Two-sided thermal resistance estimates for heat transfer through an anisotropic solid of complex shape

Two-sided estimate of effective thermal conductivity coefficients of a textured composite with anisotropic ellipsoidal inclusions

“…To take into account the texture of the composite and the anisotropy of the inclusions, it is necessary to consider for each main axis OX ν of the tensor with the main value Λ ν the cylindrical region V with bases perpendicular to this axis, and to use for each of these regions the dual variational formulation of the stationary thermal conductivity problem [6,9], which includes both the minimized functional…”

“…The subsequent averaging of components of such a tensor over the entire set of spatial orientations of inclusions, which determines the texture of the considered composite, makes it possible to calculate the desired values of the effective thermal conductivity coefficients of this composite. The reliability of the obtained results and the possible error of calculations can be determined by means of two-sided estimates based on the dual variational formulation of the problem of stationary thermal conductivity in an inhomogeneous body [6][7][8][9].…”

Development of the method of approximate solution to the nonstationary problem on heat transfer through a flat wall

“…In paper [6], mathematical model of the heat transfer process is based on the variational approach. Heat transfer through the anisotropic body is investigated, which is interesting.…”

“…Heat transfer through the anisotropic body is investigated, which is interesting. However, [6] solves a stationary problem. In article [7], authors examine nonstationary heat transfer in a recuperative heat exchanger.…”

“…Heat flow from one part to another part of the plate is not transferred through this cross-section. Therefore, the model for each of the parts is composed only of a preservation equation (6) and the boundary condition of the third kind at the surface of the plate (7). For the case of nonstationary heat transfer, the pattern is different.…”