LAUSR

Abstract We investigate the thermal-electric-elastic fields around two circular holes in a thermoelectric material. Solutions describing electric, thermal and elastic fields are obtained via complex variable and numerical methods. Our results show that the presence of the holes has the same effect on the effective electric and thermal conductivities but no effect whatsoever on the effective Seebeck coefficient and consequently on the thermoelectric figure of merit. The maximum values of electric potential and temperature around one hole are increased by the presence of the second hole but decrease sharply as the distance between the two holes continues to increase. For two holes of equal size, the interaction effects on the corresponding electric and thermal fields are negligible when the distance between the holes is twice that of the common radius. In comparison to the thermoelectric field, the interaction effect on the stress field decreases much slower with the increase of distance, especially when the difference in the radii between the two holes is large. Numerical results show that the interaction effect on hoop stress between two holes of equal size is five times that of the corresponding effect on the temperature field and that the interaction effect is essentially negligible if one hole is more than twice the size of the other. It is worth pointing out that the two adjacent holes generate an extreme stress distribution in thermoelectric materials when the distance between the two holes is far less than the smaller of the two radii which is in stark contrast to the analogous case encountered in classical thermoelastic problems.