Taylor-Couette-Poiseuille (TCP) flow, a fundamental fluid dynamics model, characterizes the behavior of a viscous fluid confined between two relatively rotating cylinders. This model is widely utilized in engineering, such as the main helium circulator of high temperature gas-cooled reactors (HTGR), where rotating fluids are confined within narrow gaps (e.g., motor air gaps and shaft seals). Variations in gap width significantly influence the Taylor number( \(Ta\propto {\delta }^{3}\) ) and axial Reynold number, which directly affects the thermal and hydraulic performance, thereby influencing flow regime, frictional losses, and heat transfer. This study conducted numerical simulations incorporating linearly-varying gap width to investigate how different linearly gap-width configurations affect one rotating fluid system representative. Results show that reducing the gap width can raise the global Nusselt number by up to 19.2%, yet frictional losses may increase by as much as 67.8%. Further analysis indicates that changes in the axial Reynolds number have a more decisive effect than variations in the Taylor number, particularly under the reduction of the gap width. These findings underscore the need to balance geometric design and flow parameters for optimizing cooling performance in rotating machinery operating under Taylor-Couette-Poiseuille flow conditions.