The Blasius boundary layer is a classical solution for the laminar flow over an isothermal flat plate. It provides an analytical expression for the velocity and temperature profiles within the boundary layer. The resulting compressible Blasius solution would provide expressions for the velocity, density, pressure, and temperature profiles within the compressible boundary layer. However, it's worth noting that obtaining an analytical solution for the compressible case is generally much more challenging compared to the incompressible case. The concept proposed used power law model and Sutherland’s viscosity model. The power law model uses a simple mathematical equation to relate shear stress and shear rate, which facilitates calculations and model implementation. The equation is of the form τ = K * γ^n, where τ is the shear stress, γ is the shear rate, K is the consistency index, and n is the flow behavior index. Sutherland's viscosity model allows for the extrapolation of viscosity data beyond the range of experimental measurements. This makes it particularly useful when dealing with extreme temperatures or when experimental data is limited. Proper treatment of boundary conditions is crucial in fluid dynamics simulations. The Runge-Kutta method requires appropriate handling of boundary conditions to ensure that the flow variables satisfy the prescribed conditions at the domain boundaries. The method also has limitations in terms of stability, accuracy, and computational cost, which need to be considered when selecting the appropriate numerical scheme. The overall mixed approach provides more accurate calculations related to fluid dynamics.