: This research concentrates on condensation of a single vapor bubble in a vertical, two-dimensional channel where an upward liquid flow imposed. Initially, the bubble is completely present in the solution domain so, the effect of injecting or producing bubble is not included. The upward flow is laminar, viscous and incompressible. Both fluids are considered with constant physical properties. The problem is investigated numerically using a finite difference/front-tracking method. Fluids are at rest initially and the outflow boundary condition is implemented in a way such that the outflow velocity becomes fully developed. Consequently, the whole length of a vertical channel is investigated in this research. This thesis has successfully identified the entire non-dimensional parameters governing the problem. This identification is done computationally. While some significant conclusions are made specifically based on the analysis of the problem non-dimensional parameters, two major results are achieved which are thoroughly novel. The first conclusion is that the condensation rate of a single bubble can generally be constant. This results a constant rate of reduction in the bubble’s area. The other achievement is that the bubble rising velocity is also constant. Although the outcomes may seem questionable, experimental measurements, even in a turbulent medium, confirm this. (Al Issa, S. M. and Macian-Juan, R., International Journal of Multiphase Flow, Vol. 94, p. 173–188, 2017.) Keywords: Front -tracking method-two-phase flow- vertical channel - Direct numerical - simulations - Direct - contact -condensation