BULETINUL INSTITUTULUI POLITEHNIC DIN IAŞI

72 Bogdan Horbaniuc et al
of equations will be solved via the Gauss elimination technique which is best
suited for this case, due to the simple structure of the matrix.
3. Results and Discussion
The presented mathematical model and the numerical treatment have
been applied to an example involving a single tube arrangement and the
temperature field as well as the stored/extracted heat have been determined in
order to analyze the process dynamics.
The tube material is steel (λ W = 50 W/mK, a W = 13.8 m 2 /s). The
thermophysical properties of the soil (type: clay soil) are (Arya, 2001):
λ S = 0.25 W/mK, a S = 0.18 m 2 /s, c S = 0.89 kJ/kgK, ρ S = 1600 kg/m 3 ). The tube
geometry: R 0 = 25 mm, R W = 28 mm, L = 10 m. The radius of the SSM domain:
R = 428 mm. Temperatures: t HF = 100°C, t ∞ = 12°C. The convective heat
transfer coefficient: k = 1000 W/m 2 K. Finite difference grids: number of nodes
in the wall: N W = 5; number of nodes in the SSM region: N S = 100. The time
step has been set to 1 second.
The duration of the charge, respectively discharge processes has been set
to 8 hours (28,800 seconds). A single charge/discharge cycle has been
considered. Two computer programs have been written: one for charge and one
for discharge. Exit data from the first program are entry data for the discharge
one. Figs. 2 through 4 refer to the heat storage charging process.
Fig. 2 represents the plot of the temperature field in the SSM versus time.
Fig. 2 – Temperature field evolution during the charging process.