An Analytical Model for Transient Heat Transfer with a Time-Dependent Boundary in Solar- and Waste-Heat-Assisted Geothermal Borehole Systems: From Single to Multiple Boreholes +
Footnote †: This paper is an extended version of our paper published in the 15 th International Conference on Heat Transfer, Fluid Mechanics and Thermodynamics and Editorial Board of Applied Thermal Engineering (ATE HEFAT 2021). [PERSON]  
1 Mining Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia; [EMAIL_ADDRESS]  
[PERSON]  
2 Department of Mining and Materials Engineering, McGill University, Montreal, QC H3A 2A7, Canada; [EMAIL_ADDRESS]  
[PERSON]  
2 Department of Mining and Materials Engineering, McGill University, Montreal, QC H3A 2A7, Canada; [EMAIL_ADDRESS]  
[PERSON]  
3 Disk Mining Engineering Institute, The University of British Columbia, Vancouver, BC V6T 1Z4, Canada; [EMAIL_ADDRESS]  
[PERSON]  
4 Mechanical Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia; [EMAIL_ADDRESS]  
[PERSON]  
1 Mining Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia; [EMAIL_ADDRESS]  
[PERSON]  
4 Mechanical Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia; [EMAIL_ADDRESS]  
[PERSON]  
1 Mining Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia; [EMAIL_ADDRESS]  
[PERSON]  
4 Mechanical Engineering Department, King Abdulaziz University, Jeddah 21589, Saudi Arabia; [EMAIL_ADDRESS]  
[PERSON]  
2 Department of Mining and Materials Engineering, McGill University, Montreal, QC H3A 2A7, Canada; [EMAIL_ADDRESS]  
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pandemic and economic downturn. A rapid transformation from the fossil-fuel-dependent energy system towards a more sustainable one based on renewable energy sources is one of the most important challenges facing humankind. Geothermal energy is a renewable energy source with great potential in lowering environmental impact and greenhouse gases emissions [1]. Unlike other renewable energy sources (e.g., solar, wind, tidal), geothermal energy can be extracted regardless of meteorological conditions, thus rendering it a stable source of energy [2]. Worldwide applications of direct use of geothermal energy was recently reviewed in [3; 4]; some of the new trends in various kinds of geothermal systems were listed in [5]. Numerous studies on geothermal technology have been investigated: from straight pipes [6] to helical loops [7], from ground-based to phase-change-materials-based energy storage [8], from energy- to exergy-technical assessments [9], and from techno-economic evaluations to policy making [10; 11; 12]. Among all geothermal technologies, ground-source heat pump (GSHP) systems coupled with vertical geothermal borehole heat exchangers (BHEs) have been recognized to be one of the most energy efficient solutions for space heating and cooling in residential and commercial buildings [13; 14]. Those in a coaxial closed-loop configuration (a.k.a., coaxial closed-loop heat exchangers) have shown great promise as a feasible technique in deep geothermal reservoirs [15] because of larger heat exchanging areas and better performance [16; 17; 18]. Since the working fluid is circulated from the geothermal boreholes to the heat pump, an accurate thermal evaluation of the boreholes is of great interest in a GSHP. The thermal analysis of geothermal boreholes cannot only predict the energy performance of a GSHP, but also allows engineers to optimize the GSHP design, e.g., the number of boreholes used, the depths and layout of boreholes. There have been considerable modeling approaches to BHEs, traditionally categorized as numerical, hybrid (or semi-analytical), and analytical methods.