Analytical solution of the governing equations for heat and mass transfer in evaporative cooling process

Abstract

In this work, the governing equations of the heat and mass transfer in evaporative cooling process are solved by using the power series method. The physical properties, including the Lewis factor, are considered constant along the cooling process. The water loss from water stream vaporization is taken into account. An iterative procedure is developed for calculating the expansion coefficients of the humidity ratio, the air enthalpy, and the number of transfer units. In all study cases, the power series solution is convergent for the heat and mass transfer equations, except for the number of transfer units equation. Thus, Gauss quadrature technique is implemented as an alternative method for determining the number of transfer units profile. As a comparison, the study cases are also solved numerically by the Dormand-Prince Runge-Kutta method. The numerical and analytical results are found to be in excellent agreement when the mass flow-rate ratio between water and dry air is low. The computational execution time of the analytical solution is 50 times faster than the numerical solution. Furthermore, the proposed technique was applied to a study case previously reported and the results were properly represented with an average error of 3%.