The objective of this report is to examine the steady, transient, and start-up behavior of heat pipes as well as a transient analysis related to a thermal energy storage module. A detailed experimental and numerical analysis of low temperature heat pipes with multiple heat sources is also performed. The performance of a thermal energy module is simulated numerically. The change of phase of the phase-change material (PCM) and transient forced convective heat transfer for the transfer fluid with a low Prandtl number are solved simultaneously as a conjugate problem. The start-up process of a frozen heat pipe is described and a complete model for the start-up of the frozen heat pipe is developed based on the existing experimental data, which is simplified and solved numerically. Finally, a unique and efficient transient two-dimensional compressible analysis of high temperature heat pipes with a pulsed heat input is given. Keywords: Heat pipes; Phase changes; Reactor start up sources; Storage modules; Mathematical models. (cp)