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• Transient analysis code is developed and validated for heat-pipe-cooled reactor system. • Multi-node thermal resistance network coupling closed-form solution is setup for heat pipe heat transfer analysis. • Safety analysis is performed on KRUSTY under three postulated accidents. The heat pipe cooled reactor is a type of nuclear reactor system that utilizes heat pipe technology for core cooling. It characterizes in high reliability, compactness and modularity, making it suitable for deep-space exploration, and other applications. To gain a deeper understanding of the system's dynamic behavior and evaluate its performance, a transient analysis code is developed with the reactor point kinetics model, core heat transfer model, improved heat pipe startup and operation models, and Stirling engine model established. The reliability and accuracy of the models and code are validated by comparing the simulation results of the various models with experimental data based on heat pipe startup, operation experiments and KRUSTY test results. The safety limits are developed for the KRUSTY and this paper conducts the transient analysis on KRUSTY and evaluates the safety performance of KRUSTY in accidents including the unexpected shutdown of the Stirling engine, reactivity insertion accident (RIA), and combined partial Stirling engine failure and RIA accidents. KRUSTY shows good thermal stability and controllability under hypothetical accident conditions where no safety limit is exceeded. [ABSTRACT FROM AUTHOR]