Study on Jeffery–Hamel nano-fluid flow with uncertain volume fraction using semi-analytical approach

This study examines the flow of a Jeffery–Hamel nanofluid between two rigid, non-parallel plane walls forming an angle of 2ω. An extension of the classical Jeffery–Hamel flow problem is investigated by incorporating the effects of nanoparticle volume fraction and various parameters on the velocity distribution. The volume fraction of nanoparticles is treated as an uncertain parameter, modeled as a triangular fuzzy number (TFN) ranging between 0.0% and 0.2%. To analyze the velocity distribution under both precise and fuzzy conditions at different channel positions, as well as under varying velocity constraints at other positions within the channel, a novel homotopy analysis method (HAM) is introduced along with its convergence analysis. Finally, the obtained results are validated to assess the efficiency of the proposed approach, and numerical outcomes are compared with the available data under crisp conditions.