## 1 Introduction  
Rotating detonation combustors represent a potential efficiency leap for gas turbine power plants [1]. This boost in efficiency is due to the pressure gain obtained through the detonation process, which leads to a more efficient thermal cycle. A rotating detonation combustor is characterized by an annular channel where combustible mixture is injected and ignited by a self-sustained spinning detonation front at supersonic speeds. However, practical implementation is currently constrained by important thermal management issues due to the high-speed flow and high temperature levels reached inside the combustor. The combustor walls are periodically swept by shock waves at several kilohertz, which results in extraordinary heat-flux levels that limit the operability of the combustor. Therefore, it is critical to perform a detailed analysis of the convective heat transfer and develop predictive tools that allow a preliminary design of the cooling system. To address this issue, we present a reduced-order model that predicts the convective heat transfer in a rotating detonation combustor (RDC) with a numerical approach that is three orders of magnitude faster than three-dimensional unsteady Reynolds-averaged solvers. RDCs have been experimentally tested, for example, in the US [2; 3; 4], Japan [5], Russia [6] and France [7]. The tests uncovered enormous heat-flux release threatening the integrity of the combustor and limiting its runtime to fractions of a second. The thermal optimization of these combustors is constrained by the availability of precise and time-effective thermal solvers that can evaluate the thermal performance in a timely manner. Currently, RDCs are numerically examined with computationally-expensive Euler [8; 9] or unsteady Reynolds-averaged Navier-Stokes solvers [10], where the injection process is either modeled as premixed mixture or as non-premixed flow. The detonation process can be modeled in several ways: using one-step reaction kinetics [11] with a limited number of species; or with two-step chemical reaction models [12]; or with an induction parameter which allows for larger grid size and time steps [13; 14; 15; 16]; or with detailed reaction kinetics [17] which lead to expensive computations. Due to the use of a coarse computational grid, most of the Navier-Stokes (URANS) simulations cannot resolve the boundary layer with sufficient accuracy to predict the actual convective heat-transfer level. Therefore, we need to develop time-efficient models that can provide a fast and accurate calculation of the heat-flux levels to allow a proper design of the necessary cooling strategies. [PERSON] and [PERSON] [18] presented a low-order analytical performance model to determine the range of design parameters on the performance of rocket-mode RDCs. [PERSON] and [PERSON] [19] presented a reduced-order model based on the two-dimensional method of characteristics (MOC) and the detonation conditions. Similarly, [PERSON] et al. [20] demonstrated via a reduced-order model based on a two-dimensional MOC that the system naturally evolves to a specific radius to detonation height ratio that minimizes entropy rise across the combustor. Regarding heat-transfer analysis, [PERSON] et al. [21] estimated the heat load within the RDC walls with unsteady conduction simulations using OpenFoam with periodic convective boundary conditions. [PERSON] et al. [22] developed a conjugate heat-transfer model within the same open-source flow solver. [PERSON] et al. [23] measured the heat flux within the walls of a RDC using high-frequency heat-flux gages and observed an almost constant heat flux along the axial position. In 2018, [PERSON] et al. [24] measured the instantaneous and bulk heat fluxes for several equivalence ratios with a twelve-sensor heat-flux gage array. This paper first evaluates the boundary layer in the RDC with URANS simulations.