American Journal of Aerospace Engineering

| Peer-Reviewed |

Numerical Solution of Solar Energy Absorbed in Porous Medium with a New Approach for Vapor Pressure Calculation and Consideration of Solute Crystallization

Received: 29 October 2014    Accepted: 17 November 2014    Published: 25 November 2014
Views:       Downloads:

Share This Article

Abstract

The goal of the study is to enhance the productivity of solar stills using an unsaturated porous medium initially saturated by salty water and using concentrating reflector. This paper concentrates only on the mathematical model for the porous medium and its solution using a finite-volume approach. The previous studies dealt with wick medium with high water content and liquid saturation in the wick medium was not determined. A physical model for the initially saturated porous medium was developed. The model takes into consideration the salt concentration in the solution, surface and internal water diffusions to humid air with vapor pressure determined from vapor mass balance. The system of transient one-dimensional differential equations was developed together with the boundaries and initial conditions. A finite-volume method was used for discretisation of the differential equations. A fully-implicit scheme was used for unsteady term discretisation while the convective terms (liquid solution, vapor and dry air) in the energy equation are handled by an upwind scheme method. The nonlinear equations are solved simultaneously by updating the coefficients matrix at one time step until the five variables converge to prescribed tolerance. Matlab was used as a programming tool. Solution of the model is obtained and discussed.

DOI 10.11648/j.ajae.s.2015020101.18
Published in American Journal of Aerospace Engineering (Volume 2, Issue 1-1, January 2015)

This article belongs to the Special Issue Hands-on Learning Technique for Multidisciplinary Engineering Education

Page(s) 93-105
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2024. Published by Science Publishing Group

Keywords

Porous Medium, Solute Concentration, Vapor Pressure, Absorbed Solar Radiation

References
[1] H. Ni, A. K. Datta and K. E. Torrance, Moisture transport in intensive microwave heating of biomaterials: a multiphase porous media model. International Journal of Heat and Mass Transfer, 42 (1999) 1501- 1512.
[2] A. Khodaparast and Haghi, Relations for water vapor transport through fibers. Journal of Computational and Applied Mechanics, 5 (2) (2004) 263- 274.
[3] V.A.F. Costa, M.L. Mendonca, and A.R. Figueiredo, Modeling and simulation of wetted porous thermal barriers operating under high temperature or high heat flux. International Journal of Heat and Mass Transfer; 51(2008) 3342–3354.
[4] A. Neale, D. Derome, B. Blocken and J. Carmerliet, Coupled Simulation of Vapor Flow between Air and a Porous Material, ASHRAE, 2007.
[5] K. Murugesan, H. N. Suresh, K. N. Seetharamu, P. A. Aswatha Narayana and T. Sundararajan, A theoretical model of brick drying as a conjugate problem, International Journal of Heat and Mass Transfer, 44 (2001) 4075- 4086.
[6] H. Stephen Lee, Wallance W. Carr, Haskell W. Beckham, and Johannes Leisen, A model of through-air drying of tufted textile materials", International Journal of Heat and Mass Transfer, 45(2002) 357- 366.
[7] D. Le, H. Hoang, and J. Mahadevan, Impact of capillary driven liquid films on salt crystallization ". Transp. Porous Med, 80 (2009) 229–252.
[8] M. Koniorczyk, and D. Gawin, Numerical modeling of salt transport and precipitation in non-isothermal partially saturated porous media considering kinetics of salt phase changes. Transp. Porous Med, 87 (2011) 57–76.
[9] M. Kaviany, Principles of heat transfer in porous media, Handbook of Heat Transfer, Second edition, McGraw-Hill, New York, (1995) 2, 28, 479, 491.
[10] M. M. Elsayed, I. S. Taha, and J. A. Sabbagh, Design of Solar Thermal Systems. Scientific Publishing Centre; King Abdulaziz university, Saudi Arabia, (1994).
[11] D. Kraus, Two phase plow in homogenous porous media- The role of dynamic capillary pressure in modeling gravity driven fingering, Master's Thesis, 2011.
[12] Wikipedia, "Electromagnetic absorption by water" (http://en.wikipedia.org/wiki/Electromagnetic_absorption_by_water)
[13] H. H. Li, "Absorption Coefficients", Int. J. Therm., Vol1, No. I, (1980).
[14] Y. A. Cengel, Heat and mass transfer", Hand book of Heat and Mass Transfer, Third edition, A practical approach, McGraw Hill, New York, 2006.
[15] M. Koniorczyk, Modelling the phase change of salt dissolved in pore water– Equilibrium and non-equilibrium approach, Construction and Building Materials, 24 (2010) 1119–1128.
[16] T.Q. Nguyen, J. Petkovic, P. Dangla and V. Baroghel-Bouny, Modeling of coupled ion and moisture transport in porous building materials, Construction and Building Materials (2007) 1- 11.
[17] J. Bear and A. Gilman, Migration of salts in the unsaturated zone caused by heating, Letters in Mathematical Physics, 19 (1995) 139-156.
[18] S. O. Pstalle, Non-isothermal multiphase flow of brine and gas through saline media, Doctoral-Barcelona, Universitat Politecnica de Catalunya, 1995.
[19] M.C. Boufadel, M.T. Suidan, and A.D. Venosa, Numerical modeling of water flow below dry salt lakes: effect of capillarity and viscosity, Journal of Hydrology, 221 (1999), 55–74.
[20] A. Ramalingam and S. Arumugam, Experimental Study on Specific Heat of Hot Brine for Salt Gradient Solar Pond Application, International Journal of Chem. Tech Research, 4 (3) (2012), 956-961.
[21] A. Haldera and A. K. Dattab, Surface heat and mass transfer coefficients for multiphase porous media transport models with rapid evaporation, Food and Bio-products Processing , 90(2012) 475–490.
[22] V.A.F. Costa, M.L. Mendonca and A.R. Figueiredo, "Modeling and simulation of wetted porous thermal barriers operating under high temperature or high heat flux". International Journal of Heat and Mass Transfer; Vol. 51; 2008; 3342–3354.
[23] G. F. Pinder, W. G. Gray, Essentials of multiphase flow and transport in porous media, A John Wiley & Sons, Inc., Hoboken, New Jersey, 2008.
[24] S. V. Patankar, Numerical heat transfer and fluid flow, Book, Publishers, Talyor & Francis, 1980.
[25] Website of " Egyptian meteorological Authority " (http://ema.gov.eg/articles?menu=62&lang=eg)
[26] H. Na, S. Arnold, and A. S. Myerson, Cluster formation in highly supersaturated solution droplets, Journal of Crystal Growth, 139 (1994) 104-112.
[27] W. Scott Pegau, Deric Gray, and J. Ronald V. Zaneveld, Absorption and attenuation of visible and near-infrared light in water: dependence on temperature and salinity, Applied Optics, 36 (24) (1997) 6035- 646.
Author Information
  • Department of Mechanical Engineering, Faculty of Eng., Assuit University, Assuit, Egypt

  • Department of Mechanical Engineering, Faculty of Eng., Assuit University, Assuit, Egypt

  • Department of Mechanical Engineering, Faculty of Eng., Assuit University, Assuit, Egypt

  • Mech. Eng. Department, Faculty of Eng., Al Taif University, Al Taif, Saudi Arabia

  • Faculty of Industrial Education, Sohag University, Sohag, Egypt

Cite This Article
  • APA Style

    Sherif A. Mohamed, Ibrahim S. Taha, Mahmoud G. Morsy, Hany A. Mohamed, Mahmoud S. Ahmed. (2014). Numerical Solution of Solar Energy Absorbed in Porous Medium with a New Approach for Vapor Pressure Calculation and Consideration of Solute Crystallization. American Journal of Aerospace Engineering, 2(1-1), 93-105. https://doi.org/10.11648/j.ajae.s.2015020101.18

    Copy | Download

    ACS Style

    Sherif A. Mohamed; Ibrahim S. Taha; Mahmoud G. Morsy; Hany A. Mohamed; Mahmoud S. Ahmed. Numerical Solution of Solar Energy Absorbed in Porous Medium with a New Approach for Vapor Pressure Calculation and Consideration of Solute Crystallization. Am. J. Aerosp. Eng. 2014, 2(1-1), 93-105. doi: 10.11648/j.ajae.s.2015020101.18

    Copy | Download

    AMA Style

    Sherif A. Mohamed, Ibrahim S. Taha, Mahmoud G. Morsy, Hany A. Mohamed, Mahmoud S. Ahmed. Numerical Solution of Solar Energy Absorbed in Porous Medium with a New Approach for Vapor Pressure Calculation and Consideration of Solute Crystallization. Am J Aerosp Eng. 2014;2(1-1):93-105. doi: 10.11648/j.ajae.s.2015020101.18

    Copy | Download

  • @article{10.11648/j.ajae.s.2015020101.18,
      author = {Sherif A. Mohamed and Ibrahim S. Taha and Mahmoud G. Morsy and Hany A. Mohamed and Mahmoud S. Ahmed},
      title = {Numerical Solution of Solar Energy Absorbed in Porous Medium with a New Approach for Vapor Pressure Calculation and Consideration of Solute Crystallization},
      journal = {American Journal of Aerospace Engineering},
      volume = {2},
      number = {1-1},
      pages = {93-105},
      doi = {10.11648/j.ajae.s.2015020101.18},
      url = {https://doi.org/10.11648/j.ajae.s.2015020101.18},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.ajae.s.2015020101.18},
      abstract = {The goal of the study is to enhance the productivity of solar stills using an unsaturated porous medium initially saturated by salty water and using concentrating reflector. This paper concentrates only on the mathematical model for the porous medium and its solution using a finite-volume approach. The previous studies dealt with wick medium with high water content and liquid saturation in the wick medium was not determined. A physical model for the initially saturated porous medium was developed. The model takes into consideration the salt concentration in the solution, surface and internal water diffusions to humid air with vapor pressure determined from vapor mass balance. The system of transient one-dimensional differential equations was developed together with the boundaries and initial conditions. A finite-volume method was used for discretisation of the differential equations. A fully-implicit scheme was used for unsteady term discretisation while the convective terms (liquid solution, vapor and dry air) in the energy equation are handled by an upwind scheme method. The nonlinear equations are solved simultaneously by updating the coefficients matrix at one time step until the five variables converge to prescribed tolerance. Matlab was used as a programming tool. Solution of the model is obtained and discussed.},
     year = {2014}
    }
    

    Copy | Download

  • TY  - JOUR
    T1  - Numerical Solution of Solar Energy Absorbed in Porous Medium with a New Approach for Vapor Pressure Calculation and Consideration of Solute Crystallization
    AU  - Sherif A. Mohamed
    AU  - Ibrahim S. Taha
    AU  - Mahmoud G. Morsy
    AU  - Hany A. Mohamed
    AU  - Mahmoud S. Ahmed
    Y1  - 2014/11/25
    PY  - 2014
    N1  - https://doi.org/10.11648/j.ajae.s.2015020101.18
    DO  - 10.11648/j.ajae.s.2015020101.18
    T2  - American Journal of Aerospace Engineering
    JF  - American Journal of Aerospace Engineering
    JO  - American Journal of Aerospace Engineering
    SP  - 93
    EP  - 105
    PB  - Science Publishing Group
    SN  - 2376-4821
    UR  - https://doi.org/10.11648/j.ajae.s.2015020101.18
    AB  - The goal of the study is to enhance the productivity of solar stills using an unsaturated porous medium initially saturated by salty water and using concentrating reflector. This paper concentrates only on the mathematical model for the porous medium and its solution using a finite-volume approach. The previous studies dealt with wick medium with high water content and liquid saturation in the wick medium was not determined. A physical model for the initially saturated porous medium was developed. The model takes into consideration the salt concentration in the solution, surface and internal water diffusions to humid air with vapor pressure determined from vapor mass balance. The system of transient one-dimensional differential equations was developed together with the boundaries and initial conditions. A finite-volume method was used for discretisation of the differential equations. A fully-implicit scheme was used for unsteady term discretisation while the convective terms (liquid solution, vapor and dry air) in the energy equation are handled by an upwind scheme method. The nonlinear equations are solved simultaneously by updating the coefficients matrix at one time step until the five variables converge to prescribed tolerance. Matlab was used as a programming tool. Solution of the model is obtained and discussed.
    VL  - 2
    IS  - 1-1
    ER  - 

    Copy | Download

  • Sections