Dynamic response of non-homogeneous 1-D slab under periodic thermal excitation

The periodic heat conduction in a non-homogeneous slab is studied and an approximate analytic solution, valid for weakly non homogeneous slabs, is found. An exact solution for a well defined non-homogeneity is also
found and compared to the approximate solution to estimate the accuracy of the result. The solution allows to extend the method of thermal quadrupoles to weakly non-homogeneous 1D-slabs.