Rapid Mission Planning for Aircraft Thermal Management

Differential equations are derived based on the principles of the conservation of mass and energy for an aircraft that recirculates fuel through heat exchangers to manage heat loads. Several of these differential equations are solved analytically for special cases that arise over major segments of the aircraft mission. The resulting algebraic equations can be solved sequentially to estimate the temperature of the fuel at points of interest in the system. Each differential equation solution represents the transition of the temperature states over intervals of time where mass flow and heating rates are constant. These algebraic equations are expected to be useful for rapidly computing solutions to aircraft thermal management planning problems as they eliminate the need for numerical integration over over the corresponding mission segments. Planning problems are therefore transformed from difficult boundary value problems involving differential equations to nonlinear root finding problems involving algebraic equations. An example planning problem is solved to demonstrate the viability of the approach.