Axially symmetric problems of heat conduction in a periodically laminated layer with vertical cylindrical hole

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

“…The continuity conditions on the interfaces lead to some difficulty in analytical and numerical approaches. For small thickness of the fundamental lamina l with a comparison to the thickness of the nonhomogeneous layer h, l ( h it is suitable to use the homogenized model with microlocal parameters (see Woźniak [2], Matysiak and Perkowski [8]) to the approximated formulation of the considered problem. This model has been derived by using the non-standarard analysis combined with some a priori postulated assumptions.…”

“…The governing equations of the homogenized model with microlocal parameters in the stationary axisymmetric case take the form (Matysiak and Perkowski [8]):…”

“…The homogenized model with microlocal parameters was applied to solve many problems, which were partially reassumed in papers of Matysiak [6], Woźniak and Woźniak [7]. The problems of heat conduction in a periodically stratified layer with a vertical, cylindrical hole was considered by Matysiak and Perkowski [8]. In this paper, zero temperature or zero radial heat flux on the lateral surface of hole is assumed and the body is heated by given temperature on the upper boundary plane.…”

On Some Thermoelastic Problem of a Nonhomogeneous Long Pipe

“…Another approach to the problems of periodic body heat condition is a use of the homogenized model with microlocal parameters [17][18][19] or the application of the tolerance model [20,21]. The homogenized model with microlocal parameters is widely used to solve a number of problems for the composite bodies with periodic structure [22][23][24][25][26][27][28][29][30][31].…”

The normalized acoustic power of a thin clamped annular plate vibrating in a flat screen around a perpendicular semi-infinite circular cylinder

“…On the other hand, the Weber transform [32][33][34][35][36][37] is much more suitable for this case. It was originally presented by Titchmarsh and used to solve such problems as the heat conduction in a steel plate with a hole, or the wave equation in ice cover frozen to a cylindrical column submerged in seawater, and others [38][39][40][41][42]. The transform was used recently to find rigorously a solution of the problem of scattering and transmission of the incident flat acoustic wave on a circular aperture in a thick wall penetrated by a cylinder of radius being smaller than the radius of aperture [43].…”