<p>Topology optimization has been used to design fluid flow devices since its extension to fluid flow problems. One quite particular type of fluid flow device which can be quite challenging, due to inherently three-dimensional characteristics and rotational/stationary parts, are axial pump-type devices. Also, the complexity of the flow increases when considering a non-Newtonian fluid, which is largely present in food-related and blood flow applications. All of these pose an even larger issue when considering the highly flexible topology optimization method, highly increasing the computational effort, due to the additional computation of the adjoint model, the high quantity of design variable values (distributed over the whole mesh), and the multiple optimization iterations. Thus, a novel topology optimization formulation based on a 2D model is developed for the axial non-Newtonian pump-type design, considering a radial velocity profile assumption, and a translational movement-based frozen rotor. The objective function considers energy dissipation and pressure head, and the design variable is nodal. The optimization algorithm is an integer variable-based one (<i>Topology Optimization of Binary Structures</i>, TOBS), and the implementation is done in a finite element-based computing platform (FEniCS/dolfin-adjoint). Some numerical examples are presented for the novel formulation. This work aims to develop a viable approach to design an axial non-Newtonian pump-type device using topology optimization, offering a computationally efficient approach that balances energy dissipation and pressure head.</p>