Mathematical modeling of falling liquid film evaporation process M. El Haj Assad*, Markku J. Lampinen Laboratory of Applied Thermodynamics, Helsinki University of Technology, PO Box 4400, FIN-02015, Finland Received 21 December 2000; received in revised form 13 July 2001; accepted 16 July 2001 Abstract A mathematical model of evaporation process from a laminar falling liquid film on a vertical plate of constant temperatureispresented.Themodelisdevelopedwithandwithoutinterfacialshearstressduetothevaporflowatthe liquidfilmsurface.Thevaporpressuredrop,vaporexitvelocityandcoolingratearecalculatedfordifferentliquidmass flow values. It is shown that lower liquid mass flow produces higher cooling rate. The results also show that the inter- facial shear stress has a considerable negative effect on the cooling rate. It is proved that there exists an optimum dis- tance between the plates, which gives the maximum volumetric cooling rate. # 2002ElsevierScienceLtdandIIR.All rights reserved. Keywords: Liquid; Falling film; Evaporation; Modelling Mode´lisation mathe´matique du processus d’e´vaporation dans un film tombant Mots cle ´s : Liquide;Filmtombant;E ´ vaporation ; Mode´lisation 1. Introduction Falling film evaporation is quite similar to falling liquid film condensation from mathematical point of view. However, both evaporation and condensation processes are not the same from performance behavior point of view. Falling liquid film flow has been given great attention due to its wide applications in industrial processes involvingheatandmasstransfer[1–4].Heatexchangers, filmcondensers,filmevaporatorsandabsorptiontowers are common process equipments utilizing film flow. The liquid film (water) flows downward along a ver- tical plate in x direction as shown in Fig. 1. As the film flows down, its thickness and mass flow rate decrease due to evaporation which occurs at the liquid–vapor interface. It is assumed that evaporation occurs at saturation temperature T,whichissmallerthanthewall temperature T P . Due to this temperature difference, there is a heat transfer from the wall to the liquid film. 0140-7007/02/$22.00 # 2002 Elsevier Science Ltd and IIR. All rights reserved. PII: S0140-7007(01)00064-0 International Journal of Refrigeration 25 (2002) 985–991 www.elsevier.com/locate/ijrefrig * Corresponding author. E-mail addresses: melhajas@cc.hut.fi (M. El Haj Assad), markku.lampinen@hut.fi (M.J. Lampinen).