Nonlinear Boundary-Value Problem of Heat Conduction for a Layered Plate with Inclusion

Mathematical Modelling of Stationary Thermoelastic State for a Plate with Periodic System of Inclusions and Cracks

“…By satisfying the boundary conditions (1) and (2) with the help of the complex temperature potential (7), we obtain in the heat conduction problem the system of N SIEs of the first and second kinds for the unknown functions ( )( = 1, ) on the contours of inclusions and ′ ( ) ( = + 1, ) on the contours of cracks:…”

“…Using the method of generalised integral transforms, the problem reduces to the solution of an SIE with a Cauchy kernel (Rashidova and Sobol, 2017). Local frictional heating of surface of a layered plate with inclusion was investigated in Havrysh (2017Havrysh ( , 2015.…”

Research into non-stationary temperature field in the protected metallic structure under conditions of fire

“…Paper [9] considered a nonlinear boundary problem of thermal conductivity for an isotropic infinite thermosensitive layered plate with thermally insulated face surfaces and a foreign through heat-producing inclusion. By applying the proposed transform, a partial linearization was performed of the original heat conductivity equation; a numerical-analytical solution to this equation was found with boundary conditions of the second kind using an integral Fourier transform.…”