Boundary-value problem of heat conduction for a piecewise homogeneous layer with foreign inclusion

Abstract

By using distributions, we deduce the heat-conduction equation with discontinuous and singular coefficients for an isotropic piecewise homogeneous layer containing a foreign cylindrical inclusion with heat release. With help of a piecewise linear approximation of temperature on the boundary surfaces of the inclusion and the Hankel integral transformation, we construct the numerical-analytic solution of the boundary-value problem of heat conduction with heat transfer. We also perform the numerical analysis for the case of a three-element layer containing an inclusion in the middle element.