A Numerical Model for Heat and Moisture Transfer in Porous Media of Building Envelopes
Received: 6 June 2022 | Revised: 23 July 2022 | Accepted: 2 August 2022 | Online: 10 August 2022
Corresponding author: T. Scussiato
This study presents a one-dimensional quantitative analysis of unsaturated flow in natural stones using a numerical model (Finite Difference Method) and a mass balance for the heat flow. For that, we considered heat and moisture transfer between the external environment and a porous media (sandstone and limestone) with homogeneous characteristics. For unsaturated water flow, Richards’ equation and the formulation proposed by Gardner for volumetric water content and hydraulic conductivity were considered. The results of the numerical analysis showed that the evaporation of porewater throughout summer days (January 3rd and 4th) considerably reduced the temperature of the roof by about 8°C. The accumulated conductive heat flow and the volumetric water content were also reduced due to the evaporation process. This fact indicates that evaporation can be useful in providing thermal comfort and, consequently, in improving the energy efficiency of buildings with natural stones as envelopes.
Keywords:Richards’ equation, heat transfer, thermal comfort, porous media
L. Zhang, R. Zhang, Y. Zhang, T. Hong, Q. Meng, and Y. Feng, The Impact of Evaporation Process on Thermal Performance of Roofs Model Development and Numerical Analysis. Berkeley, CA, USA: Lawrence Berkeley National Laboratory, 2016.
G. N. Tiwari, A. Kumar, and M. S. Sodha, "A review—Cooling by water evaporation over roof," Energy Conversion and Management, vol. 22, no. 2, pp. 143–153, Jan. 1982. DOI: https://doi.org/10.1016/0196-8904(82)90036-X
P. M. Cuce and S. Riffat, "A state of the art review of evaporative cooling systems for building applications," Renewable and Sustainable Energy Reviews, vol. 54, pp. 1240–1249, Feb. 2016. DOI: https://doi.org/10.1016/j.rser.2015.10.066
L. Zhang, X. Liu, Q. Meng, and Y. Zhang, "Experimental study on the impact of mass moisture content on the evaporative cooling effect of porous face brick," Energy Efficiency, vol. 9, no. 2, pp. 511–523, Apr. 2016. DOI: https://doi.org/10.1007/s12053-015-9377-8
N. Grich, W. Foudhil, S. Harmand, and S. B. Jabrallah, "Numerical simulation of water spray transport along a plate of a heat exchanger," Journal of Thermal Analysis and Calorimetry, vol. 143, no. 5, pp. 3887–3895, Mar. 2021. DOI: https://doi.org/10.1007/s10973-020-09356-w
N. B. Khedher, "Numerical Study of the Thermal Behavior of a Composite Phase Change Material (PCM) Room," Engineering, Technology & Applied Science Research, vol. 8, no. 2, pp. 2663–2667, Apr. 2018. DOI: https://doi.org/10.48084/etasr.1824
S. Ahmadi, M. Irandoost Shahrestani, S. Sayadian, M. Maerefat, and A. Haghighi Poshtiri, "Performance analysis of an integrated cooling system consisted of earth-to-air heat exchanger (EAHE) and water spray channel," Journal of Thermal Analysis and Calorimetry, vol. 143, no. 1, pp. 473–483, Jan. 2021. DOI: https://doi.org/10.1007/s10973-020-09268-9
J. I. Kindangen and M. K. Umboh, "Design of evaporative-cooling roof for decreasing air temperatures in buildings in the humid tropics," AIP Conference Proceedings, vol. 1818, no. 1, Mar. 2017, Art. no. 020023. DOI: https://doi.org/10.1063/1.4976887
T. Chati, K. Rahmani, T. T. Naas, and A. Rouibah, "Moist Air Flow Analysis in an Open Enclosure. Part A: Parametric Study," Engineering, Technology & Applied Science Research, vol. 11, no. 5, pp. 7571–7577, Oct. 2021. DOI: https://doi.org/10.48084/etasr.4344
P. Tewari, S. Mathur, and J. Mathur, "Thermal performance prediction of office buildings using direct evaporative cooling systems in the composite climate of India," Building and Environment, vol. 157, pp. 64–78, Jun. 2019. DOI: https://doi.org/10.1016/j.buildenv.2019.04.044
E. Zanchini and C. Naldi, "Energy saving obtainable by applying a commercially available M-cycle evaporative cooling system to the air conditioning of an office building in North Italy," Energy, vol. 179, pp. 975–988, Jul. 2019. DOI: https://doi.org/10.1016/j.energy.2019.05.065
W. Aich, "3D Buoyancy Induced Heat Transfer in Triangular Solar Collector Having a Corrugated Bottom Wall," Engineering, Technology & Applied Science Research, vol. 8, no. 2, pp. 2651–2655, Apr. 2018. DOI: https://doi.org/10.48084/etasr.1857
J. E. Ramis, "Modelagem da transferência de calor em lajes de cobertura de terminais de passageiros aeroportuários," Ph.D. dissertation, Instituto Tecnológico de Aeronáutica, São José dos Campos, Brasil, 2016.
ASHRAE, Fundamentals: 2001 Ashrae Handbook, Inch-Pound Edition. New York, NY, USA: American Society of Heating, Refrigerating and Air-Conditioning Engineers, 2001.
W. H. Ito et al., "On the Thermal Stresses Due to Weathering in Natural Stones," Applied Sciences, vol. 11, no. 3, Jan. 2021, Art. no. 1188. DOI: https://doi.org/10.3390/app11031188
M. Iqbal, An Introduction To Solar Radiation. New York, NY, USA: Academic Press, 1983.
M. A. Goforth, G. W. Gilchrist, and J. D. Sirianni, "Cloud effects on thermal downwelling sky radiance," in Proceedings of SPIE, Orlando, FL, USA, Apr. 2002, vol. 4710, pp. 203–213.
T. L. Bergman, F. P. Incropera, D. P. DeWitt, and A. S. Lavine, Fundamentals of Heat and Mass Transfer, 7th edition. Hoboken, NJ, USA: John Wiley & Sons, 2011.
S. Whitaker, Elementary Heat Transfer Analysis. New York, NY, USA: Pergamon, 1976.
M. N. Ozisik, Heat Transfer: A Basic Approach, International Ed edition. New York, NY, USA: McGraw-Hill, 1985.
W. H. McAdams, Heat transmission, 3rd edition. New York, NY, USA: McGraw-Hill, 1954.
J. Monteith and M. Unsworth, Principles of Environmental Physics: Plants, Animals, and the Atmosphere, 4th edition. Amsterdam, Boston: Academic Press, 2013.
O. Tetens, "Uber einige meteorologische Begriffe," Zeitschrift Geophysic, vol. 6, pp. 297–309, 1930.
F. W. Murray, "On the Computation of Saturation Vapor Pressure," Journal of Applied Meteorology and Climatology, vol. 6, no. 1, pp. 203–204, Feb. 1967. DOI: https://doi.org/10.1175/1520-0450(1967)006<0203:OTCOSV>2.0.CO;2
L. A. Richards, "Capillary conduction of liquids through porous mediums," Physics, vol. 1, no. 5, pp. 318–333, Nov. 1931. DOI: https://doi.org/10.1063/1.1745010
M. N. Ozisik, Heat Conduction, 2nd ed. New York, NY, USA: Wiley, 1993.
J. Thomas, R. R. Frost, and R. D. Harvey, "Thermal conductivity of carbonate rocks," Engineering Geology, vol. 7, no. 1, pp. 3–12, Jun. 1973. DOI: https://doi.org/10.1016/0013-7952(73)90003-3
C. D. Kern, Evaluation of Infrared Emmission of Clouds and Ground as Measured by Weather Satellites. Office of Aerospace Research, US Air Force, 1965.
E. Barreira, E. Bauer, N. Mustelier, and V. Freitas, "Measurement of materials emissivity – Influence of the procedure," in 13th International Workshop on Advanced Infrared Technology & Applications, Pisa, Italy, Sep. 2015.
M. Farzamian, F. A. Monteiro Santos, and M. A. Khalil, "Estimation of unsaturated hydraulic parameters in sandstone using electrical resistivity tomography under a water injection test," Journal of Applied Geophysics, vol. 121, pp. 71–83, Oct. 2015. DOI: https://doi.org/10.1016/j.jappgeo.2015.07.014
P. A. Domenico and F. W. Schwartz, Physical and chemical hydrogeology. New York, NY, USA: Wiley, 1990.
K. Parajuli, M. Sadeghi, and S. B. Jones, "A binary mixing model for characterizing stony-soil water retention," Agricultural and Forest Meteorology, vol. 244–245, pp. 1–8, Oct. 2017. DOI: https://doi.org/10.1016/j.agrformet.2017.05.013
M. Th. van Genuchten, "A Closed-form Equation for Predicting the Hydraulic Conductivity of Unsaturated Soils," Soil Science Society of America Journal, vol. 44, no. 5, pp. 892–898, 1980. DOI: https://doi.org/10.2136/sssaj1980.03615995004400050002x
M. Mannich, "Desenvolvimento de Solucoes Analiticas e Numericas da Equacao de Richards," Ph.D. dissertation, Universidade Federal do Parana, Curitiba, Brazil, 2008.
W. R. Gardner, "Some Steady-State Solutions of the Unsaturated Moisture Flow Equation with Application to Evaporation from a Water Table," Soil Science, vol. 85, pp. 228–232, Apr. 1958. DOI: https://doi.org/10.1097/00010694-195804000-00006
How to Cite
MetricsAbstract Views: 374
PDF Downloads: 180
Copyright (c) 2022 T. Scussiato, W. H. Ito, J. Ramis, P. I. Braga de Queiroz
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish with this journal agree to the following terms:
- Authors retain the copyright and grant the journal the right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) after its publication in ETASR with an acknowledgement of its initial publication in this journal.