A NOVEL ANALYTICAL SOLUTION OF MERKEL EQUATION FOR COUNTERFLOW COOLING TOWERS

Accurate performance analysis of direct-contact air-water counterflow cooling towers is important in practice for energy conservation and cost savings purposes. In general, accurate analysis can often be made using Merkel’s theory. However, a simple and accurate analytical solution of the Merkel equation is not yet available.  In this paper, a novel and accurate analytical solution is presented, obtained from direct integration of the Merkel equation. The new method gives excellent agreement when compared with the use of standard Merkel’s method when predicting the outlet water temperatures with maximum root-mean-square error of 0.2% for a practical range of operating conditions. The new method also predicts the outlet water temperatures for four experimental cooling towers with maximum root-mean-square error of 0.8%. A limited validation shows that the method is also applicable to performance analysis of an actual crossflow cooling tower. The new method is a valuable addition to the existing methods of solving the Merkel equation.