Balancing and ε-NTU Analogies

Desalination systems have much in common with classical heat exchangers. Many use a counter-flowing streams or multiple stages to transfer energy and mass from one stream to another. Our group has exploited this commonality to improve the energy efficiency of desalination systems and components.

In heat exchanger theory, the effectiveness-NTU method provides a powerful tool for design and rating heat exchangers. Further, “balancing” counterflowing streams is a well-established means of maximizing heat exchangers effectiveness and minimizing entropy production. Balancing has a close connection to the concept of equipartitioning entropy generation. We have developed both balancing methods and effectiveness-NTU models to a wide variety of thermal and osmotic technologies.

Selected Papers on Balancing and Equipartitioning

J.H. Lienhard V, “Energy savings in desalination technologies: reducing entropy generation by transport processes,” J. Heat Transfer, online 17 May 17 2019, 141(7):072001, July 2019. (doi link) (preprint) An overview of much of the work our group has done

J. Swaminathan, H.W. Chung, D.M. Warsinger, and J.H. Lienhard V, “Membrane Distillation Model Based on Heat Exchanger Theory and Configuration Comparison,” online 23 Oct. 2016, Applied Energy, 184:491-505, 15 Dec. 2016. (doi link) (preprint)

K.M. Chehayeb, G.P. Narayan, S.M. Zubair, and J.H. Lienhard V, “Thermodynamic balancing of a fixed-size two-stage humidification dehumidification desalination system,” Desalination, 369:125-139, 3 August 2015; online 16 May 2015. (doi link) (preprint)

E.W. Tow, R.K. McGovern, and J.H. Lienhard V, “Raising forward osmosis brine concentration efficiency through flow rate optimization,” Desalination, 366:71-79, 15 June 2015; online 13 November 2014. (doi link) (preprint)

G.P. Thiel, R.K. McGovern, S.M. Zubair, and J.H. Lienhard V, “Thermodynamic equipartition for increased second law efficiency,” Applied Energy, 118C:292-299, April 2014. (doi link) (preprint)

K.M. Chehayeb, G.P. Narayan, S.M. Zubair, and J.H. Lienhard V, “Use of multiple extractions and injections to thermodynamically balance the humidification dehumidification desalination system,” Intl. J. Heat Mass Transfer, 68:422–434, Jan. 2014. (doi link) (preprint)

G.P. Narayan, K.M. Chehayeb, R.K. McGovern, G.P. Thiel, S.M. Zubair, and J.H. Lienhard V, “Thermodynamic balancing of the humidification dehumidification desalination system by mass extraction and injection,” International Journal of Heat and Mass Transfer, 57(2):756-770, Feb. 2013 (doi link) (preprint)

G.P. Narayan, J.H. Lienhard V, and S.M. Zubair, “Entropy Generation Minimization of Combined Heat and Mass Transfer Devices,” International Journal of Thermal Sciences, 49(10):2057-2066, Oct. 2010. (doi link) (preprint)

Balancing a direct-contact membrane distillation module

Balancing a direct-contact membrane distillation module (Swaminathan et al., Applied Energy, 2018)

Selected Papers on Heat Exchanger Analogies

G.P. Thiel and J.H. Lienhard V, “An effectiveness-NTU relationship for evaporators with non-negligible boiling point elevation increases,” Journal of Heat Transfer, 138(12):12180, December 2016. (doi link) (preprint)

J. Swaminathan, H.W. Chung, D.M. Warsinger, and J.H. Lienhard V, “Membrane Distillation Model Based on Heat Exchanger Theory and Configuration Comparison,” online 23 Oct. 2016, Applied Energy, 184:491-505, 15 Dec. 2016. (doi link) (preprint)

L.D. Banchik, M.H. Sharqawy, and J.H. Lienhard V, “Limits of Power Production Due to Finite Membrane Area in Pressure Retarded Osmosis,” J. Membrane Sci., 468:81-89, 15 October 2014. (doi link) (preprint)

L.D. Banchik, M.H. Sharqawy, and J.H. Lienhard V, “Effectiveness-Mass Transfer Units (ε–MTU) Model of a Reverse Osmosis Membrane Mass Exchanger,” J. Membrane Science, 458:189-198, 15 May 2014. (doi link) (preprint)

M.H. Sharqawy, L.D. Banchik, and J.H. Lienhard V, “Effectiveness-Mass Transfer Units (ε-MTU) Model of an Ideal Pressure Retarded Osmosis Membrane Mass Exchanger,” Journal of Membrane Science, 445:211-219, 15 October 2013. (doi link) (preprint)

L.D. Banchik, A.M. Weiner, B. Al Anzi, J.H. Lienhard V, “System scale analytical modeling of forward and assisted forward osmosis mass exchangers with a case study on fertigation,” J. Membrane Sci., 510:533-545, 15 July 2016. (doi link) (preprint)

G.P. Narayan, J.H. Lienhard V, and S.M. Zubair, “Entropy Generation Minimization of Combined Heat and Mass Transfer Devices,” International Journal of Thermal Sciences, 49(10):2057-2066, Oct. 2010. (doi link) (preprint)

G.P. Narayan, K.H. Mistry, M.H. Sharqawy, S.M. Zubair, J.H. Lienhard V, “Energy Effectiveness of Simultaneous Heat and Mass Exchange Devices,” Frontiers in Heat and Mass Transfer, 1(2):1-13, Aug. 2010. (doi link) (pdf)

Effectiveness NTU (or MTU) plots for a counterflow heat exchanger, a reverse osmosis mass exchanger, and a pressure-retarded-osmosis mass exchanger.

Effectiveness NTU (or MTU) plots for a counterflow heat exchanger, a reverse osmosis mass exchanger, and a pressure-retarded-osmosis mass exchanger.