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We investigate the properties of a kinematic flux transport solar dynamo model. The model is characterized by a solar-like internal differential rotation profile, a single-cell meridional flow in the convective envelope that is directed poleward at the surface, and a magnetic diffusivity that is constant within the envelope but decreases sharply at the core-envelope interface. As in earlier flux transport models of the Babcock-Leighton type, we assume that the poloidal field is regenerated as a consequence of the emergence at the surface, and subsequent decay, of bipolar active regions exhibiting a systematic tilt with respect to the east-west direction. Inspired by recent simulations of the rise of toroidal magnetic flux ropes across the solar convective envelope, we model this poloidal field regeneration mechanism as a nonlocal source term formulated in such a way as to account for some of the properties of rising flux ropes revealed by the simulations. For a broad range of parameter values the model leads to solar cycle-like oscillatory solutions. Because of the solar-like internal differential rotation profile used in the model, solutions tend to be characterized by time-latitude (butterfly) diagrams that exhibit both poleward- and equatorward-propagating branches. We demonstrate that the latitudinal shear in the envelope, often omitted in other flux transport models previously published in the literature, actually has a dominant effect on the global morphology and period of the solutions, while the radial shear near the core-envelope interface leads to further intensification of the toroidal field. On the basis of an extensive parameter space study, we establish a scaling law between the time period of the cycle and the primary parameters of the model, namely the meridional flow speed, source coefficient, and turbulent diffusion coefficient. In the parameter regime expected to characterize the Sun, we show that the time period of the cycle is most significantly influenced by the circulation flow speed and, unlike for conventional mean field αΩ dynamos, is little affected by the magnitude of the source coefficient. Finally, we present one specific solution that exhibits features that compare advantageously with the observed properties of the solar cycle.