ALL the domains considered so far have been unbounded, either in the spanwise direction (ch. 5); the vertical direction (ch. 7); or both (ch. 4). This is, of course, a serious practical limitation, since real enclosures must be bounded. In this chapter, I present some results for the difficult problem of nonisothermal vapour transport across bounded gas-filled enclosures. Only the low mass transfer rate limit is considered.