This paper presents a new analytical solution to investigate the mechanism of transient confined-unconfined flow in a confined aquifer induced by pumping with a large rate during mine drainage. The study focuses on understanding the impact of non-Darcian effect on flow towards a fully penetrated pumping well. The nonlinear relationship between specific discharge and the hydraulic gradient is described using Izbash's equation. A novel approximate method is developed to linearize the mathematical model, and the solution is derived using the Boltzmann transform. The proposed solution is validated by comparing it with previous works. The findings indicate that increased non-Darcian index, quasi-hydraulic conductivity, and specific storage have negatively affect the development of the unconfined region and aquifer drawdown, as greater turbulence flow accelerates recharge to the pumping well. Drawdown is found to be sensitive to the non-Darcian index, quasi-hydraulic conductivity, while it is unaffected by specific yield and specific storage. The conclusions provide valuable insights for mine drainage and the application of geological and hydrological conditions.