Analytical heat transfer analysis for CMS support infrastructure in the Phase-2 Upgrade

This report presents an analytical modelling approach to estimate heat transfer across the Compact Muon Solenoid (CMS) subdetectors at the High-Luminosity Large Hadron Collider (HL-LHC). A thermal screen isolates the subdetectors at their respective operating temperatures, with active thermal control provided by an array of heater foil elements. The required power generation from the array is dependent on the heat flux at the outer surface of the Barrel Tracker Support Tube (BTST). A reduced order analysis was performed to estimate the heat flux in this location, with empirical and analytical models used to approximate the thermal behaviour of the BTST core. Including a 30% safety factor, empirical estimations exceed analytical counterparts by 13% and predict a maximum heat flux of 92 W/m^2. Previous approximations suggest 123 W/m^2 is suitable. The accuracy of empirical modelling results remains uncertain until test specifics are acquired from the core manufacturer. Minimal gas dependency is shown over the operating conditions.