Solving the heat and mass transfer equations for an evaporative cooling tower through an orthogonal collocation method

Abstract

In this paper, the orthogonal collocation technique is utilized to solve the Poppe method equations for heat and mass transfer in counter flowing wet-cooling towers. The six differential equations for unsaturated and supersaturated air from the Poppe method are simplified, yielding three differential equations that use the Heaviside function. The humidity ratio is demonstrated to be a finite power series at a normalized water temperature. The air enthalpy is expressed as a function of the normalized water temperature and the unknown coefficients of the expansion from the humidity ratio. The discrete formulation is solved using the Newton–Raphson method using an explicit Jacobian. The proposed methodology is applied to eight examples, and the results are compared to the results obtained when the governing equations are integrated with the Dormand–Prince method. The results indicate that the accuracy is similar between both techniques. However, the orthogonal collocation requires less CPU time.