A 3-D finite element algorithm, with incorporated explicit pipe-like elements, is developed to solve the coupled time-dependent heat transport and fluid flow differential equations and yield the internal temperature and fluid velocity fields for TAG-like mounds. A range of models with permeable and impermeable upper boundaries and different thermal conductivities are investigated. The solutions have three common features: a central high-temperature zone which coincides with a non-magnetic zone inferred from magnetic data; fluid upflow along the vertical high-permeability column, surrounding a central pipe; and a maximum fluid velocity of the order of the observed maximum value at the central black smokers. Thermal conductivity variations strongly influence the temperature distribution but not the fluid velocity pattern. ¿ American Geophysical Union 1996