## 1 Introduction  
Heat pipes are highly efficient heat transfer devices, functioning on the principles of fluid phase transition and thermal conduction. They come in various geometries and sizes, typically in the form of sealed tubular devices filled with a specific type and amount of working fluid. The fluid undergoes vaporisation at the evaporator section, which is in contact with a heat source. Using the pressure generated by temperature differences, the vapour travels to the condenser, where it releases its latent heat to a cold source. The fluid then condenses back into liquid form and is passively pumped by the Wick structure back to the evaporator through capillary action. This combination of liquid and vapour phases enables extremely efficient heat transfer. Since heat pipes are closed-circuit systems, they operate continuously. Heat pipes exhibit non-linear performance and require modelling encompassing heat transfer, fluid flow, and thermodynamics. These devices find wide applications in the aerospace industry, whether as individual heat pipes [1], pulse oscillating heat pipes [2], or loop heat pipes [3; 4]. The advantage of loop heat pipes over standard heat pipes lies in their ability to dissipate substantial heat power over long distances without any loss in performance. Heat switches (HS) are devices designed to regulate heat conduction within specific temperature ranges, typically from 0.05 K to nearly 400 K [5]. Heat switch technology finds important applications in \"vibration-free\" sorption compressors used in cryogenic Joule-Thompson coolers [5]. These advanced cooling systems are employed in space and ground scientific missions, such as Planck [6], Metis [7], and other Earth observation infrared missions [8; 9; 10]. The incorporation of heat switches in these systems ensures reliable performance by eliminating disruptive vibrations, leading to enhanced accuracy and precision in scientific measurements. Among the various heat switch technologies, the gas-gap heat switch (GGHS) [5; 8; 11; 12; 13; 14; 15; 16; 17; 18; 19] is most commonly used. A recent developed sorption compressor system, part of the vibration-free cryogenic cooler project at Nova University (Portugal), as referenced in [9; 10], has implemented a gas-gap heat switch that did not meet performance expectations. Unexpectedly long periods of both cooling and heating were observed due to higher thermal conductance in the elements between the sorption cell and the cooling source. This discrepancy is likely attributed to the OFF state of the gas-gap heat switch, which is almost three times higher than expected [10]. The design requirements for this cryogenic cooler unit included maintaining an evaporator temperature (cold tip) at 80 K, achieving a cooling power between 1 W and 1.5 W and fitting the system within a volume of 0.2 m\({}^{3}\). The cooler system comprises four adsorption cells, each containing 600 m of active medium made of HKUST-1, and a set of valves that regulate gas flow. After the compressed refrigerant gas exits the compression unit, it undergoes cooling through the heat exchanger. Subsequently, during its expansion through a Joule-Thomson valve, the refrigerant absorbs heat from the device being cooled. The adsorption cells of the compressor operate within the temperature range of 150 K to 400 K. Electric heaters and heat sinks are employed for heating and cooling the cells, respectively. Heat switches are used to establish thermal contact between these heated sorption cells and the heat sink (cold plate at 150 K). The OFF state of the switch is activated when heating the cell for gas desorption (compression), while the ON state is employed when the aim is gas adsorption during expansion, allowing heat dissipation into the cold source (heat sink). The malfunctioning gas-gap heat switch has been identified as a contributing factor, leading to undesired extended cycle duration and increased heating power requirements for the sorption cell.