Mathematical modeling of soil temperature change depending on heat amount

Year 2020, Volume: 24 Issue: 2, 229 - 240, 24.06.2020

İmanverdi Ekberli , Coşkun Gülser

https://doi.org/10.29050/harranziraat.638162

Cited By: 1

Abstract

Change in the amount of heat in soil layers has a significant effect on thermo-physical properties of soil, soil microclimate, soil formation processes and etc. In this study, one dimensional thermal conductivity equation of soil is investigated according to similarity theory in case of instant cooling of soil layer. The solution is simply expressed using the error and complementary error functions. During the cooling process of the soil layer, the change in temperature of soil depth with respect to time is shown with a theoretical expression as a function of soil depth and heat amount. The gravimetric heat capacity of the research soil was determined as 950.404 J kg-1 °C-1. Volumetric heat capacity and heat quantity of the soil were determined in the range of 2.324∙ 106 - 2.654 ∙ 106 J m-3 °C-1 and 1.027∙106 - 3.227∙107 J m-2, respectively. The soil temperature decreases by an average of 49.20% after 10 hours of heat treatment in the 0-10 cm soil layer in case of constant heat amount. The temperature decrease in the lower layers of the soil occurs at a low level. The reduction process is also significantly dependent on the gravimetric heat capacity, volumetric heat capacity and the coefficient of thermal diffusion of the soil.

Keywords

Soil temperature, Heat quantity, Similarity theory, Heat capacity, Soil depth

Toprak sıcaklığının ısı miktarına bağlı olarak değişiminin matematiksel modellenmesi

Abstract

Toprak katmanlarındaki ısı miktarının değişimi, toprağın termo-fiziksel özellikleri, toprak mikro iklimi, toprak oluşum süreçleri vb. üzerinde önemli bir etkiye sahiptir. Bu çalışmada, toprak profilindeki katmanların anlık soğuması durumunda toprağın bir boyutlu ısı iletkenlik denklemi benzerlik teorisine göre incelenmiştir. Çözüm, hata ve tamamlayıcı hata fonksiyonları kullanılarak basit bir şekilde ifade edilmiştir. Toprak katmanının soğuma sürecinde, toprak derinliği boyunca sıcaklığın zamana göre değişimi, toprak derinliği ve ısı miktarının bir fonksiyonu olarak teorik bir ifade ile gösterilmiştir. Araştırma toprağının gravimetrik ısı kapasitesi 950.404 J kg-1 °C -1 olarak saptanmıştır. Araştırma dönemlerinde toprağın hacimsel ısı kapasitesi ve ısı miktarı sırasıyla (2.324-2.654)∙106 J m-3 °C -1 ve 1.027∙106-3.227∙107 J m-2 aralığında belirlenmiştir. Isı miktarının sabit olması durumunda, toprağın 0-10 cm katmanında 10 saat boyunca kaybedilen ısı işleminden sonra toprak sıcaklığı ortalama %49.20 azalmaktadır. Toprak profilinin alt katmanlarında ise sıcaklığın azalması düşük düzeyde gerçekleşmektedir. Azalma süreci aynı zamanda toprağın gravimetrik ısı kapasitesine, hacimsel ısı kapasitesinin ve ısısal yayınım katsayısının değişimine de önemli derecede bağlı olmaktadır.

Keywords

Toprak sıcaklığı, Toprak sıcaklığı, Isı miktarı, Benzerlik teorisi, Isı kapasitesi, Toprak derinliği

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