No abstract

Using the two-dimensional Fourier transform and the elementary theory of distributions, we solve the heat-conduction problem for shells with a system of diathermanous cuts. We take account of heat exchange according to Newton's law on the lateral surfaces of the shells. For a spherical shell urith two cuts of identical length we carry out numerical studies of the influence of the thermophysical properties of one cut on the jump in temperature of the adjacent cut. Three figures. Bibliography: 6 titles Kit and Krivtsun [1] have solved the heat-conduction problem for a plane with a system of diathermanous cuts, and the first author and V. P. Shevchenko [2] have solved it for a shell with one diathermanous cut.In the present paper we use the results of [2] to solve the heat-conduction problem for a shell with a system of diathermanous cuts.Consider a thin isotropic shell of thickness 2h referred to an orthogonal coordinate system xi (i = 1, 2, 3) directed respectively along the lines of principal curvature of the middle surface of the shell and along the normal to that surface. The shell is weakened by a system of N diathermanous cuts and is 'in thermal contact with the surrounding medium. The heat equations that take account of convective heat exchange according to Newton's law have the following form [3]: