New explicit analytical solutions of equations for heat and mass transfer in a cooling tower energy system

The aim of this article is to develop an accurate and fast analytical method for heat and mass transfer model in a cooling tower energy system. Some algebraic explicit analytical solutions of the one-dimensional differential equation sets describing the coupled heat and mass transfer process in a cooling tower are derived. The explicit solutions have not yet been published before. The explicit equations of heat and mass transfer are expressed in elementary functions. By solving these differential equations in a cooling tower, the temperature distribution of liquid and gas, the moisture content in the air can be obtained in each section over the vertical height of the tower. A comparison of analytical and experimental results was given in this article, and good agreements were shown for the typical cases studied. The analytical solutions can serve as a benchmark to check the results of numerical calculation.