In the paper, the flow in a coaxial pipe with a shifted central cylinder is investigated. Optimization of flows in circular pipes is an important and interesting problem. Such tubes are used, for example, in ground heat exchangers. The volume flux dependence from the diameter of the central cylinder and its position in the pipe at a constant pressure gradient, and from deformation of the outer wall is investigated. We found that displacement of inner conduit from the center of pipe was the cause of increased volume flux. R-functions method allows us to construct an exact region boundary equation for the region where we want to find the solution of the boundary problem. This area can be divided into several sub-areas, the boundaries of which are defined by elementary functions. We construct the equation of original region boundary from these subregions by the logical operations: R-conjunction, R-disjunction, and others. Next, the solution structure must be constructed, which approximate the solution of the differential equation and exactly satisfies the boundary conditions. The proposed method is more suitable for flow optimization by comparison with the finite element method, as it does not require the creation of grid for each case of pipe geometry, deformations of the channel is produced continuously. The presented method allows us to place more than one inner elements into a pipe and proposes complex geometry boundaries.