The Finite Element Method at Design of the Greenhouse Floor Heating System: Mathematical Model and Simulation

Abstract

in this study, the greenhouse floor heating system was modelled and simulated by the finite element method. The floor cross-section envisaged layers which were formed soil 30 cm , fine sand 6 cm , coarse sand 6 cm , perlite 6 cm and gravel 12 cm was devided to 100 triangular elements with 66 nodal points. The distance between heating lines in the floor heating system is 30 cm. The temperature changes being in connection with source heat of 3.5 W m-1, 4.0 W m-1 and 4.5 W m-1 were investigated under boundary conditions which were the air temperature of 15 °C and the convection transfer coefficent of 10 W m-2°C-1 on the soil surface. In these source fluxes, temperature values at heating point were determined as 28.10, 29.97 and 31.84°C, respectivelly. The temperature values at nodal points were calculated changing between 17.67 and 31.47 °C at conditions which were sol! moisture of 0.15 m3m-3 , soil thermal conductivity of 0.819 W m-1°C-1 and source heat fiux of 4 W m-1. The different conditions were analysed and presented using temperature contour lines. As a result, in practices of the greenhouse floor heating, the finite element method could be used as a powerful tool of design.

Keywords

• Floor heating in greenhouses, finite element method, mathematical modeIling, simulation

Sera Taban Isıtma Sisteminin Tasarımında Sonlu Eleman Yöntemi: Matematiksel Model ve Simülasyon

Abstract

Bu çal ışmada, sera taban ı s ı tma sistemi, sonlu eleman yöntemi kullan ı larak modellenmi ş ve simüle edilmiştir. Toprak 30 cm , ince kum 6 cm , kaba kum 6 cm , perlit 6 cm ve çak ı l 12 cm tabakalar ı ndan oluştuğ u öngörülen taban kesiti, 66 düğ üm noktal ı 100 adet üçgen elemana bolünmüştür. Taban ı s ı tma sisteminde ı s ı tma hatlar ı aras ı uzakl ı k 30 crrı 'd ı r. Toprak üst yüzeyinde hava s ı caklığı n ı n 15 °C ve konveksiyonla ı s ı transfer katsay ı s ı n ı n 10 W m-2 °C-1 olduğ u s ı n ı r koşullar alt ı nda 3.5 W m'1, 4.0 W m-1 ve 4.5 W rn'l 'lik ı s ı akı ları ndan kaynaklanan s ı cakl ı k değişimleri araşt ı rı lm ışt ı r. Bu kaynak ak ı lannda ı s ı tma noktas ı ndaki sı cakl ı k değerleri s ı ras ı yla 28.10, 29.97 ve 31.84°C olarak saptanm ışt ı r. Toprak neminin 0.15 m3m-3, toprak ı s ı l kondüktivitesinin 0.819 W m-1°C-1, ve kaynak ı s ı akı s ı n ı n 4 W m-1 olduğ u koş ullarda dü ğ üm noktalar ı ndaki s ı cakl ı k değerleri 17.67 ile 31.47 °C aras ı nda değ iştiği hesaplanm ışt ı r. Farkl ı koşullar eş s ı cakl ı k eğ rileri kullan ı larak irdelenmiştir. Sonuç olarak, sera taban ı s ı tma uygulamalar ı nda sonlu eleman yöntemi, güçlü bir tasar ı m arac ı olarak kullan ı labilir.

Keywords

• Seralarda taban ı s ı tma, sonlu eleman yöntemi, matematiksel modelleme, simillasyon

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