Experiments with an annular thermoacoustic engine employing quasiadiabatic interaction between traveling acoustic waves and an inhomogeneously heated porous material indicate the presence of a closed-loop mass flux. A qualitative modeling of the enthalpy flux in the thermoacoustic core provides an opportunity to estimate the thermal convection associated with this mass flux, by using temperature measurement at different positions in the system. The estimated acoustically induced mass flux is in accordance with recent theoretical results.