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 mechanism of heat transfer intensification recently brought about by nanofluids is analyzed in this article, in the light of the non-Fourier dual-phase-lagging heat conduction model. The physical problem involves an annular geometry filled with a nanofluid, such as typically used for measurements of the thermal conductivity with Blackwell's line heat source probe. The mathematical formulation for this problem is analytically solved with the classical integral transform technique, thus providing benchmark results for the temperature predicted with the dual-phase-lagging model. Different test cases are examined in this work, involving nanofluids and probe sizes of practical interest. The effects of the relaxation times on the temperature at the surface of the probe are also examined. The results obtained with the dualphase-lagging model are critically compared to those obtained with the classical parabolic model, showing that the increase in the thermal conductivity of nanofluids measured with the line heat source probe cannot be attributed to hyperbolic effects.

In this research, the thermal diffusivity of composites based on ethylenevinyl acetate (EVA) copolymer filled with two kinds of reinforcement graphite materials was investigated. The reinforcement graphite fillers were untreated natural graphite (UG) and expanded graphite (EG). Composite samples up to 29.3 % graphite particle volumetric concentrations (50 % mass concentration) were prepared by the meltmixing process in a Brabender Plasticorder. Upon mixing, the EG exfoliates in these films having nanosized thicknesses as evidenced by TEM micrographs. Thus, the thermal diffusivity and electrical conductivity of composites based on the ethylene-vinyl acetate matrix filled with nanostructuralized expanded graphite and standard, microsized graphite were investigated. From the experimental results it was deduced that the electrical conductivity was not only a function of filler concentration, but also strongly dependent on the graphite structure. The percolation concentration of the filler was found to be (15 to 17) vol% for micro-sized natural graphite, whereas the percolation concentration of the filler in nanocomposites filled with expanded graphite was much lower, about (5 to 6) vol%. The electrical conductivity of nanocomposites was also much higher than the electrical conductivity of composites filled with micro-sized filler at similar concentrations. Similarly, the values of the thermal diffusivity for the nanocomposites, EG-filled EVA, were significantly higher than the thermal diffusivity of the composites filled with micro-sized filler, UG-filled EVA, at similar concentrations. For 29.3 % graphite particle volumetric concentrations, the thermal diffusivity

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