Parametric low-order models in transient heat diffusion by MIM. Estimation of thermal conductivity in a 2D slab

Abstract

Classical modeling methods based on spatial discretization of local governing equations lead to fine meshes, resulting in large size models which require huge computing times. In applications such as on-line inverse or real-time feedback control problems, this issue becomes crucial. Several techniques have been developed for building low-order models, involving a smaller set of equations and able to reproduce the thermal behavior of a reference large-size model or an actual system, whatever the time-varying boundary conditions and/or heat source terms, or for a range of values of a thermophysical parameter. But low-order models able to mimic heat transfer dynamics for both a time-varying thermal load and a physical parameter range are not frequently encountered. Such a problem is addressed here, through an extension of the Modal Identification Method. The approach is illustrated on a simple linear 2D transient heat diffusion problem, with a time-varying heat flux density applied on one side and a thermal conductivity in the 15 to 45 W.m -1.K-1 range. The low-order model is used for the estimation of the thermal conductivity from the knowledge of both the applied heat flux and a simulated transient temperature measurement on the opposite side. The approach remains valid for 3D cases in complex geometries involving more independent thermal loads. © Published under licence by IOP Publishing Ltd.