heat conduction

A BRIEF OVERVIEW OF STATIONARY TWO-DIMENSIONAL THERMOELASTIC STATE MODELS IN HOMOGENEOUS AND PIECEWISE-HOMOGENEOUS BODIES WITH CRACKS

Purpose. A two-dimensional mathematical model of the problem of thermo-elasticity for piecewise-homogeneous component plate containing a crack has been built. The stress intensity coefficients in the vertices of the crack increase affecting strength of the body significantly. This leads to the growth of a crack and, as a result, to further local destruction of a material. Therefore, such a model reflects, to some extent, the destruction mechanism of the elements of engineering structures with cracks.

Mathematical modeling of stationary thermoelastic state in a half plane containing an inclusion and a crack due to local heating by a heat flux

The two-dimensional stationary problems of heat conduction and  thermoelasticity for a semi-infinite elastic body containing an inclusion and a crack  are  considered.  For this purpose, mathematical models of these  two-dimensional problems in the form of a system of singular integral equations (SIEs) of the first and the second kinds are constructed.  The numerical solution of the system of integral equations in the case of a half plane  containing an inclusion and thermally insulated crack due to local heating by a heat flux is obtained using the method of mechanical quadratures.  We pre

Modelling of temperature conditions in electrical devices of inhomogeneous structure

Mathematical modelling of heat exchange processes for an electric device of inhomogeneous structure and the analytical numerical estimate of the relevant boundary problem of heat conduction have been considered.