The objective of this paper is to introduce applications of Bayesian filters to state estimation problems in heat transfer. A brief description of state estimation problems within the Bayesian framework is presented. The Kalman filter, as well as the following algorithms of the particle filter: sampling importance resampling and auxiliary sampling importance resampling, are discussed and applied to practical problems in heat transfer.
The analytical thermal quadrupole method is suitable for the modeling of multidimensional transient heat diffusion in homogeneous media, especially when applied to multilayered media. Here, we propose a new approach in order to extend the quadrupole frame to heterogeneous media. A seminumerical general solution is proposed for transient heat transfer in finite or semi-infinite media in both axial and radial coordinate systems, when the variation of thermal properties is one-dimensional. The presentation of the method is explained with a 2-D two-layer slab case. Some application examples are then presented from this basic case. The analytical expressions allow deep insight about the physical phenomenon.
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