Nonlinear transmission conditions for thin curvilinear low-conductive interphases

Abstract

In this paper, we consider the heat transfer problem in a cylindrical composite material with an adhesive interphase of closed curvilinear shape. The interphase exhibits nonlinear behaviour and at the same time has physical characteristics (size, thermal conductivity) that significantly vary from the properties of the surrounding components. As the latter complicates the direct use of FEM, we use asymptotic method to replace the interphase with an imperfect interface of zero thickness, preserving the essential features of the thermal behaviour of the interphase through the evaluated transmission conditions. Carefully designed numerical simulations verify their validity. We place special emphasis on the impact of geometric properties of the interphase, in particular, the curvature of its boundaries, on the accuracy of the conditions.

Fractional heat conduction in solids connected by thin intermediate layer: nonperfect thermal contact

“…Institute of Mathematics and Computer Science, Jan Dlugosz University in Czestochowa, Czestochowa, Poland E-mail: j.povstenko@ajd.czest.pl T. Kyrylych Institute of Law, Administration and Management, Jan Dlugosz University in Czestochowa, Czestochowa, Poland transmission conditions including nonlinear effects [26,27] and thin interfaces with large curvature [28][29][30] still attract the attention of researchers.…”

Nonlinear transmission conditions for thin highly conductive interphases of curvilinear shape

“…For deriving the transmission conditions in this case, we follow our approach [3,2] of rescaling the interphase by means of rescaling its width:…”

“…More commonly, however, the interphase layer is represented in the model as an imperfect interface with a set of transmission conditions that simulate the physical behaviour of the original interphase [4,5,24,22,23,26,42]. Having developed this method for low-conductive curvilinear layers in [2,3], we moved on to apply a similar approach for the situation when the interphase is, contrarily, highly conductive [39]. Such a setting is similar to considering composites with stiff interphases [10,25].…”