Global Solutions to Rasmussen’s Problem by Homotopy Renormalization Method

In this study, we employ the homotopy renormalization (HTR) method to analytically investigate Rasmussen’s problem, which characterizes the viscous fluid motion between a pair of infinitely large, coaxially rotating disks. The original set of nonlinear ordinary differential equations is reformulated within a homotopy-based framework, allowing us to construct global asymptotic approximations with closed-form expressions. The HTR method overcomes the limitations of traditional perturbation and renormalization techniques, and avoids the need for asymptotic matching. In addition, the analytic expressions allow for direct estimation of flow parameters such as boundary layer thickness. These results demonstrate the effectiveness of the HTR method in asymptotic analysis and highlight its potential for broader applications in nonlinear fluid dynamics.