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Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process
American Journal of Applied Mathematics
Volume 8, Issue 3, June 2020, Pages: 89-97
Received: Mar. 26, 2020; Accepted: May 12, 2020; Published: May 27, 2020
Authors
Mohammed Hirpho Tobe, Department of Mathematics, Ambo University, Ambo, Ethiopia
Zerihun Kinfe Birhanu, Department of Mathematics, Hawassa University, Hawassa, Ethiopia
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Abstract
Investigating the heat transfer in aquifer thermal energy storage system is of interest since a deeper understanding of this phenomenon can be used to improve the behavior of a building, including relevant thermal parameters such as heating, cooling, and control systems. In this paper, we have presented a pair of coupled partial differential equations, which characterize the temperature distribution within the aquifer thermal energy storage system during the thermal injection process. The heat transfer equation is considered when the temperature difference between the solid and fluid phases is very small. We showed the solution to the model is positive and bounded. Simulations have been carried out for a constant Peclet number of 0.5, 500 and 100. Hot water is considered being injected throughout the depth of a single injection well into the aquifer at one end of the domain and the temperature of the hot water is assumed to be constant throughout the whole injection period. The finite element method has been utilized to solve the governing equations numerically. The results showed that the temperature front of injected hot water passes through the aquifer from left to right and the temperature of the aquifer increases gradually with the passage of injection time. Furthermore, if the Peclet number is very high the temperature of injected hot water makes a high change on the aquifer temperature, while if Peclet number is less than 1 there is a little change on the aquifer temperature as time t increases.
Keywords
Porous Media, Heat Transfer, Fluid Flow, Finite Element Method, Homogeneous Aquifer Thermal Energy Storage System
Mohammed Hirpho Tobe, Zerihun Kinfe Birhanu, Numerical Investigation of Temperature Distribution in a Homogeneous Aquifer Thermal Energy Storage System During Thermal Injection Process, American Journal of Applied Mathematics. Vol. 8, No. 3, 2020, pp. 89-97. doi: 10.11648/j.ajam.20200803.13
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