This research paper is undertaken to simulate the combustion of gaseous hydrogen and gaseous oxygen for a transient case, and analyze the axial wall heat flux. The model utilized in the study is the Penn State preburner combustor, also known as the rocket combustion modeling test case RCM-1, which features a single coaxial injector. The simulation was carried out in a two-dimensional (2D) axisymmetric computational domain with a combustion chamber pressure of 5.2 MPa. The flow in the combustion chamber is turbulent and was modeled using unsteady Reynolds-averaged Navier–Stokes (URANS) based on two-equation eddy viscosity model and steady laminar flamelet model which was used to model the turbulent non-premixed flame. ANSYS commercial computational fluid dynamics software was used for the simulations, and the results acquired from the study were consistent with experimental data.