Fiber-based devices with advanced functionalities are emerging as promising solutions for various applications in flexible electronics and bioengineering. Multimaterial thermal drawing, in particular, has attracted strong interest for its ability to generate fibers with complex architectures. Thus far, however, the understanding of its fluid dynamics has only been applied to single material preforms for which higher order effects, such as the radial dependency of the axial velocity, could be neglected. With complex multimaterial preforms, such effects must be taken into account, as they can affect the architecture and the functional properties of the resulting fiber device. Here, we propose a versatile model of the thermal drawing of fibers, which takes into account a radially varying axial velocity. Unlike the commonly used cross section averaged approach, our model is capable of predicting radial variations of functional properties caused by the deformation during drawing. This is demonstrated for two effects observed, namely, by unraveling the deformation of initially straight, transversal lines in the preform and the dependence on the draw ratio and radial position of the in-fiber electrical conductivity of polymer nanocomposites, an important class of materials for emerging fiber devices. This work sets a thus far missing theoretical and practical understanding of multimaterial fiber processing to better engineer advanced fibers and textiles for sensing, health care, robotics, or bioengineering applications.