Equivalent Enthalpy Model and Log-Mean Enthalpy Difference Method for Heat-Mass Transfer in Cooling Towers

Abstract

In industrial processes involving both heat and mass transfer, the enthalpy or total energy difference, not the temperature difference, is a more comprehensive driving-force potential for the design of heat exchanger systems, such as cooling towers. However, current enthalpy methods based on the Merkel integral require numerical integration with implied linear distributions of water temperature. If the cooling range of the cooling tower is relatively small, the outcome of the integration may carry little error. However, for a large cooling range and a substantially increased temperature, the error involved may be significant. Like log-mean temperature difference, a log-mean enthalpy difference method may require only the inlet and outlet conditions without prior knowledge of the enthalpy distributions of the fluids within the heat exchanger. The known Berman's enthalpy difference method requires correction factors and was derived based on the linearization of the interfacial enthalpy and the enthalpy difference between the interfacial moist air and the bulk moist air without underlying interpretation to demonstrate that the method could be broadly used. In this paper, an equivalent enthalpy model is proposed, and the log-mean enthalpy difference is derived without retaining model assumptions. The derived method is compared with some results of Merkel's method from literature with excellent agreement. Thus, the work in this paper would open up the possibility for broad uses of the log-mean enthalpy difference method for many industrial processes involving both heat and mass transfer.