On the modelling of heat conduction problem in laminated bodies

On axisymmetric heat conduction problem for multilayer graded coated half-space

“…Another approach is using a homogenized model (Choi and Paulino, 2008;Diao, 1999) in which properties of the homogenized coating are determined on the base of properties of the components. Applying the homogenized model to the coating, we solve the boundary value problem described by the equation (Matysiak and Woźniak, 1987;Woźniak, 1987)…”

“…In the first of these approaches the layers are considered as separate continuous media. The second approach is based on the analysis of a homogenized uniform coating whose properties are determined on the basis of the material properties and geometric characteristics of the strip of periodicity (Matysiak and Woźniak, 1987;Woźniak, 1987). The solution obtained for the laminated half-space is compared with Kulchytsky-Zhyhailo and Matysiak (2005).…”

“…The boundary surface is heated by the given heat flux. In parallel, we obtain: 1) analytical solutions of the problems for the coating whose heat conductivity coefficient is described by a continuous function of the distance to the boundary surface; 2) the solution for the multilayered coating with a periodic structure which is described by a homogenized uniform layer (Matysiak and Woźniak, 1987;Woźniak, 1987). We analyze the difference between the temperature and heat flux in the non-homogeneous half-space caused by the use of two different models of nonuniform coatings.…”

Application of the method of generalized coupling problems in the thermoelasticity of piecewise-homogeneous bodies under nonideal contact

“…In particular cases, due to the structural peculiarities, the thermomechanical contact on the interface of such structures cannot be regarded as ideal, since the bonding of the homogeneous components admits sliding, but the friction on the interface comes about due to the presence of thin intermediate layers. The modeling of such piecewisehomogeneous bodies and methods of determining their thermoelastic state has been rather completely described in monographs and survey publications [3,4,11,13,15,17], and the results of corresponding studies published in [1,6,7,10,14,18,20]. We remark that the first thermal conditions on the frictional separation of two bodies under a contact interaction taking account of heat production were stated by F. Ling [17] In what follows the method of generalized coupling problems [5,12,16], which is based on the application of the machinery of distributions, is applied in the thermoelasticity of bodies of piecewise-homogeneous structure in nonideal thermomechanical contact on the interfaces.…”

Temperature distributions in a periodically stratified layer with a vertical dug well

“…Some effective approaches to the modeling of heat conduction problem in periodic composites are presented in papers of Aurialt [3], Bufler [4], Bufler and Meier [5]. One of the models is the homogenized model with microlocal parameters devised by Woźniak [2] and developed for microperiodic layered composites by Matysiak and Woźniak [1]. It is important that this model satisfies continuity conditions for temperature and heat fluxes on interfaces (the conditions of perfect thermal contact).…”