Abstract
The purpose of this paper is to obtain the annual variation in underground temperature distribution around a buried heat source through unsteady heat conduction analysis using the finite element method. In district heating/cooling systems, there is a considerable quantity of heat flow by conduction from the buried district piping into the soil, so it is often required to take into consideration its thermal effect on the surroundings in the preliminary design. The ground temperature, however, varies with time in a periodic manner under the influence of the outside air temperature, and there is a time lag in thermal conduction due to the large heat capacity of the ground. On that account, analysis in such a temperature field is apt to become so difficult that the steady heat conduction analysis has been generally used so far disregarding the temperature gradient of the ground characteristic. Consequently these results have been far apart from the reality. To settle this problem, we shall try the unsteady heat conduction analysis applying the finite element method. This method is used in various fields now because of good conformity to boundaries, simple treatment of boundary conditions and general application of computer programs. Here, using the weighted residual method (Galerkin process) we shall formulate the unsteady two-dimensional heat-conduction equation and the boundary conditions in a finite element form. In this case, difference calculus is applied to approximate the unsteady term. Before applying this method of analysis, we first solved a simple problem of which the analytical solution is known and assessed the accuracy and practicability of the algorithms. Then as a real problem, the underground temperature distribution around the buried concrete trench used to pass district piping through is for reference obtained at summer, winter and intermediate season by the steady state analysis. We also analyze the same problem by the unsteady state one. When the yearly variation (disregarding the daily variation) of the outside air temperature is applied as a cosine function and the unsteady state computation is continued for several-year periods, then a periodic steady state will be established in the temperature field with time. If at the same time, the air temperature within the trench is provided, then we can obtain the almost real underground temperature distribution. Making time step of about five-days, we divided a year into 72 equallength portions and calculated four-year period. From these results, the annual variation in underground temperature distribution around the buried trench was obtained. And also the temperature-time history for several points around the trench was obtained. As a result of this analysis, it will be seen that near the ground surface the temperature distribution of the season characteristic is shown, but as depth increases, the seasonal variation decreases by degrees and only the isotherms expand little by little and uniformly with time. Further more, comparing these results with steady state ones, obvious differences are recognized between them, and in particular at summer. This results from the simple linear gradient in the temperature field in steady state analysis. Therefore the steady state analysis is not practicable, but the unsteady state one is desirable in the analysis of temperature distribution in a field which varies in a complex manner throughout a year like the ground temperature.
