During the last few decades, plasma actuators have emerged as promising devices for aerodynamic flow control. This study focuses on the use of nanosecond plasma actuators for such purposes. A thermal phenomenological model is employed to simulate the effects of these actuators. The propagation of shock waves and their interactions for two specific geometries of plasma actuators, linear and annular plasma synthetic jet actuators, are examined here. A comparative analysis of the performance of these two configurations is presented. Furthermore, the geometric characteristics and temperature model are analyzed to provide insights that can be applied to practical problems. The influence of the actuators on a projectile in the transonic flow is also investigated. The results of the present study show that actuators placed in the conical and cylindrical regions of the object do not contribute to drag reduction. Conversely, actuators positioned at the boat-tail and base of the object effectively reduce drag. This drag reduction is primarily attributed to thermal disturbances in the separation area. Additionally, it is observed that the effects of shock waves and their interaction with stationary waves around the projectile are negligible in terms of drag force reduction.