A considerable amount of the evaporation originates from the close vicinity the three-phase contact line in an evaporating extended meniscus due to the low thermal resistance across the ultra thin film. Evaporation taking place within the thin film region is commonly modeled using the uni-directional flow assumption of the liquid following the lubrication approximation. Although the uni-directional flow based models may yield practically reasonable results in terms of the cumulative quantities such as total evaporation rate, the underlying physics of the problem cannot be explained solely by uni-directional flow, especially when the dominant transverse liquid motion is considered near the close proximity of the contact line. The present study develops a solution methodology to enable the solution of steady, incompressible, 2-D conservation of mass and linear momentum equations for the liquid flow in an evaporating thin film. Solution methodology includes the coupling of an uni-directional solver with high precision numerics, a higher order bi-directional spectral element solver and a finite element solver. The novelty of the present study is that steady, 2-D conservation of mass and linear momentum equations are considered in the modeling of thin film evaporation without the exclusion of any terms in the conservation equations. (C) 2017 Elsevier Masson SAS. All rights reserved.