This study conducts an investigation and feasibility study on different Reynolds numbers (6000-12000) and Rotation numbers (0.05-0.25) in a matrix cooling geometry. An intended geometry that can be used in gas turbine blades is provided based on flow and heat transfer performance given in these Reynolds and rotation number ranges for stationary and rotational state and then compared with experimental data. In this work, a 3D simulation method for each states (stationary and rotation) has been used for two layers matrix cooling with four inlets in each layer in a straight rectangular channel. The results indicate that among the common methods used in the trailing edge of a gas turbine blade, the matrix cooling method has heat transfer in stationary and rotary states $2-3 times higher than those of a smooth channel. Also results showed that rotation significantly affects heat transfer characteristics. Heat transfer increases in the pressure-side by a factor of 3 (at a Rotation number of 0.15 and Reynolds number 6000) which is an important property of rotation. According to the specific rotation direction chosen in this study, in comparison with previous studies, the pressure side and suction side location in stationary and rotation states are different and this results in lower decrease of heat transfer in the suction side for the rotation state. It is observed that using this structure increases the thermal performance about 30% by changing the flow behavior between stationary and rotary states.