Consideration of the nonlinear behavior of environmental material and a three-dimensional internal heat sources in mathematical modeling of heat conduction

Zhuravchak L. M., Kruk O. S.
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Abstract: 
A numerical-analytical method of determining the heat field in a finite solid with taking into account the dependence of the coefficients of heat conductivity and of heat release on the temperature and the intensity of internal heat sources is suggested. The effectiveness of the combination of indirect methods of boundary and near-boundary elements with Kirchhoff transformation for partial linearization of nonlinear 3D problems of heat conduction, by which the process is modelled, is substantiated.
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Math. Model. Comput. Vol.2, No.1, pp.107-1133 (2015)