This work presents a numerical analysis of the quasi-steady combustion of an infinite stream of droplets in the limit of infinite Damkohler number and stagnant ambient conditions. The small and large length-scale phenomena associated with the process are addressed by splitting the physical domain into near- and far-field subdomains. Within the inner subdomain, validated expressions are used during the grid generation procedure, allowing the development of appropriate finite-difference expressions and control of the distribution of points. Analytical transformations are developed and applied to the outer subdomain coordinate system in order to match the inner and outer grids along the domain interface and to properly address the outflow boundary conditions using a regularly spaced grid. A system of transformed governing equations is obtained and discretized into a coupled system of algebraic equations, which are solved by standard scientific subroutines, incorporating automatic control of error. The developed transformations are inverted and the solutions within the physical domain are obtained. Interdroplet interaction effects are presented in terms of droplet mass vaporization rate, droplet lifetime, and flame-sheet shape and position for different droplet spacings and fuels. The results indicate interaction effects present over a broad range of interdroplet spacings and are compared with theoretical and experimental ones available in the literature.