A combined numerical-experimental framework for the characterisation of heat-flux sensors in vacuum

Heat-flux sensors are employed in a variety of applications, including spacecraft thermal control and energy systems, where their performance is strongly dependent on operating conditions. When manufacturer calibration data are unavailable, limited, or not representative of the actual operating environment, in-house setup-specific characterisation becomes necessary. In this work, high vacuum p 10 − 4 mbar is adopted as a controlled experimental condition to suppress gas-phase heat transfer, simplify the energy balance, and support the reconstruction of the net heat flux incident on the sensor. A combined experimental–numerical approach is proposed for the static characterisation of thin-film heat-flux sensors, in which a dedicated experimental setup promotes predominantly one-dimensional heat flow across the sensor and a validated finite-element model quantifies residual conductive and radiative losses within the assembly. The resulting voltage–heat-flux characteristic exhibits stable and linear behaviour over the investigated operating range, yielding C t = 2.14 μ V W − 1 m 2 . A dedicated metrological uncertainty analysis, combining Type A regression uncertainty, GUM-based propagation of the reconstructed heat-flux uncertainty, and Monte Carlo propagation to the calibration slope, resulted in an expanded uncertainty of approximately ± 0.03 μ V W − 1 m 2 . The obtained C t is about 7% higher than the manufacturer-reported calibration constant, consistently with the expected increase associated with the transition from nominal/air calibration conditions to high-vacuum operation. The comparison with a simplified analytical loss-estimation approach confirms the importance of accurately resolving setup-specific parasitic losses in low-heat-flux measurements. Overall, the proposed methodology provides a practical and physically consistent framework for the in-house characterisation of thin-film heat-flux sensors.