Analytical and Numerical Studies of Transient Heat Transfer in Soil for Geothermal Systems

The study of geothermal systems requires a good knowledge of heat transfers in the depth of the soil. The aim of this work is to study the distribution of temperature in the ground under the climatic conditions of Togo. The analytical and numerical solutions of unidirectional heat transfer equation assuming the soil as a semi-infinite medium are found. The analytical solution is validated by comparing the results of the present work to those found in literature. A good qualitative agreement between these results was noted. The results show that the attenuation depth decreases when the attenuation accuracy of the thermal wave increases. The analysis of the effect of moisture content indicates that the increasing in soil conductivity with moisture result in the decreasing of the attenuation depth. Soil temperature increases when increasing soil thermal diffusivity. It is found also that, soil temperatures decrease with depth and stabilize around an average value of 30°C for depths greater than about 5.8 m for all type of soil studied in the month of March which is the hottest month of the year in Togo. A gradual decrease in temperature can be seen from March to August (hot period) followed by stabilization at around 28°C with a depth of 5.8 m. The phenomenon is reversed for the months of September to February (cold period). The soil warms up slowly during the day and cools down slowly at night because of the thermal inertia of the soil. A decrease in amplitude of the thermal wave near ground surface, is observed when the Leaf Area Index (LAI) increases. However, ils influence on the stabilization depth is not very significant. Stabilization of soil temperatures in March month is observed at a depth of about 40 cm for all LAI with a value of 37°C.