The effect of the presence of a cold wall on the downstream changes in size distribution of a spray of fuel droplets undergoing vaporization and combustion is theoretically analyzed. The fuel is considered to be in the form of discrete liquid droplets which have an arbitrary range of sizes and differ in their rates of vaporization. In fact, the total number of discrete droplet sizes needed to simulate actual fuel sprays can be immense. To avoid the dimensionality problem associated with the discrete form of population balance equations of an ensemble of individual burning or evaporating particles, "sectional conservation equations" are used. The method, based on dividing the droplet size domain into sections and dealing only with one integral quantity in each section (e.g., number, surface area of droplets, or volume), has the advantage that the integral quantity is conserved within the computational domain and the number of conservation equations required is simply equal to the number of sections. Employing known solutions for the boundary layer flow field, the "sectional size conservation equations" are solved assuming that droplets follow streamlines. New solutions for the changes in size distributon of droplets as a function of temperature and distance from the wall are presented. Since the present analysis uses an arbitrary droplet size distribution as an initial condition, it may be used to evaluate the performance of various atomizers, as demonstrated in the present study.