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.

149 factors, thermophysical (thermal conductivity, specific heat, coefficient of linear expansion of bodies, etc.) and also mechanical ones (elasticity, hardness of contacting bodies, etc.) play an important role. The conditions of friction, wear and heat generation are also determined by the characteristics of the so-called ―third body‖, i.e., thin near-surface and intermediate layers, the physical and mechanical properties of which differ from those of the interacting bodies, and by the microgeometry of their surfaces in the contact zone [1, p. 1251]. Aim. Investigation and analysis of analytical solution of non-stationary contact problem of thermoelasticity with heat generation after friction on the bound of two half-spaces is an aim of the paper. The method of determination of thermal contact conductance in mathematical modelling of contact interaction with considering friction and hear generation by ―third body‖ is presented. Let assume that after-action and existence of burnishing zones and established work regime effects are consequence of changes in the ―third body‖. Besides, we must take into account of wear processes delayed effect in new contact zones in the solution of contact problems with wear. We use this model for plane contact problem of rectangular punch and elastic half-plane consideration in stationary statement, therefore wear is representative by linear function with time        Bt p x w x t A   , . Introduction of new function ―ageing‖ or ―forgetting‖ gives the opportunity to take account of difficult transformations and changes, which takes place in what is called ―third body‖ [2, p. 165]. Statement of problem. For investigation of contact thermoelasticity with taking account of friction and heatgeneration the generalized conditions of heat contact [3, p. 101].                     t Q c t n t n t t t 2 2 2 1 2 2 1 1 2 1                       ,                           2 1 2 1 2 2 1 1 2 1 12 2 t t c t h t n t n t t t                        ,