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Carbon fibers can be considered cylindrically orthotropic. Depending on the arrangement of basal planes, predominant configurations are circumferential and radial, but in the core of the fiber, the alignment is undetectable, and consequently it is considered as transversely isotropic. In composites reinforced with these types of fibers, the effective thermal conductivity transverse to the fiber direction will be affected by the core and by the thermal resistance between the fiber and the matrix. The analytical models available are not adequate because they assume that the fiber is totally homogeneous. In this paper, a model of finite elements is presented, which allows combination of the effects of core with the cylindrical orthotropic of the fiber and the thermal contact resistance between the fiber and the matrix. The effective conductivity of composites with orthotropic and inhomogeneous fibers are compared to those with orthotropic and homogeneous fibers. This allows evaluation of the effect for the different morphology of the fibers. The model reveals a significant effect for radially orthotropic fibers (pitch-based). The model also contributes to a better understanding of the heat flux paths in cylindrically orthotropic and inhomogeneous fibers. Finally, this numerical simulation can be of interest first, in the microstructural studies focused on the relationship between the transverse thermal conductivity of carbon fibers and some microstructural parameters, and secondly, in the studies designed to estimate the interfacial contact resistance.

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Sequential methods that use future times in order to solve an inverse heat conduction problem can be re-formulated as a sequential digital filter algorithm. The aim of this paper is to explore the filter effect of the function specification method and the truncated singular value decomposition method, in a sequential form. For this purpose, the power spectral densities of the corresponding filter coefficients are evaluated and it is shown that they act as band-pass filter. Three numerical tests with different frequency spectra are considered in order to solve a linear one-dimensional transient inverse problem. Furthermore, three models of crescent complexity are used in each method. It is shown that both methods provide similar results and in most cases, the optimum estimations require the same number of future times. As it is expected, similar estimations correspond to a similar band-pass filter. The effect of the number of future times, the influence of the frequency spectrum of the input and the complexity of the model used can be clearly interpreted in the spectral space. The most complex models act as a highly selective band-pass filter, but they require greater number of future times. 555 design problems, for example, the identification of the boundary shape of a domain subject to natural convection from temperature measurements on the other boundary [5]. The IHCP is a clear example of an ill-posed problem [1]. The main difficulty of this type of problem is the instability. From a mathematical point of view, the algebraic formulation of IHCP leads to an ill-conditioned problem, so that a small perturbation in the measured data (due to the unavoidable measurement errors) may cause great oscillations in the estimated function. This difficulty (from a physical point of view) is a consequence of the diffusive nature of heat flow, so that the thermal response at some distance of the boundary is damped and lagged with respect to the active input at the boundary [1]. In order to add stability at the solution of the inverse problem, many and different methods have been reported to solve IHCPs. Among the more versatile methods (applicable to solve multidimensional and non-linear IHCP) the following can be mentioned: Tikhonov regularization [6], iterative regularization [7], mollification [8] and the function specification method (FSM) [1]. The first two methods are considered as 'whole domain' because all the measured temperature data (N ) are used in order to estimate simultaneously all the components of the unknown input. In these methods, the sensitivity matrix can be of great dimensions (N × N ). In contrast, the last two methods are sequential. Therefore, only a small part of the available measurement is used in each step and only one component of the unknown input is estimated at each step. This fact can be an advantage in an online process. A considerable number of contributions have been published considering combinations, modifications and comparisons of the previous methods [9][10][11][12][13][14].Another ...

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