On heat conduction in a semi-infinite laminated layer. Comparative results for two approaches

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

“…where A, B, C, D are unknowns, which should be determined from boundary conditions (15), (17), (19) and (20). Satisfying these boundary conditions by " h I ðn; zÞ given in (28) and " h II ðn; zÞ given in (29) we obtain four linear algebraic equations for unknowns A, B, C, D and the solution takes the form…”

“…The boundary conditions are satisfied exactly, the equation of heat conduction with the periodically pice-wice constant coefficients is replaced by the equation with constant coefficients. The analysis of accuracy of the model were investigated in papers (Kulchytsky-Zhyhailo and Matysiak [18,19], Matysiak and Perkowski [20]), where the satisfactory consistency of the results obtained within the framework of homogenized model with microlocal …”

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

“…Therefore, the homogenized model with microlocal parameters [1,2] will be employed in order to seek an approximate solutions. We next recall only a brief outline of governing relations of this model; for a more detailed treatment see the papers [1][2][3][4][5][6][13][14][15].…”

“…[3]). The results obtained within the framework of the homogenized model were compared with the solutions of the classical heat condition in [4][5][6], where good consistencies of temperature and heat fluxes within the both approaches for some problems of semi-infinite layer have been stated.…”

“…In the both cases the lower surface is kept at zero temperature and the upper surface is kept at a known temperature dependent on the radius. The above formulated problems are solved within the framework of the homogenized model with microlocal parameter [1][2][3][4][5][6] and by using the Weber-Orr integral transforms suitable for the considered boundary value problems. These transforms were introduced firstly by Weber and Orr; however, the exact proofs of the forms of inverse transforms and the transform properties were presented in refs.…”