This paper reports an analytical study of the second law in the case of gas absorption into a laminar falling viscous incompressible liquid film. Velocity, temperature, and concentration profiles are determined and used for the entropy generation calculation. Irreversibilities due to heat transfer, fluid friction, and coupling effects between heat and mass transfer are derived. The obtained results show that entropy generation is mainly due to coupling effects between heat and mass transfer near the gas-liquid interface. Total irreversibility is minimum at the diffusion film thickness. On approaching the liquid film thickness, entropy generation is mainly due to viscous irreversibility. 1. Introduction Gas-liquid (and vapor-liquid) flows occur in a wide variety of situations such as: power generation, chemical processing, and energy production facilities. Some practical applications include condensers and reboilers, gas-liquid reactors (used in the production of pharmaceuticals and specialty chemicals), wetted wall absorbers, power systems, core cooling of nuclear power plant, and falling film reactors. In addition to normal gravity applications, gas-liquid (and vapor-liquid) flows also occur in many planned space operations such as: power cycles, active thermal control systems [1], propulsion devices, and storage and transfer of cryogenic fluids. Gas-liquid flows can be grouped into a number of different flow patterns. These flow patterns are based on the spatial and temporal distribution of the gas and liquid phases. Gravity is the major reason for such two-phase flows to exhibit a wide range of flow patterns with different characteristics. Gas-liquid absorption is one of the most important separation processes, the gas-liquid contactors in which absorption takes place are typically spray, trayed, or packed systems involving falling films. Falling film flow has found wide applications in modern equipments, because it is widely used in modern process industries such as vertical condensers, film evaporators, distillation columns, and packed and absorption towers. Various works are elaborated in order to study the coupled heat and mass transfer processes in gas or vapor absorption into a liquid film. The theoretical analysis of combined heat and mass transfer processes in the case of gas or vapor absorption into a laminar and/or turbulent liquid film as well as the temperature evolution and the concentration profiles in the film are developed [2–5]. Conlisk and Mao [6] considered the condensation of a two-component vapor mixture into a two-component
References
[1]
A. A. M. Delil, “Research issues on two-phase loops for space applications,” in Proceedings of the Symposium on Space Flight Mechanics, Institute of Space and Astronautical Science, Sagamihara, Japan, 2000.
[2]
G. Grossman, “Analysis of interdiffusion in film absorption,” International Journal of Heat and Mass Transfer, vol. 30, no. 1, pp. 205–208, 1987.
[3]
G. Grossman and M. T. Heath, “Simultaneous heat and mass transfer in absorption of gases in turbulent liquid films,” International Journal of Heat and Mass Transfer, vol. 27, no. 12, pp. 2365–2376, 1984.
[4]
L. P. Kholpanov and E. Y. Kenig, “Coupled mass and heat transfer in a multicomponent turbulent falling liquid film,” International Journal of Heat and Mass Transfer, vol. 36, no. 14, pp. 3647–3657, 1993.
[5]
B. J. C. van der Wekken and R. H. Wassenaar, “Simultaneous heat and mass transfer accompanying absorption in laminar flow over a cooled wall,” International Journal of Refrigeration, vol. 11, no. 2, pp. 70–77, 1988.
[6]
A. T. Conlisk and J. Mao, “Nonisothermal absorption on a horizontal cylindrical tube—1. The film flow,” Chemical Engineering Science, vol. 51, no. 8, pp. 1275–1285, 1996.
[7]
W. A. Miller and M. Keyhani, “Experimental analysis of local heat and mass transfer data for vertical falling film absorption,” Tech. Rep., Japan Aerospace Exploration Agency (JAXA), Tokyo, Japan, 1999, Fluid Mechanics and Thermodynamics.
[8]
R. Islam, N. E. Wijeysundera, and J. C. Ho, “Simplified models for coupled heat and mass transfer in falling-film absorbers,” International Journal of Heat and Mass Transfer, vol. 47, no. 2, pp. 395–406, 2004.
[9]
J. D. Killion and S. Garimella, “A critical review of models of coupled heat and mass transfer in falling-film absorption,” International Journal of Refrigeration, vol. 24, no. 8, pp. 755–797, 2001.
[10]
S. M. Yih and R. C. Seagrave, “Mass transfer in laminar falling liquid films with accompanying heat transfer and interfacial shear,” International Journal of Heat and Mass Transfer, vol. 23, no. 6, pp. 749–758, 1980.
[11]
G. Grossman, “Simultaneous heat and mass transfer in film absorption under laminar flow,” International Journal of Heat and Mass Transfer, vol. 26, no. 3, pp. 357–371, 1983.
[12]
M. Danish, R. K. Sharma, and S. Ali, “Gas absorption with first order chemical reaction in a laminar falling film over a reacting solid wall,” Applied Mathematical Modelling, vol. 32, no. 6, pp. 901–929, 2008.
[13]
H. L. Goff, A. Ramadane, and P. L. Goff, “Modélisation des transferts couples de matière et de chaleur dans l'absorption gaz-liquide en film ruisselant laminaire,” International Journal of Heat and Mass Transfer, vol. 28, no. 11, pp. 2005–2017, 1985.
[14]
K. Othmer, Encyclopedia of Chemical Technology, Springer, New York, NY, USA, 4th edition, 1993.
[15]
C. L. Yaws, Handbook of Thermal Conductivity, Gulf Publishing Corporation, Houston, Tex, USA, 1997.
[16]
O. D. Makinde, “Exothermic explosions in a slab: a case study of series summation technique,” International Communications in Heat and Mass Transfer, vol. 31, no. 8, pp. 1227–1231, 2004.
[17]
O. B. Adeyinka and G. F. Naterer, “Optimization correlation for entropy production and energy availability in film condensation,” International Communications in Heat and Mass Transfer, vol. 31, no. 4, pp. 513–524, 2004.
[18]
A. Galovi？, “Non-dimensional entropy analysis of condenser and/or evaporator type heat exchangers,” International Journal of Heat Exchangers, vol. 5, no. 2, pp. 337–346, 2004.
[19]
K. G. Boulama, N. Galanis, and J. Orfi, “Entropy generation in a binary gas mixture in the presence of thermal and solutal mixed convection,” International Journal of Thermal Sciences, vol. 45, no. 1, pp. 51–59, 2006.
[20]
C. G. Carrington and Z. F. Sun, “Second law analysis of combined heat and mass transfer phenomena,” International Journal of Heat and Mass Transfer, vol. 34, no. 11, pp. 2767–2773, 1991.
[21]
M. Magherbi, H. Abbassi, N. Hidouri, and A. Ben Brahim, “Second law analysis in convective heat and mass transfer,” Entropy, vol. 8, no. 1, pp. 1–17, 2006.
[22]
S. Saouli and S. A？boud-Saouli, “Second law analysis of laminar falling liquid film along an inclined heated plate,” International Communications in Heat and Mass Transfer, vol. 31, no. 6, pp. 879–886, 2004.
[23]
O. D. Makinde and E. Osalusi, “Entropy generation in a liquid film falling along an inclined porous heated plate,” Mechanics Research Communications, vol. 33, no. 5, pp. 692–698, 2006.
[24]
R. S. R. Gorla and D. M. Pratt, “Second law analysis of a non-Newtonian laminar falling liquid film along an inclined heated plate,” Entropy, vol. 9, no. 1, pp. 30–41, 2007.
[25]
I. Chermiti, N. Hidouri, and A. Ben Brahim, “Entropy generation in gas absorption into a falling liquid film,” Mechanics Research Communications, vol. 38, no. 8, pp. 586–593, 2011.
[26]
S. A？boud-Saouli, S. Saouli, N. Settou, and N. Meza, “Thermodynamic analysis of gravity-driven liquid film along an inclined heated plate with hydromagnetic and viscous dissipation effects,” Entropy, vol. 8, no. 4, pp. 188–199, 2006.
[27]
S. J. Lee and W. K. Lee, “Physical absorption of oxygen in laminar falling films of dilute polymeric aqueous solutions,” Korean Journal of Chemical Engineering, vol. 1, no. 1, pp. 51–57, 1984.
[28]
P. A. Nikrityuk, Computational Thermo-Fluid Dynamics: In Material Sciences and Engineering, John Wiley & Sons, New York, NY, USA, 2011.
[29]
N. Gabbiye, Modeling and simulation of interface mass transfer with chemical reaction [M.S. thesis of Sciences in Chemical Engineering], Faculty of Technology, Department of Chemical Engineering, Addis Ababa University, 2004.
[30]
R. B. Bird, W. E. Stewart, and E. N. Lightfoot, Transport Phenomena, John Wiley & Sons, New York, NY, USA, 2nd edition, 2002.
[31]
R. K. Sharma, M. Danish, and S. Ali, “Solution of physical gas absorption in falling liquid film by alternate analytical methods,” Indian Chemical Engineering Journal, vol. 48, no. 3, pp. 190–193, 2006.
[32]
J. R. Bourne, U. V. Stockar, and G. C. Coggan, “Gas absorption with heat effects. I. A new computational method,” Industrial and Engineering Chemistry Process Design and Development, vol. 13, no. 2, pp. 115–123, 1974.
[33]
J. Y. San, W. M. Worek, and Z. Lavan, “Entropy generation in combined heat and mass transfer,” International Journal of Heat and Mass Transfer, vol. 30, no. 7, pp. 1359–1369, 1987.
[34]
J. O. Hirschfelder, C. F. Curtiss, and R. B. Bird, The Molecular Theory of Gases and Liquids, John Wiley & Sons, New York, NY, USA, 1954.
[35]
I. Mahmoud, Mass and Heat Transfer during Absorption of Ammonia Vapor into Ammonia-Water Mixture, Department of Energy and Materials Science, Graduate School of Science and Engineering, Saga University, Saga, Japan, 2004.
