Two mathematical models (a one-dimensional (1D) and a two-dimensional (2D)) were adopted to study, numerically, the thermal-hydrodynamic characteristics of flow inside the cooling channels of a nuclear thermal rocket (NTR) engine. In the present study, only one of the cooling channels of the reactor core is simulated. The 1D model adopted here assumes the flow in this cooling channel to be unsteady, compressible, turbulent, and subsonic. The governing equations of the compressible flow in the cooling channel are discretized using a second-order accurate (MacCormack) finite-difference scheme. The steady-state results of the proposed model were compared to the predictions by a commercial CFD code. The 2D CFD solution was obtained in two domains: the coolant (gaseous hydrogen) and the ZrC fuel cladding. The wall heat flux which varied along the channel length (as described by the nuclear variation in the nuclear power generation) was given as an input. Numerical experiments were carried out using both codes to simulate the thermal and hydrodynamic characteristics of the flow inside a single-cooling channel of the reactor for a typical Nuclear Engine for Rocket Vehicle Application (NERVA)-type NTR engine. It is concluded that both models predict successfully the steady-state axial distributions of temperature, pressure, density, and velocity of gaseous hydrogen flow in the NTR cooling channel.