An Analytical Approach to Wet Cooling Towers Based on Functional Analysis

Abstract

An analytical solution for computing the temperature distribution of air and water over the height through the cooling tower is so complex that finding the exact solution takes too much time. The purpose of this paper is to present efficient and accurate analytical expressions for the heat and mass transfer model in cooling towers. Based on the method of functional analysis, we derived an analytical solution for temperature distribution of water and air by using the method of solving linear differential equations. The error estimation, the existence, and uniqueness of the solution are given by using Banach contraction mapping theorem. The basic equation of the model on the basis of the additional assumptions on the cooling tower is solved, and the outlet parameters are also obtained.