Proceedings of the International scientific and practical conference ―Current Issues in Science‖ (January 9-11, 2026) / Publisher website: www.naukainfo.com. – Dresden, Germany, 2026. – 179 p.

150 were used. Here h – coefficient of contact thermal conductivity, indexes «1» та «2» correspond to first and second bodies, n – is normal to contact surface of bodies;  – corresponding coefficient of heat conductivity;  – Laplace‘s operator; с – corresponding heat capacity; Q – intensity of heat sources. Numerical analysis shows insignificant of influence of coefficient  on the distribution of heat fields in the friction couple, but coefficient of contact thermal conductivity coefficient of contact thermal conductivity has significant influence on its processes. Thus for practical computation we can recommend following simplified heat conditions on the contact area :               t Q t c n t n t         2 1 2 2 1 1 2     ,                     2 1 2 1 2 2 1 1 6 2 t t c t h t n t n t              . Solution of problem with these boundary conditions is the first step to obtaining of value h . For obtaining of influence of its parameters on the temperature and feat fluxes we consider non-stationary contact problem of thermoelasticity with heat generation after friction on the bound of two half-spaces. Mathematical model. Let assume that two elastic half-spaces with zero temperature are motionless first, and in the time moment 0   get closer and start movement with friction and relative constant velocity V . The process of friction on the contact limit is accompanied of heat generation, heat boundary conditions use the coefficient of contact thermal conductivity h . Mathematical problem consists of solving of equations of thermoelasticity       i i i i i x t x u       2 2 ,             i i i i t x a t 1 2 2 , with conditions:   0 0    i t , 2 1 x x    ,     const u u   2 1 ,         2 1 2 2 2 1 1 1 x x fV fV x t x t            ,