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Evaporative heat and mass transfer for the diffusion driven desalination process

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Abstract

An innovative Diffusion Driven Desalination process was recently described where evaporation of seawater is driven by diffusion within a packed bed. This work describes the evaporative heat and mass transfer analysis for the packed bed. Temperature and humidity data have been collected over a range of flow conditions at the inlet and outlet of the packed bed. The analysis agrees very well with the experimental data collected during this investigation and that which has been reported in the literature.

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Abbreviations

A :

Control surface area (m2)

a :

Specific area of packing material (m2 /m3)

C p :

Specific heat of air (kJ/kg)

d p :

Diameter of packing (m)

D :

Molecular diffusion coefficient (m2/s)

g :

Gravity (m/s2)

G :

Air mass flux (kg/m2 s)

h :

Enthalpy (kJ/kg)

h fg :

Latent heat of vaporization (kJ/kg)

k :

Mass transfer coefficient (m/s)

L :

Water mass flux (kg/m2 s)

M V :

Vapor molecular weight (kg/kmol)

m :

Mass flow rate (kg/s)

P :

Pressure (Pa)

P sat :

Partial pressure of vapor (Pa or kPa)

T :

Temperature (°C or K)

U :

Heat transfer coefficient (W/m2 K)

Φ:

Relative humidity

α:

Heat diffusion coefficient (m2 /s)

μ:

Dynamic viscosity (kg/m s)

ρ:

Density (kg/m3)

σL :

Liquid/gas interfacial surface tension (N/m)

σC :

Critical surface tension of packing (N/m)

ω:

Humidity ratio

a:

Air

evap:

The portion of liquid evaporated

G:

Air/vapor mixture

GA:

Gas side parameter based on the specific area of packing

L:

Water in liquid phase

LA:

Liquid side parameter based on the specific area of packing

LW:

Liquid side parameter based on the specific wet area of packing

V:

Water in vapor phase

References

  1. Bourouni KM, Chaibi MT, Tadrist L (2001) Water desalination by humidification and dehumidification of air: state of the art, desalination. 137(1–3):167–176

  2. Al-Hallaj S, Farid MM, Tamimi AR (1998) Solar desalination with a humidification–dehumidification cycle: performance of the unit, desalination. 120(3):273–280

  3. Assouad Y, Lavan Z (1988) Solar desalination with latent heat recovery. J Sol Energy Eng 110(1):14–16

    Article  Google Scholar 

  4. Muller-Holst H, Engelhardt M, Scholkopf W (1999) Small-scale thermal seawater desalination simulation and optimization of system design, desalination. 122(3):255–262

  5. Al-Hallaj S, Selman JR (2002) A comprehensive study of solar desalination with a humidification–dehumidification cycle, a report by the middle east desalination research center, Muscat, Sultanate of Oman

    Google Scholar 

  6. Klausner JF, Li Y, Darwish M, Mei R (2004) Innovative diffusion driven desalination process. J Energy Resour Technol 126(3):219–225

    Article  Google Scholar 

  7. Merkel F (1925) Verdunstungskuhlung, VDI Forschungsarbeiten, 275, Berlin

    Google Scholar 

  8. Baker DR, Shryock HA (1961) A comprehensive approach to the analysis of cooling tower performance. J Heat Transfer 339–350

  9. Sutherland JW (1983) Analysis of mechanical-draught counterflow air/water cooling towers. J Heat Transfer 105:576–583

    Google Scholar 

  10. Osterle F (1991) On the analysis of counter-flow cooling towers. Int J Heat Mass Transfer 34(4/5):1316–1318

    Google Scholar 

  11. El-Dessouky HTA, Ai-Haddad A, Ai-Juwayhel F (1997) A modified analysis of counter flow wet cooling towers. J Heat Transfer 119:617–626

    Article  Google Scholar 

  12. Kays WM, Crawford ME, Weigand B (2005) Convective heat and mass transfer, 3rd edn. Springer, Berlin Heidelberg New York

    Google Scholar 

  13. McAdams WH, Pohlenz JB, St. John RC (1949) Transfer of heat and mass between air and water in a packed tower. Chem Eng Prog 45:241–252

    Google Scholar 

  14. Huang CC, Fair JR (1989) Direct-contact gas–liquid heat transfer in a packed column. Heat Transfer Eng 10(2):19–28

    Article  Google Scholar 

  15. Onda K, Takechi H, Okumoto Y (1968) Mass transfer coefficients between gas and liquid phases in packed columns. J Chem Eng Jpn 1:56–62

    Article  Google Scholar 

  16. Eckert ERG (1976) Analogies to heat transfer processes. In: Eckert ERG, Goldstein RJ (eds) Measurements in heat transfer. Hemisphere Publications, New York, pp 397–423

    Google Scholar 

  17. Huang CC (1982) Heat transfer by direct gas–liquid contacting. MS thesis, University of Texas, Austin

Download references

Acknowledgements

This paper was prepared with the support of the U.S. Department of Energy under Award No. DE-FG26-02NT41537. However, any opinions, findings, conclusions, or recommendations expressed herein are those of the authors and do not necessarily reflect the views of DOE.

Author information

Authors and Affiliations

  1. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, 32611, USA

    James F. Klausner, Yi Li & Renwei Mei

Authors
  1. James F. Klausner
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  2. Yi Li
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  3. Renwei Mei
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Corresponding author

Correspondence to James F. Klausner.

Appendix A

Appendix A

1.1 Onda’s Correlation

Onda’s correlation

$$k_{\rm{L}} = 0.0051Re_{{\rm{Lw}}} ^{2/3} {\rm{Sc}}_{\rm{L}} ^{ - 0.5} ({\rm{ad}}_{\rm{p}} )^{0.4} \left[ {\frac{{\mu _{_{\rm{L}} } g}}{{\rho _{_{\rm{L}} } }}} \right]^{1/3} $$
$$ k_{\rm{G}} = 5.23Re_{{\rm{GA}}} ^{0.7} {\rm{Sc}}_{\rm{G}} ^{1/3} ({\rm{ad}}_{\rm{p}} )^{ - 2} a{\rm{D}}_{\rm{G}} $$
$$ a_{\rm{w}} = a\left\{ {1 - \exp \left[ { - 2.2\left( {\frac{{\sigma _{\rm{c}} }}{{\sigma _{\rm{L}} }}} \right)^{3/4} {\rm{Re}}_{{\rm{LA}}} ^{1/2} {\rm{Fr}}_{\rm{L}} ^{ - 0.05} {\rm{We}}_{\rm{L}} ^{1/5} } \right]} \right\} $$
(21)
$$Re_{{\rm{LW}}} = \frac{L}{{a_{\rm{w}} \mu _{\rm{L}} }},\quad Re_{{\rm{GA}}} = \frac{G}{{a\mu _{\rm{G}} }},\quad Re_{{\rm{LA}}} = \frac{L}{{a\mu _{\rm{L}} }}$$
$$ {\rm{Sc}}_{\rm{L}} = \frac{{\mu _{\rm{L}} }}{{\rho _{\rm{L}} D_{\rm{L}} }},\quad {\rm{Sc}}_{\rm{G}} = \frac{{\mu _{\rm{G}} }}{{\rho _{\rm{G}} D_{\rm{G}} }},\quad {\rm{Fr}}_{\rm{L}} = \frac{{L^2 a}}{{\rho _{\rm{L}} g}},\quad {\rm{We}}_{\rm{L}} = \frac{{L^2 }}{{\rho _{\rm{L}} \sigma _{\rm{L}} a}} $$

This equation 21 has been modified from the Onda’s original correlation.

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Klausner, J.F., Li, Y. & Mei, R. Evaporative heat and mass transfer for the diffusion driven desalination process. Heat Mass Transfer 42, 528–536 (2006). https://doi.org/10.1007/s00231-005-0649-2

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