Numerical study of laminar wall jet with transpiration and moving wall

Laminar wall jet is a unidirectional flow without any pressure gradient and is driven by its own momentum. This paper represents this phenomenon for two important cases-stationary wall without transpiration and moving wall with transpiration. Continuity and momentum equations have been developed for these two conditions. Similar to Glauerts theory, similarity transformation has been applied to find out the governing equation, a third order ordinary differential equation. Shooting method is applied to find out the proper boundary condition to solve the governing equation. Finally, an algorithm for 4th order Runge Kutta method has been augmented to find out the solution using MATLAB. As the jet moves forward in the case of a stationary wall without any transpiration, the maximum velocity, which is slightly greater than 0.4 m/s, occurs at a distance from the wall. The velocity curve for this case does not show any rapid change in the flow. But for the second case (moving wall with transpiration), the maximum velocity is obtained near the wall surface which is slightly greater than the wall velocity, 1.13 m/s. As the jet proceeds, due to suction, the velocity decreases rapidly. Again, the dominance of suction force forces the transverse velocity to achieve a lower value in the second case rather than in first case. The flow physics behind these scenarios is studied in detail in this work and is discussed for a range of operating conditions.