Applying multivariate inverse heat conduction problem to determine thermal contact resistance in aircraft embedded systems

Abstract

In the field of heat transfer, inverse problems deal with the estimation of parameters that are difficult to measure directly. The usefulness of inverse techniques is such that, due to severe conditions, direct measurement of a certain variable becomes inaccessible. This works aims to perform inverse estimation in two problems. The first case is related to the estimation of the heat flux boundary condition and thermal contact resistance between two SAE 1020 steel plates. The first case is used as validation for the second case and is solved using the finite volume method for the discretization of the diffusion equation and Successive Over Relaxation (SOR) for solving the system of linear eqs. A set of seven one-dimensional experiments were performed varying the roughness and contact pressure at the interface of the samples and, as expected, it was found that the thermal conductance is a function of these parameters. The second case consists in the estimation of three thermal resistances in an aircraft embedded system consisting of four components and ambient air. In this case, the direct problem is solved using fourth-order Runge-Kutta to solve the system of ODEs. In both cases a future times regularization technique approach combined with Markov Chain Monte Carlo (MCMC) optimization method is used to solve the inverse problem. The embedded system inverse problem is also solved using a new and simple approach based on the Quadrilateral Optimization Method (QOM) with future time steps regularization and the result is compared with the MCMC method. The results of this work consolidate a low-cost inverse estimation setup and attest to the capacity of multivariate estimation in inverse heat transfer problems.