Stationary heat conduction in a macro- and microperiodically layered solid

Summary This paper deals with the stationary heat conduction in a solid consisting of planar, isotropic or transversely isotropic layers. The following cases are considered: (1) arbitrarily layered solid, (2) macroperiodically layered solid, consisting of equal pairs of different basic layers with finite thicknesses, (3) microperiodically layered solid, consisting of equal layer groups of two or more different basic layers of infinitesimal thicknesses. Assuming a perfect contact between the layers, exact solutions for the plane, the axisymmetric and the general three-dimensional problem of macro- and microperiodically layered semispaces, respectively, are derived using integral transforms and the transfer-matrix method. It is proved that the microperiodically layered solid with isotropic or transversely isotropic basic layers is equivalent to a homogeneous transversely isotropic solid. Received 31 March 1999; accepted for publication 21 May 1999