Variational methods\ bounds and size e}ects for two!phase composites with coupled heat and mass transport processes at the two!phase interface

New variational principles are developed for the e}ective heat conductivity tensor of aniso! tropic two!phase composites in the presence of coupled mass and heat transport processes at the two!phase interface[ We focus on physical situations where an imposed temperature gradient causes impurities or lattice defects to concentrate on the two!phase interface and di}use along it[ This is accompanied by the release and absorption of heat as the impurities\ respectively\ enter or leave the interface[ We investigate the e}ect of the inclusion geometry on the overall thermal conductivity[ For randomly distributed inclusions new size e}ects are given in terms of the inclusion size distribution and nearest neighbor distribution function for the included phase[ Þ 0888 Elsevier Science Ltd[ All rights reserved[ Keywords] A[ Di}usion^ Bulk^ B[ Ceramic material^ C[ Variational calculus