Asymptotic modelling and design of some microlayered functionally graded heat conductors

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Abstract

The paper presents a new method of modelling for certain microlayered heat conductors. So far the main attention related to the modelling of composite materials with deterministic structure was mainly restricted to the periodic composites (Bensoussan, Lions, and Papanicolaou [1]). The main future of the presented approach is that it can be also applied to the class with a non periodic structure. These structures can by referred to as functionally graded in the direction normal to the interfaces between layers. At the same time the non-homogenous material structure of the composite is slowly varying in this direction. That is why the obtained model equations have functionally but slowly varying coefficients. Moreover, this equations can by applied for designing functionally graded heat conductors with given a priori class of temperature fields.

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