2.1.1. Theoretical and Numerical Simulations
Several theoretical models based on differential equations have been reported in the literature to simulate the thermodynamic behaviour of GSHPs [
12]. The main goal of these mathematical models is to determine the heat temperature carried by the fluid along the pipe from the borehole under certain operating conditions. For example, based on the transient heat conduction in the borehole, the temperature distribution of the ground might be obtained by solving the following partial differential equation:
where
T stands for the ground temperature distribution at a distance
r,
represents the borehole radius,
q is the heating rate per length of the source,
t is the time,
is the initial temperature of the ground, and
and
are the thermal conductivity and diffusivity of the ground. Some numerical methods are commonly used to solve the previous equations. However, additional models are required to improve the approximations of the heat temperature carried by the fluid along the pipe, as in [
12]. Moreover, such models must consider the GSHP fluid properties to obtain accurate results to optimize the GHSP performance.
Therefore, nanofluids are attractive in the effort to achieve higher efficiencies and reduce the system size. The volumetric concentrations of nanofluids in the range from 0.1% to 1% can result in a reduction in the borehole thermal resistance. Additionally, they can reduce the borehole length depending on the kind of nanofluid.
For example, with a 1% concentration of Cu, graphite, Ag, and CuO, the reductions in the length of boreholes were
,
,
and
, respectively [
13]. The authors who found this discussed and compared different papers focused on nanofluids used in geothermal systems to improve heat transfer. They concluded that a heat transfer enhancement is dependent on several factors, including the type of nanofluid, concentration, and system specification. Thus, the reduction in the heat exchanger sizes and the borehole sizes used in the geothermal-based system affect the efficiency of the system.
The application of nanofluids in heat pipes, due to their superior thermophysical properties, was addressed in [
14]. This work summarizes and provides the outcomes of experimental and theoretical studies of some nanofluids as working fluids in heat pipes, such as metals (Cu, Ag, and Gold, etc.) and metal-oxides (Al
2O
3, CuO, MgO, ZnO, TiO
2, Fe
2O
3, and SiO
2, etc.) to obtain an enhanced thermal performance. The results include the calculations of thermal efficiency, thermal resistance, the effective thermal conductivity, surface temperature gradient and the convective heat transfer coefficient in the evaporator and condenser section. Different configurations of heat pipes were reported according to different sizes and shapes related to the application requirements, integrating summaries and tables. In conclusion, the heat transfer mechanisms depend on the type of heat pipe, the characteristics of the nanofluids, the design and operating parameters of the heat pipes, etc.
An important drawback in the vertical GHE is the existence of possible nanoparticle sedimentation when the system remains static. To solve this, the paper [
15] carried out numerical simulations with nanoparticles of Al
2O
3-water and Fe
3O
4-water at constant temperature (
C) to visualize the sedimentation inside the exchanger. When the fluid is static, the nanoparticles accumulate after many hours of sedimentation. This can be averted by a high-speed flow, a pulsed flow, or by optimizing the geometry of the bottom borehole. This work simulates important data, such as the effects of soil temperature, the Reynolds number, the effect of the size, type, the concentration of the nanoparticles, the suspension stability of composites, gravity, the effects of a pulsed flow, the borehole geometry and the turbulent eddy diffusivity.
The recent report in [
16] shows that the heat transfer characteristics of current fluids are greatly improved by suspending nanosized solid particles with diameters of less than 100 nm. Recent research of nanofluids has analyzed the convective heat transfer rate, thermal achievement rate, viscosity, surface tension, friction factor, environmental impact, thermo-physical properties, the effect of fluid temperature, inlet velocity, the use of a surfactant to achieve a better stability of nanofluids, particle size, and the volume concentration effects, for instance, [
17,
18,
19]. Several types of nanoparticles have been widely studied by researchers. Thus, the suspension of small amounts of nanoparticles of oxides (Al
O
, CuO, TiO
, Fe
O
, SiO
, etc.), metals (Cu and Ag), and carbon nanotubes (CNTs) in traditional base fluids (water, ethylene glycol, propylene glycol, engine oil, etc.) have increased thermal conductivity [
16].
On the other hand, some works study the relevance of the physical properties of a nanofluid. The work [
20] presents an approach using nanofluids in geothermal energy applications as working fluids to extract more energy from reservoirs and for space heating/cooling and industrial applications. In this research, a sensitivity analysis was performed to demonstrate the importance of the fluid viscosity and the heat capacity in geothermal energy production. The potential to apply nanofluids as working fluids in abandoned oil wells converted into double-pipe heat exchangers is studied, taking advantage of the significant improvement in the heat transfer of nanofluids. This research remarks on the importance of the thermophysical properties of nanofluids; for example, the viscosity and specific heat capacity and the fluid circulation rate improve the performance and the cost-efficient production of geothermal energy.
A study of the effects of the Al
O
-water nanofluid, as the heat transfer fluid, to reduce the length of a vertical GHE in a GSHP is presented in [
21]. The authors used an innovative nanofluid which was engineered by dispersing solid nanoparticles in conventional heat transfer fluids. They evaluated the impact of the optimized thermophysical properties of nanofluids, such as the thermal conductivity and viscosity, which play prominent roles in convection heat transfer, both of which are optimized by using the Multi-Objective Flower Pollination Algorithm (MOFPA). The bore length computation with an Al
O
-water mix reduced the borehole length by 1.3% more than when just using water. Another important result revealed that the use of tubes and grout reduces the bore length due to their thermal resistances.
Some applications of nanorefrigerants and nanolubricants, mainly in air conditioning and heat pumps, were realized in [
22]. The physical-thermal properties of suspended nanoparticles in refrigerants and lubricating oils of refrigeration systems were reviewed, classifying them into six topics: studies related to the Al
O
, CuO, TiO
, CNT, and Cu nanoparticles and studies related to other nanoparticles (
/polyester mixtures with SiO
, CuO, POE and other
mixtures with NiFe
O
). The solubility of the mineral-based nanorefrigeration oil (MNRO) in different fluids,
,
,
, and
was experimentally investigated. The conclusion of this work is that nanorefrigerants have a much higher and stronger temperature dependence on thermal conductivity at very low particle concentrations than conventional refrigerants. Additionally, the effect of carbon nanotubes (CNTs) enhances heat transfer.
In [
7] is presented an exhaustive review of theoretical and experimental works related to the use of nanotechnology in renewable energy systems (solar, hydrogen, wind, biomass, geothermal and tidal energies). This review includes works for all renewable energies, with the use of nanofluids, nanomaterials, and nanoparticles. In the case of geothermal energy, different applications with nanotechnology were addressed, with two of them being highlighted. The first to be addressed was the use of nanofluids to cool fluids inside pipes exposed to high temperatures, using nanofluids to cool sensors and electronic devices in drilling machines and GHE depending on temperature (low, medium or high), and district heating applications using networks piped hot water to heat many buildings in entire communities. Second, the authors noted that nanofluids can be used as a working fluid to extract energy from the ground and process it in a power plant system or produce large amounts of working energy.
Similarly, the paper [
23] summarizes works with the use of suspended nanoparticles to enhance the heat transfer characteristics into the heat pipes. The researchers found new opportunities with the use of nanofluids, e.g., to improve the thermal efficiency and reduce the thermal resistance of the heat pipe. This work summaries experimental and theoretical studies of some of the preparation methods, processes and heat transfer characteristics of nanofluids. The thermal performance of the nanofluid heat pipe was superior to that of the conventional working fluid, usually water.
A preliminary evaluation of the potential of nanofluids that guarantee the vertical temperature of the heat carrier in the borehole was performed in [
24], using the mathematical model in [
25]. Some assumptions were imposed on the model, for example, the variations of temperature with depth, the heat conduction in the vertical direction within the pipe wall, the grout, the borehole thermal resistance between the pipe and the borehole wall, and the ground. The objective was to know which nanoparticle leads to the best performance in the borehole heat exchanger, showing the properties and comparative cost of various nanoparticles. The best thermal performance was found with Cu, followed by graphite, SiO
, and Ag. On the other hand, Al
O
and CuO were the worst choices. The mixes tested using CuO, Al
O
, Ag, SiO
, Al, graphite and Cu with a volumetric concentration of 1% allowed reductions in the borehole length to
,
,
,
,
,
and
%, respectively. Therefore, the cost of GHE increases using nanofluids depending on the shape and size of the particles, plus the energy consumption of the circulation pump due to the increased pressure drop. However, this cost is marginal compared to the costs of nanoparticles due to the low value of the mass flow rate.
The results of numerical simulations for the application of the CuO-water and Al
O
-water nanofluids, as the working fluids of a geothermal GHE, were reported in [
26]. The simulations were compared with literature data. The Reynolds Averaged Navier–Stokes (RANS) equations with the shear stress transport (SST) k-
turbulence model were numerically solved to represent the flow and the physical properties of the nanofluids using the available correlations. Fluent software and the SIMPLEC algorithms were used for the coupling between pressure and velocity, and the finite volume method on collocated cells was applied to discretize the RANS equations. In the same research, some studies of the influences of natural factors in the analytical method, such as groundwater flow on heat pump design, was presented to obtain the temperature distribution along the heat exchanger. Additionally, the modeling and optimization of a novel combined cooling, heating, and power (CCHP) cycle driven by geothermal and solar energies using the CuO-water nanofluid are presented. The results show that the CuO-water nanofluid allows a higher heat extraction than the alumina-water nanofluid, but at the cost of higher pressure losses and pumping powers.
A numerical solution to optimize MgO-water nanofluids to reduce the cost and increase the heat transfer coefficient is analyzed in [
27]. The optimization was performed by the non-dominated sorting genetic algorithm (NSGA-II), which has a significant capability to achieve an optimal response. For this purpose, the solid volume fraction (
), Reynolds number (Re) and the diameter of nanoparticles (Dp) were selected as the optimization variables. Thus, to reach the heat transfer coefficient of 280 W/m
K, the cost is equal to USD 355 per liter in the first generation and USD 218 per liter in the last generation (total population of 50 members and repetition of 15 times) according to the Pareto diagram. This result proves that theoretically the optimization has been able to reduce the cost by up to 38%.
The work of [
28] presents some numerical and theoretical studies of heat transfer applied to rotating machines that convert electrical energy into mechanical energy or vice versa, using the CuO-
(ethylene glycol) nanofluid under different conditions inside the heat pipe. The properties of nanofluids were implemented in a wide range of numerical models, using experimental data to study the effects of the mass of the fluid to be inserted in the pipe, the speed of rotation of the machine, and the size and concentration of nanoparticles to evaluate the performance of heat transfer. A new methodology based on Particle Swarm Optimization (PSO) in MATLAB© was presented to solve the equations (flow of nanofluids inside the heat pipe) and the heat transfer equation. The authors give the thermo-physical properties of pure CuO and pure
at the reference temperature and the thermophysical properties of the CuO-
nanofluid. The heat transfer through the heat pipe depends on various factors such as the input nanofluid mass, the rotation speed of the heat pipe, nanoparticle size and nanoparticle concentration.
Recent studies found, by using numerical simulations, several novel phenomena such as a radiative effect for an electrically conductive Williamson nanofluid [
29]; a radiative effect for a Casson nanofluid with solar thermal radiation [
30]; variability in the viscosity and conductivity of hybrid nanofluids [
31]; and heat transfer in a magneto two-phase nanofluid enclosed in an adiabatic rotating cylinder [
32]. All of these have potential applications in GSHPs.
A summary of the results reported by the previous researchers using theoretical and numerical simulations, classified by the type of applied nanofluid and its application, is shown in
Table 1 and
Table 2.
2.1.2. Experimental Work
An experimental study was presented in [
11] using Al
O
/ethylene glycol-water (EG-water) nanofluids applied to a spiral and U-type GHEs. The GSHP system was used to heat a 21 m
room located in Sivas Cumhuriyet University Campus, Turkey, where normally the weather is cold. The authors addressed the improvement of thermal conductivity only in Al
O
nanofluids, but these studies do not provide test results related to the use of nanofluids in the specific system of GHEs or GSHPs. Other studies show that nanofluids have better heat transfer properties than base fluids under constant heat flow. Their effects have been investigated in many areas, such as radiators, heat exchangers and electronic devices. Researchers have described the experimental setup, including the heat load calculation, the trench depth and GHE design based on the ASHRAE book, using a 25% EG ratio of the fluid to prevent freezing. The experiments showed that a concentration of
% nanofluid in the U-type heat exchanger increased the performance by 19% compared to glycol-water and by
% compared to the nanofluid with a concentration of
%. The nanofluid with a concentration of
% increased the heat transfer rate by up to 2% in a U-type GHE and
% in a spiral GHE according to the unit pipe length heat exchange rates.
The thermal performances and economic efficiencies of different nanofluids (Ag, MgO,
and
), comparing the price, the efficiencies and the benefices, to improve the heat transfer are addressed in [
33]. The experiments compared the relative thermal conductivity and the relative viscosity of
-water,
-water, Ag-water and MgO-water. The
-water nanofluid showed higher relative thermal conductivity (
vol.%) and relative viscosity than the other nanofluids. Some factors influenced the thermal conductivity of nanofluids, e.g., the method of nanofluid production (single and two stage), the type of surfactant, sonication rate, the device of characteristic measurement, nanoparticle size and shape. The thermal efficiency of carbon nanofluids is slightly better than that of oxide nanofluids, although their price is several times higher. For this reason, the authors state that the use of nanofluids for heat transfer is not profitable and can only be used in high-tech and high-profit industries.
The existence of two different methods (one- and two-step methods) useful for the preparation of nanofluids is explained in [
34]. The authors noted that thermal conductivity and viscosity are important parameters to study the potential for heat transfer enhancement. They presented experimental and theoretical studies affecting thermal conductivity, for example, particle type, charge, size, and shape, including environmental parameters such as the base fluid, concentration, temperature, and dwell time. In summary, the material type has a great effect on the thermal conductivity of nanofluids such as graphene,
, Au, Ag, etc., which are more conductive than the TiO
,
, and SiO
nanofluids. However, it appears that the type of material has little effect on the viscosity of nanofluids. Most of the results reveal that the viscosity and thermal conductivity increase as the particle load increases [
34].
Olson [
35] patented a nanofluid to increase heat transfer, introducing nanoparticles into the GHE (propylene glycol or a heat transfer oil). The inventor improved the thermal conductivity by 40% or more, achieved with only a
% nanoparticle concentration. These nanofluids are quite different from conventional two-phase flow mixtures because it is recommended to use a new parameter for nanofluids, the so-called Mouromtseff number (Mo), which is a function of the viscosity (
), the conductivity thermal (
), density (
) and specific heat (Cp). The improved heat transfer reduced the installation cost because the circulation loop can be smaller and the pumping cost is also less expensive.
An experimental study in a closed loop of cold water with a storage tank is presented in [
36]. An electrical heater controlled by adjusting the voltage and a cooling coil immersed inside a storage tank using a refrigerant (R11) with a mixture of titanium nanoparticles sized 21 nm were implemented. The aim of this research was to improve the efficiency of the heat transfer inside the pipe. The authors prepared five mixtures of different nanofluid concentrations using an ultrasonic homogenizer. The experiments were conducted with different work conditions and the experimental device was designed in a modular form using various heat fluxes.
A summary of the results reported by the previous researchers with experimental work given in
Table 3.