Abstract: This study investigates the conceptual core design of a megawatt-class compact heat pipe reactor (HPR), targeting enhanced performance and safety for mobile and space-based applications. The reactor leverages the passive heat transfer capability of sodium heat pipes within a molybdenum-rhenium alloy matrix to achieve efficient cooling without active pumping systems, thereby significantly improving system compactness, reliability, and safety margins. The main objective is to propose a core design that minimizes size and weight, with a total core mass of less than 2 t and a volume of less than 1 m³, while ensuring long-term operation exceeding 15 a at a thermal power around 1 MW. The core physics calculations were conducted using the open-source Monte Carlo neutron transport code OpenMC, with nuclear data library JEFF3.3. Reflector material selection was systematically evaluated based on neutron reflection efficiency and material density, leading to the adoption of beryllium oxide as the primary reflector layer due to its favorable nuclear and thermo-mechanical properties in high-temperature environments. Radial fuel enrichment zoning was employed in a three-region layout (73%, 55%, and 19.75% ²³⁵U) to flatten the radial power distribution and reduce the power peak factor below 1.35, thereby mitigating fuel thermal stress risks. Reactivity control was achieved through a combination of sliding reflector layers composed of stainless steel and beryllium oxide, along with control rods featuring boron carbide and beryllium oxide neutron absorbers. These systems provide sufficient reactivity worth (6 705 pcm for sliding reflectors and 7 698 pcm for control rods) to enable effective shutdown and compensation during normal and transient operating states. Thermal-hydraulic performance was analyzed using finite element modeling in COMSOL, integrating the spatial power distributions from core physics to evaluate steady-state temperature fields. Results reveal maximum fuel temperatures remain below 1 543 K, satisfying design limits even when accounting for thermal expansion and corresponding porosity changes, with axial thermal expansion displacement exceeding radial expansion due to core geometry. Hot spots identified in the heat pipe gap regions exhibit temperature elevations approximately 40 K higher than adjacent fuel rods but remained within acceptable margins. Neutronic feedback calculations confirm the presence of inherently negative Doppler effects, contributing to natural safety characteristics of the design. Burnup simulations indicate the core maintains criticality with k_eff above 1 over the intended 15 a lifespan without control rod insertion, demonstrating strong fuel utilization and long-term operational feasibility. Thermal-mechanical coupling is essential for accurate peak temperature prediction, revealing a moderate increase compared to pure thermal analysis. The identified non-uniform power distribution (hot spots) in fuel rods near heat pipe interstices and the significant axial thermal expansion require specific engineering solutions in detailed design. This core design provides a valuable reference for developing high-power, transportable HPR systems.