Open AccessGeneralized functions in non-linear thermal conductivity problem for two-layer structure with heat source
Author(s) -
G. V. Mikheeva
Publication year - 2021
Publication title -
journal of physics. conference series
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.21
H-Index - 85
eISSN - 1742-6596
pISSN - 1742-6588
DOI - 10.1088/1742-6596/1889/2/022025
Subject(s) - heaviside step function , thermal conductivity , mathematical analysis , mathematics , piecewise linear function , boundary value problem , piecewise , function (biology) , boundary layer , physics , thermodynamics , evolutionary biology , biology
Based on the generalized functions theory an exact analytical solution to the stationary non-linear problem of thermal conductivity for two-layer plate with heat sources for the asymmetrical Newton’s limiting conditions. Dependence of thermal conductivity factors of each layer on the temperature was assumed to be linear. The problem for a two-layer structure, using the Heaviside asymmetric unit function, is normalized to a single-layer one with piecewise homogeneous (discontinuous) properties of the medium. The advantage of this method for obtaining analytical solutions is that there is no need to directly fulfill the conjugation conditions at the layers’ contact points, since, thanks to the use of the Heaviside function, they are included in the generalized differential equation of the boundary value problem and are fulfilled in the process of obtaining its solution. A specific example of calculating the temperature state of a two-layer plate is provided.