On thermic exposure of piezo-thermoelastic plates

We consider a plate infinite in extent, bounded by two parallel planes, filled by a heat-conducting piezoelectric material with hexagonal symmetry. It is completely coated by electrodes which are infinitesimally thin, so that all their mechanical effects may be ignored. On the lower face the displacement is prescribed, as when e.g. the panel is welded above a fixed rigid body, and on the upper face the stress vanishes. We study quasi-static processes controlled by a thermic exposure on the upper plane, which varies very slowly with the time, e.g. solar exposure. The difference of electric potential between the two bounding planes is computed in terms of the temperature on the upper face.