The variations in the dimensionless velocity due to changes in similarity variables of wedge flows with different wedge angles were obtained using the Runge-Kutta method by solving the third-order nonlinear ordinary differential equation of the dimensionless stream function that was obtained through similarity transformation

which described the wedge flow in the laminar boundary layer. The second-order linear homogeneous differential equation of dimensionless temperature based on the similarity variable in the laminar boundary layer of the subsonic wedge flow and the second-order linear non-homogeneous differential equation of dimensionless temperature on the similarity variable in the laminar boundary layer of the supersonic wedge flow were derived. The general temperature distribution solutions in the laminar boundary layers of subsonic and supersonic wedge flow

the similarity solutions and exponential form approximation solutions of dimensionless temperature in the laminar boundary layers under the condition of constant wall temperature for subsonic wedge flow and the condition of adiabatic wall for supersonic wedge flow were obtained by solving the above two differential equations. The effects of compressibility and viscosity of the supersonic gas in the laminar boundary layer on velocity and temperature were investigated using the wedge flow of wedge angle of 0 as a representative example. It is shown that the maximum absolute value of relative errors between the similarity solution obtained under the condition of incompressible and constant properties and the similarity solution obtained under the condition of compressible and variable properties is less than 9.8%. Results show that: the larger the Pr of the wedge flow

the more dramatic the change in dimensionless temperature in the area close to the wall; the viscous dissipation causes the temperature of the wedge flow from the wall to the main flow in the boundary layer to first increase and then decrease under supersonic flow conditions and with temperatures lower than the adiabatic wall temperature.