# Dynamic and Static Investigation of Ground Heat Exchangers Equipped with Internal and External Fins
## 1 Introduction  
Ground source heat pump systems (GSHPs) offer the potential for significant energy savings, through low maintenance costs and contribute to reducing greenhouse gas emissions. GSHPs are used for heating/cooling residential and commercial buildings and for providing domestic hot water [1, 2]. The use of GSHPs proved to be a technically feasible and economically viable solution as compared to other heating, ventilation, and air conditioning (HVAC) systems in cooling dominated environments such as the Arabian Peninsula where the air conditioning (A/C) systems account for 65% of the energy consumption strictly from fossil fuels [3]. The GSHPs are fully capable of meeting the cooling demands of buildings in hot climates, specifically, in the Middle East [4]. The most common type of ground heat exchangers is the vertical ground heat exchanger with the length of 100-150 m [5, 6]. The empty space between pipe and borehole wall is usually filled with grout which helps to improve the heat transfer rate between circulating fluid inside pipes and ground [7]. Since the initial costs of vertical borehole heat exchangers (BHEs) are relatively high due to the limitations of drilling and manpower, efforts are being made to increase the heat transfer rate between fluid and soil around the pipes in various ways, and thus reducing the borehole depth [8]. Several methods have been proposed to calculate and reduce borehole resistance. In most thermal response test (TRT) analyses, the average of inlet and outlet temperatures of the fluid is used tocalculate the fluid temperature along the ground heat exchanger (GHE). Some researchers have shown that the average of inlet and outlet temperatures can cause significant errors in results and suggested alternative methods for estimating the average fluid temperature [9; 10; 11; 12; 13; 14; 15]. Grout materials are used to fill spaces between pipes and the soil around the borehole which can play a key role in the heat transfer rate between the fluid and undisturbed ground. Some researchers have worked on the effects of different grout materials on the thermal performance of the GSHP systems and found the best option for grout materials [16]. [PERSON] et al. [17] used four different boreholes with the same geometric and geological characteristics but different grout materials to determine the appropriate thermal conductivity. They reported a proper type of grout for the thermal response test. [PERSON] et al. [18] evaluated the performance of various grout materials and tested the effects of adding graphite on the thermal properties of grout material. Various numerical and analytical models have been developed based on linear source or cylindrical source theory. Using these models, the influences of different geometric and thermal properties on the static and dynamic behavior of a BHE has been investigated. [PERSON] [19] proposed a G-function to describe borehole performance. G-function curves based on borehole geometry were reported by calculating the soil temperature using the finite difference method. [PERSON] [20] developed an analytical solution for calculating the vertical temperature profile of the fluid inside the pipe and the ground temperature distribution by using Laplace transforms. There are several studies about GSHPs based on the Computational Fluid Dynamics (CFD) method. [PERSON] et al. [21] investigated the effects of Reynolds number, pipe diameter, and U-tube shank spacing on the thermal performance of GHEs. The results showed that by increasing the Reynolds number and the pipe diameter in laminar flow, better performance can be achieved. [PERSON] et al. [22] performed a numerical and experimental study to evaluate the temperature distribution in GHE using three U-tube BHEs with the same diameters and different depths. [PERSON] et al. [23] compared the thermal performance of U-tube heat exchangers with four different standard diameters. [PERSON] et al.