Research Article
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Mathematical modelling of soil temperature depend on two dimensional heat conductivity equation

Year 2015, Volume: 30 Issue: 3, 287 - 291, 08.12.2015

İmanverdi Ekberli Coşkun Gülser

https://doi.org/10.7161/anajas.2015.30.3.287-291
Cited By: 1

Abstract

Distribution of temperature along soil surface and profile is a factor which affects on soil properties and fertility significantly. In this research, two dimensional heat conductivity equation was investigated in case of heterogeneous heat distribution regardless of heat source in media. Also, prediction of temperature change along soil profile was shown in a numerical example using the solution obtained. ty=t(x,0)=t₀+Acos(2πx/Ʌ) boundary condition was used in prediction of soil surface temperature considering soil surface temperature (ty) as a periodic function of x and assuming that surface temperature waves are not distributed equally.

Keywords

Heat flow intensity two dimensional heat conductivity equation heat waves soil temperature

References

  • Adjali, M. H., Davies, M., Ni Riain, C., Littler, J. G., 2000 a. In situ measurements and numerical simulation of heat transfer beneath a heated ground floor slab. Energy and Buildings, 33: 75-83.
  • Adjali, M. H., Davies, M., Rees, S.W., Littler, J.G., 2000 b. Temperatures in and under a slab-on-ground floor: two- and three-dimensional numerical simulations and comparison with experimental data. Building and Environment, 35: 655-662.
  • Arias-Penas, D., Castro-García, M.P., Rey-Ronco, M.A., Alonso-Sánchez, T., 2015. Determining the thermal diffusivity of the ground based on subsoiltemperatures. Preliminary results of an experimental geothermalborehole study Q-THERMIE-UNIOVI. Geothermics, 54: 35–42.
  • Awe, G.O., Reichert, J.M., Wendroth, O.O., 2015. Temporal variability and covariance structures of soil temperature in a sugarcane field under different management practices in southern Brazil. Soil & Tillage Research, 150: 93–106.
  • Bronson, R., 1994. Diferansiyel Denklemler. Teori ve Problemleri. Schaum Serisinden. Yayın No: 210 (Türkçesi: Prof. Dr. H.Hilmi HACISALİHOĞLU), s. 77-82.
  • Brown J.W. and Churchill R.V., 1993. Fourier Series and Boundary Value Problems,McGraw-Hill, Inc., New York, s: 129-167.
  • Campbell, G. S., 1985. Soil physics with BASIC. Transport models for soil-plant systems. Developments in Soil Science, vol. 14. Dept. of Agronomy and Soils, Washington State University, Pullman, USA.
  • Chacko, P.T., Renuka, G., 2002. Temperature mapping, thermal diffusivity and subsoil heat flux at Kariavattom of Kerala. Proceedings of the Indian Academy of Science, 111:79–85.
  • Dardo, G.O., Pousa, J.L., Leonardo, P., 2001. Predicting temperature and heat flow in a sandy soil by electrical modeling. Soil Science Society of America Journal, 65:1074–1080.
  • Davison, A.V., Piedrahita, R.H., 2015. Temperature modeling of a land-based aquaculture system for theproduction of Gracilaria pacifica: Possible system modifications toconserve heat and extend the growing season. Aquacultural Engineering, 66: 1–10.
  • Demir, H., Koyun, A., Temir, G., 2009. Heat transfer of horizontal parallel pipe ground heat exchanger and experimental verification. Applied Thermal Engineering, 29:224–233.
  • Derradji, M., Aiche, M., 2014. Modeling the soil surface temperature for natural cooling of buildings in hot climates. Procedia Computer Science, 32: 615 – 621.
  • De Vries, D.A., 1963. Thermal properties of soil. In: Physics of plant environment. Amsterdam, North-Holland, p. 210-235.
  • Ekberli, İ., 2006a. Isı iletkenlik denkleminin çözümüne bağlı olarak topraktaki ısı taşınımına etki yapan bazı parametrelerin incelenmesi. O.M.Ü. Zir. Fak. Dergisi, 21(2): 179-189.
  • Ekberli, İ., Gülser, C., Özdemir, N., 2005. Toprakların Termo-Fiziksel Özellikleri ve Isısal Yayınım Katsayısının Değerlendirilmesi. O.M.Ü. Zir. Fak. Dergisi, 20(2): 85-91.
  • Elias, E.A., Cichota, R., Torriani, H.H., Lier Q. J.,2004. Analytical soil–temperature model correction for temporal variation of daily amplitude. Soil Science Society of America Journal, 68:784–788.
  • Ghasemi-Fare, O., Basu, P., 2013. A practical heat transfer model for geothermal piles. Energy and Buildings, 66:470–479.
  • Ghuman, B.S., Lal, R., 1981. Predicting diurnal temperature regime of a tropical soil. Soil Science, 132:247–252.
  • Gusak, A.A., 1973. Posobiye k reşeniyu zadaç po vısşey matematike. BGU Pres, Minsk, s. 490-497.
  • Güngör, F., 2000. Diferansiyel Denklemler. İstanbul Üniversitesi Fen-Edebiyat Fakültesi, Yayın No: 980. Beta Basım Yayım Dağıtım A.Ş., s. 77-87.
  • Haris, R.N., 2007. Variations in air and ground temperature and the POM-SAT model: results from the Northern Hemisphere. Climate of the Past, 3:611–621.
  • İsacenko, V.P., Osipova, V. A., Sukomel, A.S., 1981. Teploperedaça. Energoizdat Press, Moskova, 417s.
  • Kanjanakijkasem, W., 2015. A finite element method for prediction of unknown boundary conditions in two-dimensional steady-state heat conduction problems. International Journal of Heat and Mass Transfer, 88:891–901
  • Kupiec, K., Larwa, B., Gwadera, M., 2015. Heat transfer in horizontal ground heat exchangers. Applied Thermal Engineering, 75:270–276.
  • Lei, S., Daniels, J.D., Bian, Z., Wainaina, N., 2011. Improved soil temperature modeling. Environmental Earth Sciences, 62:1123–1130.
  • Luikov, A.V., 1948. Teploprovodnost nestaçionarnıx proçessov. Gosudarstvennoye Energetiçeskoye İzdatelstvo, Moskova-Leningrad, 232 s.
  • Mahrer, Y., Katan, J., 1981. Spatial soil temperature regime under transparent polyethylene mulch: numerical and experimental studies. Soil Science, 131:83–87.
  • Mihalakakou, G., 2002. On estimating soil surface temperature profiles. Energy and Buildings, 34:251–259.
  • Nowamooz, H., Nikoosokhan, S., Lin, J., Chazallon, C., 2015. Finite difference modeling of heat distribution in multilayer soils with time-spatial hydrothermal properties. Renewable Energy, 76:7-15.
  • Ochsner, T.E., Horton, R.,Ren, T., 2001. A new perspective on soil thermal properties. Soil Science Society of America Journal, 65:1641-1647.
  • Patron, W.J., 1984. Predicting soil temperatures in a short grass steppe. Soil Science, 138:93–101.
  • Rees, S. W., Adjali, M. H., Zhou, Z and Davies, M. and Thomas, H. R., 2000. Ground heat transfer effects on the thermal performance of earth-contact structures. Renewable and Sustainable Energy Reviews, 4: 213-265.
  • Sısyev, V.V., 1986. Modelirovaniye proçessov v landşaftno-geoximiçeskix sistemax, Moskva, Nauka, s:37-78.
  • Sofyan, S.E., Hu, E., Kotousov, A., 2014. Modelling of a horizontal geo heat exchanger with an internal source term approach. Energy Procedia, 61:104 – 108.
  • Terkot, D., şubert, Dj., 1985. Geodinamika. Geologiçeskiye prilojeniya fiziki sploşnıh sred. 1çast,. Moskva, Mir, s: 219-320.
  • Yang, W., Kong, L., Chen, Y., 2015. Numerical evaluation on the effects of soil freezing on underground temperature variations of soil around ground heat exchangers. Applied Thermal Engineering, 75: 259-269.
  • Zhang,, G., Xia, C., Sun, M., Zou, Y., Xiao, S., 2013. A new model and analytical solution for the heat conduction of tunnel lining ground heat exchangers. Cold Regions Science and Technology, 88: 59–66.
  • Zheng, D., Hunt Jr., E.R., Running, S.W., 1993. A daily soil temperature model based on air temperature and precipitation for continental applications. Climate Research, 2:183–191.

İki boyutlu ısı iletkenliği denklemine baglı olarak toprak sıcaklığının matematiksel modellenmesi

Year 2015, Volume: 30 Issue: 3, 287 - 291, 08.12.2015

İmanverdi Ekberli Coşkun Gülser

https://doi.org/10.7161/anajas.2015.30.3.287-291
Cited By: 1

Abstract

Toprak yüzeyi ve profili boyunca sıcaklığın dağılımı, toprak özelliklerine ve verimliliğine önemli düzeyde etki yapan bir faktördür. Bu araştırmada, toprak yüzeyinde sıcaklığın hotorejen yayılması durumunda, ortamda ısı kaynağını göz önüne almayan iki boyutlu ısı iletkenliği denklemi incelenmiştir. Aynı zamanda, elde edilen çözümünün kullanılması ile toprak profili boyunca sıcaklık değişiminin tahmin edilmesinin mümkünlüğü sayısal örnek üzerinde gösterilmiştir. Toprak yüzey sıcaklığının (ty) x’in periyodik fonksiyonu olduğu göz önüne alınarak, denklemin çözümünde yüzey sıcaklık dalgalarının eşit yayılmadığı varsayılmış ve toprak yüzey sıcaklığının tahmininde ty=t(x,0)=t₀+Acos(2πx/Ʌ) sınır koşulu kullanılmıştır.

Keywords

Isı akımı yoğunluğu iki boyutlu ısı iletkenliği denklemi sıcaklık dalgaları toprak sıcaklığı

References

  • Adjali, M. H., Davies, M., Ni Riain, C., Littler, J. G., 2000 a. In situ measurements and numerical simulation of heat transfer beneath a heated ground floor slab. Energy and Buildings, 33: 75-83.
  • Adjali, M. H., Davies, M., Rees, S.W., Littler, J.G., 2000 b. Temperatures in and under a slab-on-ground floor: two- and three-dimensional numerical simulations and comparison with experimental data. Building and Environment, 35: 655-662.
  • Arias-Penas, D., Castro-García, M.P., Rey-Ronco, M.A., Alonso-Sánchez, T., 2015. Determining the thermal diffusivity of the ground based on subsoiltemperatures. Preliminary results of an experimental geothermalborehole study Q-THERMIE-UNIOVI. Geothermics, 54: 35–42.
  • Awe, G.O., Reichert, J.M., Wendroth, O.O., 2015. Temporal variability and covariance structures of soil temperature in a sugarcane field under different management practices in southern Brazil. Soil & Tillage Research, 150: 93–106.
  • Bronson, R., 1994. Diferansiyel Denklemler. Teori ve Problemleri. Schaum Serisinden. Yayın No: 210 (Türkçesi: Prof. Dr. H.Hilmi HACISALİHOĞLU), s. 77-82.
  • Brown J.W. and Churchill R.V., 1993. Fourier Series and Boundary Value Problems,McGraw-Hill, Inc., New York, s: 129-167.
  • Campbell, G. S., 1985. Soil physics with BASIC. Transport models for soil-plant systems. Developments in Soil Science, vol. 14. Dept. of Agronomy and Soils, Washington State University, Pullman, USA.
  • Chacko, P.T., Renuka, G., 2002. Temperature mapping, thermal diffusivity and subsoil heat flux at Kariavattom of Kerala. Proceedings of the Indian Academy of Science, 111:79–85.
  • Dardo, G.O., Pousa, J.L., Leonardo, P., 2001. Predicting temperature and heat flow in a sandy soil by electrical modeling. Soil Science Society of America Journal, 65:1074–1080.
  • Davison, A.V., Piedrahita, R.H., 2015. Temperature modeling of a land-based aquaculture system for theproduction of Gracilaria pacifica: Possible system modifications toconserve heat and extend the growing season. Aquacultural Engineering, 66: 1–10.
  • Demir, H., Koyun, A., Temir, G., 2009. Heat transfer of horizontal parallel pipe ground heat exchanger and experimental verification. Applied Thermal Engineering, 29:224–233.
  • Derradji, M., Aiche, M., 2014. Modeling the soil surface temperature for natural cooling of buildings in hot climates. Procedia Computer Science, 32: 615 – 621.
  • De Vries, D.A., 1963. Thermal properties of soil. In: Physics of plant environment. Amsterdam, North-Holland, p. 210-235.
  • Ekberli, İ., 2006a. Isı iletkenlik denkleminin çözümüne bağlı olarak topraktaki ısı taşınımına etki yapan bazı parametrelerin incelenmesi. O.M.Ü. Zir. Fak. Dergisi, 21(2): 179-189.
  • Ekberli, İ., Gülser, C., Özdemir, N., 2005. Toprakların Termo-Fiziksel Özellikleri ve Isısal Yayınım Katsayısının Değerlendirilmesi. O.M.Ü. Zir. Fak. Dergisi, 20(2): 85-91.
  • Elias, E.A., Cichota, R., Torriani, H.H., Lier Q. J.,2004. Analytical soil–temperature model correction for temporal variation of daily amplitude. Soil Science Society of America Journal, 68:784–788.
  • Ghasemi-Fare, O., Basu, P., 2013. A practical heat transfer model for geothermal piles. Energy and Buildings, 66:470–479.
  • Ghuman, B.S., Lal, R., 1981. Predicting diurnal temperature regime of a tropical soil. Soil Science, 132:247–252.
  • Gusak, A.A., 1973. Posobiye k reşeniyu zadaç po vısşey matematike. BGU Pres, Minsk, s. 490-497.
  • Güngör, F., 2000. Diferansiyel Denklemler. İstanbul Üniversitesi Fen-Edebiyat Fakültesi, Yayın No: 980. Beta Basım Yayım Dağıtım A.Ş., s. 77-87.
  • Haris, R.N., 2007. Variations in air and ground temperature and the POM-SAT model: results from the Northern Hemisphere. Climate of the Past, 3:611–621.
  • İsacenko, V.P., Osipova, V. A., Sukomel, A.S., 1981. Teploperedaça. Energoizdat Press, Moskova, 417s.
  • Kanjanakijkasem, W., 2015. A finite element method for prediction of unknown boundary conditions in two-dimensional steady-state heat conduction problems. International Journal of Heat and Mass Transfer, 88:891–901
  • Kupiec, K., Larwa, B., Gwadera, M., 2015. Heat transfer in horizontal ground heat exchangers. Applied Thermal Engineering, 75:270–276.
  • Lei, S., Daniels, J.D., Bian, Z., Wainaina, N., 2011. Improved soil temperature modeling. Environmental Earth Sciences, 62:1123–1130.
  • Luikov, A.V., 1948. Teploprovodnost nestaçionarnıx proçessov. Gosudarstvennoye Energetiçeskoye İzdatelstvo, Moskova-Leningrad, 232 s.
  • Mahrer, Y., Katan, J., 1981. Spatial soil temperature regime under transparent polyethylene mulch: numerical and experimental studies. Soil Science, 131:83–87.
  • Mihalakakou, G., 2002. On estimating soil surface temperature profiles. Energy and Buildings, 34:251–259.
  • Nowamooz, H., Nikoosokhan, S., Lin, J., Chazallon, C., 2015. Finite difference modeling of heat distribution in multilayer soils with time-spatial hydrothermal properties. Renewable Energy, 76:7-15.
  • Ochsner, T.E., Horton, R.,Ren, T., 2001. A new perspective on soil thermal properties. Soil Science Society of America Journal, 65:1641-1647.
  • Patron, W.J., 1984. Predicting soil temperatures in a short grass steppe. Soil Science, 138:93–101.
  • Rees, S. W., Adjali, M. H., Zhou, Z and Davies, M. and Thomas, H. R., 2000. Ground heat transfer effects on the thermal performance of earth-contact structures. Renewable and Sustainable Energy Reviews, 4: 213-265.
  • Sısyev, V.V., 1986. Modelirovaniye proçessov v landşaftno-geoximiçeskix sistemax, Moskva, Nauka, s:37-78.
  • Sofyan, S.E., Hu, E., Kotousov, A., 2014. Modelling of a horizontal geo heat exchanger with an internal source term approach. Energy Procedia, 61:104 – 108.
  • Terkot, D., şubert, Dj., 1985. Geodinamika. Geologiçeskiye prilojeniya fiziki sploşnıh sred. 1çast,. Moskva, Mir, s: 219-320.
  • Yang, W., Kong, L., Chen, Y., 2015. Numerical evaluation on the effects of soil freezing on underground temperature variations of soil around ground heat exchangers. Applied Thermal Engineering, 75: 259-269.
  • Zhang,, G., Xia, C., Sun, M., Zou, Y., Xiao, S., 2013. A new model and analytical solution for the heat conduction of tunnel lining ground heat exchangers. Cold Regions Science and Technology, 88: 59–66.
  • Zheng, D., Hunt Jr., E.R., Running, S.W., 1993. A daily soil temperature model based on air temperature and precipitation for continental applications. Climate Research, 2:183–191.
There are 38 citations in total.

Details

Primary Language Turkish
Journal Section Soil Science and Plant Nutrition
Authors

İmanverdi Ekberli

Coşkun Gülser

Publication Date December 8, 2015
Published in Issue Year 2015 Volume: 30 Issue: 3

Cite

APA Ekberli, İ., & Gülser, C. (2015). İki boyutlu ısı iletkenliği denklemine baglı olarak toprak sıcaklığının matematiksel modellenmesi. Anadolu Tarım Bilimleri Dergisi, 30(3), 287-291. https://doi.org/10.7161/anajas.2015.30.3.287-291
AMA Ekberli İ, Gülser C. İki boyutlu ısı iletkenliği denklemine baglı olarak toprak sıcaklığının matematiksel modellenmesi. ANAJAS. October 2015;30(3):287-291. doi:10.7161/anajas.2015.30.3.287-291
Chicago Ekberli, İmanverdi, and Coşkun Gülser. “İki Boyutlu ısı iletkenliği Denklemine Baglı Olarak Toprak sıcaklığının Matematiksel Modellenmesi”. Anadolu Tarım Bilimleri Dergisi 30, no. 3 (October 2015): 287-91. https://doi.org/10.7161/anajas.2015.30.3.287-291.
EndNote Ekberli İ, Gülser C (October 1, 2015) İki boyutlu ısı iletkenliği denklemine baglı olarak toprak sıcaklığının matematiksel modellenmesi. Anadolu Tarım Bilimleri Dergisi 30 3 287–291.
IEEE İ. Ekberli and C. Gülser, “İki boyutlu ısı iletkenliği denklemine baglı olarak toprak sıcaklığının matematiksel modellenmesi”, ANAJAS, vol. 30, no. 3, pp. 287–291, 2015, doi: 10.7161/anajas.2015.30.3.287-291.
ISNAD Ekberli, İmanverdi - Gülser, Coşkun. “İki Boyutlu ısı iletkenliği Denklemine Baglı Olarak Toprak sıcaklığının Matematiksel Modellenmesi”. Anadolu Tarım Bilimleri Dergisi 30/3 (October 2015), 287-291. https://doi.org/10.7161/anajas.2015.30.3.287-291.
JAMA Ekberli İ, Gülser C. İki boyutlu ısı iletkenliği denklemine baglı olarak toprak sıcaklığının matematiksel modellenmesi. ANAJAS. 2015;30:287–291.
MLA Ekberli, İmanverdi and Coşkun Gülser. “İki Boyutlu ısı iletkenliği Denklemine Baglı Olarak Toprak sıcaklığının Matematiksel Modellenmesi”. Anadolu Tarım Bilimleri Dergisi, vol. 30, no. 3, 2015, pp. 287-91, doi:10.7161/anajas.2015.30.3.287-291.
Vancouver Ekberli İ, Gülser C. İki boyutlu ısı iletkenliği denklemine baglı olarak toprak sıcaklığının matematiksel modellenmesi. ANAJAS. 2015;30(3):287-91.

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