We investigate the role of the 11 yr solar cycle variations in the solar wind (SW) parameters on the flows in the heliosheath using a new three-dimensional time-dependent model of the interaction between the SW and the interstellar medium. For boundary conditions in the model we use realistic time and the latitudinal dependence of the SW parameters obtained from SOHO/SWAN and interplanetary scintillation data for the last two solar cycles (1990-2011). This data set generally agrees with the in situ Ulysses measurements from 1991 to 2009. For the first ~30 AU of the heliosheath the time-dependent model predicts constant radial flow speeds at Voyager 2 (V2), which is consistent with observations and different from the steady models that show ...