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The Phase-1 upgrade of the LHC to full design luminosity, planned for 2019 at CERN, requires the modernisation of the experiments around the accelerator. The Inner Tracking System (ITS), the innermost detector at the ALICE experiment, will be upgraded by replacing the current apparatus by new silicon pixels arranged in 7 cylindrical layers. Each layer is composed by multiple independent modules, named staves, which provide mechanical support and cooling to the chips. This thesis aims to develop and validate experimentally an ultra-lightweight cooling system for the ITS Upgrade. The moderate thermal requirements, with a nominal power density of 0.15 W/cm^2 and a maximum chip temperature of 30°C, are counterweighted by extreme low-mass restrictions, obliging to resort to lightweight, non-metallic materials, such as carbon fibre-reinforced polymers and plastics. Novel lightweight stave concepts were developed and experimentally validated, meeting thermal requirements with minimal material inventory. The proposed staves are made of thin, layered, composite high thermal conductivity carbon fibre plates, with dimensions up to 1502 × 30 mm, and innovative polyimide cooling channels, with inner diameters (IDs) ranging from 1.024 mm to 2.667 mm and thin walls. Six different stave layouts were tested with water at sub-atmospheric pressure (leak-less cooling), showing excellent cooling performances: the temperature differences between the heated surfaces and the coolant are below 7 K at 0.15 W/cm^2, with low temperature gradients. Cooling tests with evaporative C4F10 refrigerant were performed on the baseline stave prototypes, yielding similar thermal performance as with water. This indicates that the thermal resistance of conduction in the stave dominates over the convective one between the channel wall and the coolant. A two-phase coolant would display low material inventory thanks to the presence of the vapour phase, lighter than liquid. An experimental study on the two-phase coolant inventory was carried out in one stave. The results are compared with void fraction prediction methods integrated along the cooling channel length, to find the best one for calculating the material budget of the two-phase coolant. An experimental study on the two-phase pressure drop and flow boiling heat transfer in a 2.689 mm ID water-heated polyimide channel was performed, using R245fa as operating fluid. Mass fluxes ranging from 100 to 500 kg/(m^2 s^1), heat fluxes from 15 to 55 kW/m^2, vapour qualities between 0.05 and 0.80, and saturation temperatures of 35, 41 and 47°C were considered in the 300-point experimental database. The influence of the two-phase flow parameters on the mean heat transfer coefficient was analysed parametrically, being its lack of dependence on the heat flux the major finding. Finally, the results were compared with other experimental data and with prediction methods in the literature.