The Beam Dump Facility (BDF) is a new fixed target facility proposed to be installed in the North Area of CERN. Currently in its design phase, the BDF is aimed at the Search for Hidden Particles (SHiP) experiment, which purpose is to investigate the origin of dark matter and other lightly interacting particles. The BDF target/dump sits at the core of the installation, and its aim is to fully absorb the high intensity Super Proton Synchrotron (SPS) beam and produce charmed mesons. The average beam power on target is 305 kw due to which very high thermo-mechanical loads will be generated on the target/dump configuration which can lead to mechanical failure of the target material. This calls for continuous cooling and heat removal from the target material, which requires the design and optimization of a very complex cooling system to ensure the target reliability during operation. Keeping in view the high velocities that are obtained in the channels of the cooling system of the target assembly, an extensive 3D turbulence modeling of the full scale cooling system is required in order to predict the target water cooling system behavior. A comparative conjugate heat transfer (CHT) study using a simplified 2D geometry of the BDF target for different mesh size was performed for identical y+ values to validate the pressure drop in the cooling channels and the temperature profile in the target blocks with the analytical calculations. Subsequently, a 3D model of the cooling channel was simulated for different Reynolds number and an extensive study was performed to check the behaviour of the flow in the log-law layer. In addition to that the friction factor was validated with the analytical results and with the available literature for various Reynolds number. Thereafter a full scale 3D steady and transient model was simulated using the information obtained from the previous studies. All these simulations were carried out in Ansys Fluent. The energy deposition in space on the target blocks was obtained via FLUKA MonteCarlo simulations. The variation of HTC in different channels and the fluid-solid interface temperature is found out to be in accordance with the analytical calculations. The pressure drop and the temperature rise from inlet to outlet of the cooling system is also in confirmation with the design parameters. Transient simulations were performed subsequently in order to study the impact of time and space varying energy deposition in the target blocks on the overall flow. With the given inlet velocity, the boiling at the surface of the target blocks is not expected to happen. As a final part of this study, in order to make the numerical model more robust, a mesh sensitivity analysis was done in order to optimize the mesh size, especially in the boundary layer region.