This paper proposes a new mathematical formulation describing the relationship between shear stress and film thickness to model condensing falling film of liquid in vertical thermosyphons. The mathematical model incorporates various factors, encompassing the contribution of shear stress resulting from friction force and phase change at the liquid-vapor interface, the impact of subcooling, and the influence of the convective boundary on film heat transfer. Vapor phase condensation in thermosyphons with relatively longer condenser lengths, where temperature variation is inevitable, is an area of interest for using the proposed model. The novel formulation is solved iteratively with the analytical solution of conservation equations, thermal equilibrium, and thermal resistance analogy. Optimized relaxation factors are used, and when the convergence criteria are met, the model marches over the condenser wall. The high accuracy of the model in regenerating literature data allowed the implementation of parametric study analyses on the variation of ambient air temperature, heat transfer coefficient, and wind velocity. The results are verified with a numerical model based on the modified Nusselt theory, and the underestimation of the latter approach in film thickness prediction and, consequently, heat flux has been discussed. The introduced model indicated the promising potential for laminar to wavy-laminar film regimes and could be applied to similar cases, such as co-current flows and evaporating thin films by minor revision.

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