A new utility approach that is independent of the rheological model is presented for the flow of non-Newtonian fluids in concentric annulus. The novel model was developed without assuming that the generalised flow index remains constant over all shear rate ranges. Based on the slot model, the flow rate expressions for all common rheological models flowing in annuli were obtained, such as the Herschel-Bulkley model, the Robertson-Stiff model, and the Four-parameter model, and they all can be solved numerically to obtain accurate wall shear rate and shear stress. Following Metzner and Reed's study, we defined a generalised flow index for non-Newtonian fluid flow in annuli. Through a theoretical analysis, we also defined a new effective diameter for non-Newtonian fluid flow in annuli, which accounts for the effects both of annulus geometry and fluid rheology but which is different from that was proposed by Reed and Pilehvari. Through the generalised effective diameter we linked non-Newtonian annular flow with Newtonian pipe flow. A general annular Reynolds number expression was derived from this method for conditions under which the generalised flow index is variable. A theoretical calculation method for the generalised flow index and a uniform pressure loss calculation model for non-Newtonian flow in concentric annuli were developed, which are applicable to all time-independent non-Newtonian fluid. The predictions of this model have been compared with an extensive set of data from the literature. The comparisons of different fluids in different size annuli show very good agreement over the entire range of flow types.