Inverse design of underfloor heating power rates and air-supply temperature for an aircraft cabin

• Inverse design of thermal boundary conditions.
• Combined inverse and forward modeling.
• Regularized matrix inversion for target indoor temperatures.
• Model validation with a self-conducted experimental test.

Thermal boundary conditions in commercial airliner cabins are crucial for creating a comfortable cabin environment. Cabin temperature distributions depend on the thermo-fluid boundary conditions of the boundary walls and the air supply. This paper proposed a combined inverse-forward model for designers to determine the total underfloor heating rates and the air-supply temperature in an aircraft cabin. The contribution ratio of indoor climate (CRI) is applied to describe the cause–effect relationship between the boundary wall convective heat release rates and the resulting temperature rise at certain points, which can be cast into a matrix. The solution contains three sub-models: (i) regularized inversion of the cause–effect matrix with the target cabin air temperatures as the known input, which solves the convective heat rates of the underfloor heaters and the air-supply temperature, (ii) solution of underfloor heater's surface temperatures based on Newton's law of cooling, and (iii) computation of the radiative heat rates. The above model was used to determine the total underfloor heating rates and air-supply temperature in a single-aisle aircraft cabin. The design targets are to create an average temperature of 24 °C near the upper human body and 26 °C at the ankle level. An experimental test was conducted in a simplified half section of an aircraft cabin for model validation. The results show that the proposed methodology is able to provide the total underfloor heating rates and air-supply temperature in good agreement with the measurement data and forward-simulation boundary conditions.