The film condensate behaviour that forms over the condenser, evaporator, and heat pipes provides thermal resistance that slows the heat transfer rate. Myriad studies of hydrodynamic stability have ignored the impact of interfacial shear stress in favour of Nusselt's velocity and temperature profile. The steady-state numerical simulation of laminar film condensation, considering surface roughness, has been the subject of some investigations. The main objective of the current work is to simulate an undiscovered research study on unsteady initially developed film condensate moving across a hydrophilic vertical plate under the effect of gravity and surface tension forces using numerical simulation and an analytical technique. The unstable state was first numerically simulated using V_v = 2 m/s (laminar case), V_v = 6 m/s (turbulent case), and for both the cases T_w = 273.15 K, T_v = 373.15 K. The stream-wise variation of the heat transfer coefficient and film thickness through numerical simulation were explored, and the velocity and temperature were also investigated. Second-order velocity and temperature profiles were considered, considering the impacts of vapour velocity on the interface. Steady-state Nusselt's film thickness expression was used to validate the numerical simulation for the laminar case (for a long time) and shows an average error of 2%. Chun & Seban correlation for heat transfer coefficient was used to validate the numerical simulation for the unstable, turbulent scenario and shows an average error of 2.5%. The analytical equation used to validate the numerical simulations indicates a 1.3% inaccuracy for the velocity profile and a 1.6% average error for the temperature profile.