge with the increase of blowing parameter and reduce with the increase of wedge angle; the boundary layer temperature gradient near the wall is larger with lower cooling media temperatures, smaller blowing parameters, and larger wedge angles.