In order to clarify the origin of the enhancement of the thermal conductivity in the Bose-Einstein Condensed (BEC) state of field-induced triplons, we have measured the thermal conductivity along the [101] direction parallel to spin-chains, $kappa_{|[101]}$, and perpendicular to spin-chains, $kappa_{perp[101]}$, of the S=1/2 bond-alternating spin-chain system Pb2V3O9 in magnetic fields up to 14 T. With increasing field at 3 K, it has been found that both $kappa_{|[101]}$ and $kappa_{perp[101]}$ are suppressed in the gapped normal state in low fields. In the BEC state of field-induced triplons in high fields, on the other hand, $kappa_{|[101]}$ is enhanced with increasing field, while $kappa_{perp[101]}$ is suppressed. That is, the thermal conductivity along the direction, where the magnetic interaction is strong, is markedly enhanced in the BEC state. Accordingly, our results suggest that the enhancement of $kappa_{|[101]}$ in the BEC state is caused by the enhancement of the thermal conductivity due to triplons on the basis of the two-fluid model, as in the case of the superfluid state of liquid 4He.
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