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Theoretical Analysis on Application of Nanofluids in Ground Source Heat Pumps for Building Cooling
Subhabrata Mishra#1, Dr. Sikata Samantaray*2, Dr. Debendra K Das$3
#PG Student, Department of Mechanical Engineering, ITER, SOA Deemed to be University
*Associate Professor, Department of Mechanical Engineering, ITER, SOA Deemed to be University
$Visiting Professor, Department of Mechanical Engineering, ITER, SOA Deemed to be University Bhubaneswar, India, 751030
Abstract—A theoretical study has been carried out to compare the heat transfer and fluid dynamic performance of water-based nanofluids as working fluids. With different volumetric concentrations (0-4 %) of nanofluids, a theoretical analysis was done to study the performance of Heat Pump for space cooling application. Also, a comparison was made to study the effect of ground temperature on pumping power and heat transfer. One more comparison has drawn to study COP of the GSHP with ground temperature. The 4% CuO nanofluid possess highest COP index about 3.58 among all other nanofluids and basefluid. The present study reveals that nanofluids can be an effective heat transfer fluid for GSHP application which needs to be explored more in future.
Keywords-Flow rate; Ground source heat pump (GSHP); Ground temperature; Horizontal ground heat exchanger (HGHX); Inlet and outlet temperature; nanofluids; thermal conductivity; viscosity; heat transfer fluid (HTF).
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I. INTRODUCTION
Energy is a very important requirement of the modern society. The scarcity of energy is the most critical challenge for developing countries like India, China, and others. The huge demand for energy leads to spending high price for oil and gas.
Keeping that in mind renewable sector are the most efficient for coming future. For building cooling and heating GSHP are the most efficient technique in India. These are flexible for use like in summer for cooling and in winter for heating. Cooling and heating effect is available due to earth’s relative temperature.
The ground temperature in India about three meter beneath the earth surface remains constant. A study was performed by Girijasaran [19] at IIM Ahmedabad to record the ground temperature. They found that under 3-meter depth the average temperature remains constant around 27ᵒC during summer.
GSHP technology needs to adopt latest techniques to increase the COP. For space heating and cooling applications, horizontal ground heat exchangers are useful and less expensive as compared to vertical type. Recently more work is going on in this area with the objective to show an effective increase in COP of the GSHP system. For cooling purpose to meet the high demand and to reduce the length of GHX, these system are coupled with cooling towers/chillers. Karabacak et al. [3]
reported that after one year of operation the soil temperature increased by 0.5 ⁰C and they recommended to use multiple GHX with minimum distance between the heat exchangers as 4 to 5 m in order to avoid heat accumulation in the ground. Healy et. al. [5] performed a numerical analysis to understand the effects of various system parameters on the performance of GSHP system. The results revealed that GSHP systems are preferable economically over conventional systems for space heating/cooling applications. Sabruet. al. [6] performed a
review analysis on GSHP system utilization and application, heat exchanger construction and improvement to achieve better performance from GSHP system. They also concluded that the single system can be utilized for both space heating and cooling. Omer [7] performed a review analysis on GSHP system to extend its applicability and usability in UK. This study includes various design parameters like ground loops, ground systems which give a brief idea towards its application, costs and benefits. It concluded that best management practices during the installation and decommission can lead to avoiding environmental issues and promote the utilization of renewable energy.
The GSHP technology is well utilized for space heating applications in European and Western countries. Congendoet.
al. [15] performed a numerical analysis using computational fluid dynamics (CFD) modelling on horizontal air-ground heat exchangers for Zero Energy Buildings (ZEB) in Europe. The study shows significant benefits in summer as well as in winter by reducing energy consumption for space conditioning.
However, in the past decade, some of the Asian countries started focusing on the technical challenges of GSHP systems for both heating and cooling applications. Fuji et. al. [14]
studied horizontal-slinky ground heat exchangers numerically to evaluate the performance for some mild climatic region of Japan, where soil is not subjected to long term freezing in winter. This study reveals that better performance can be achieved if the ground surface will be covered with snow layers. In India, Murugesan et al. [20] had studied the viability of GSHP for Himalayan cities. The study revealed that GSHP systems are economical in term of payback time and producing no harm to the environment. It reveals that cities like Darjeeling need only 5.2 years to recover the total costs towards this system. Kaushal [17] performed a review analysis
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29 on GSHP system for space conditioning. This study concluded
that a well-designed system can reduce electricity consumption up to 25-30 %. Therefore accurate design and testing is much important to get optimum output. And these systems are more beneficial for Western Himalayan region in India.
In the present study, we have performed a theoretical analyses on GSHP with the application of nanofluids.
Nanofliuds are the mixture of liquid and solid particles having particle size of the order of less than 100 nm (1nm=10-9m). It came into existence in 1995 by S. Choi in Argonne National Laboratory [4]. In recent years nanotechnology has reached significant heat transfer applications in different sectors like Engineering and Medicine. Nanofluids attracted many researchers’ attention because of it’s unusual increment in thermal conductivity (nearly 10%) over the basefluid [20]. Das et. al. [11] performed review analysis on heat transfer characteristic of nanofluid and concluded many important results from the study of different researchers. This study concluded that nanaofluids have greater ability for heat transfer. In case of oxides nanoparticles, increment in thermal conductivity of fluids are relatively low, whereas metallic nanoparticles increase thermal conductivity substantially at lower concentrations. Heat transfer enhancement decreases with increase in particle size for the same volumetric concentration. Vajjhaet. al. [12] performed review analysis on effect of temperature and particle concentrations on the thermo- physical properties, heat transfer and pumping power of nanofluids. Viscosity, density, specific heat and thermal conductivity are the functions of nanoparticle concentration and temperature and the performance of the nanofluid varying accordingly. This study concluded that addition of nanoparticles increases thermal conductivity moderately while viscosity significantly. Also this study reveals the important correlations to estimate these properties. Vajjhaet. al. [16]
performed a numerical investigation on nanofluid heat transfer to propose new Nusselt number and friction factor correlations.
Also they proposed a modified correlation of Koo
&Kleinstreuer [24] for thermal conductivity. Xuan and Roetzel [13] proposed an improved version of Pak and Cho [4]
correlation for specific heat capacity which is used in this present study. Their study reveals that nanofliuds possess slightly better thermal capacity at higher temperature. Deyet. al.
[25] performed a review analysis on nanofluid preparation, stabilization and its thermo-physical properties to present a summary on the research and developments in this field. This study concluded that nanofluids are better than conventional heat transfer fluid (HTF) in terms of better thermo-physical property.
As previous studies of these nanofluids explored the fluid mechanics and heat transfer characteristics, here the knowledge is used as the working fluid in the GHX in order to improve the performance of GSHP. Three different nanoparticles (Al2O3, CuO, SiO2) dispersed in water been considered as working fluid to study performance of GSHP system analytically.
II. METHODOLOGY A. Ground Source Heat Pump
GSHP are the heat pumps which use the earth as a reservoir for building heating and cooling application. These systems are
better as compared to the conventional heating and cooling appliances in terms of energy consumption as well as future aspects. For heating, extracting the heat from the ground is free, so there is no fuel cost. For cooling, the ground is naturally at a lower temperature, so no energy investment is necessary to create a low-temperature sink. A schematic diagram of a GSHP is given below in Fig.1.
B. Ground heat exchanger design
Ground heat exchangers(GHX) are the heat exchangers which will exchange the heat between the working fluid and the ground(or soil). In terms of design aspect, various parameters affecting the performance of GHX are pipe material, length, working fluid and soil. Heat load can be estimated for space by referring ASHRAE cooling and heating load calculation manual. The heat load is to be taken by the GHX to provide the cooling or heating effect. The coefficient of performance can be given by ;
𝐶𝑂𝑃 = 𝑄𝐿
𝑄𝐻−𝑄𝐿 [7]
(1)
Where, QH = Load on the GHX QL= Heat pump capacity 𝑄𝐻= 𝑚𝐿× 𝐶𝐿 𝑇𝐿 𝑖𝑛− 𝑇𝐿 𝑜𝑢𝑡 (2)
Wherer, 𝑚𝐿= mass flow rate of working fluid
𝐶𝐿= Specific heat of working fluid 𝑇𝐿 = Temperature of fluid
To estimate the length of the pipe for GHX can be evaluated by using the following correlation;
𝐿 = 𝑚𝐿× 𝐶𝐿× 𝑅𝑡𝑜𝑡𝑎𝑙 ln 𝜃𝐿 𝑖𝑛
𝜃𝐿 𝑜𝑢𝑡 (3) Where, 𝐿 = length of pipe of GHX
𝑅𝑡𝑜𝑡𝑎𝑙 = Total thermal resistance in the GHX
𝜃𝐿 𝑖𝑛 = Temperature difference between inlet fluid and ground temperature
𝜃𝐿 𝑜𝑢𝑡 = Temperature difference between outlet fluid and ground temperature
Mathematically,
𝑅𝑡𝑜𝑡𝑎𝑙 = 𝑅𝐶𝑜𝑛𝑣 .+ 𝑅𝑃𝑖𝑝𝑒 + 𝑅𝑆𝑜𝑖𝑙 (4)
𝑅𝐶𝑜𝑛𝑣 .= 1
𝜋𝐷𝑖ℎ𝐿, 𝑅𝑃𝑖𝑝𝑒 = ln
𝐷 𝑜 𝐷 𝑖
2𝜋𝑘𝑝𝑖𝑝𝑒, 𝑅𝑆𝑜𝑖𝑙 = 1
𝑆𝑘𝑆𝑜𝑖𝑙,
ℎ𝐿=𝑁𝑢×𝑘𝑛𝑓
𝐷𝑖 (5)
Where, S = conduction shape factor for pipe,
𝑆 =
2𝜋𝐿
cosh −1 2𝑧 𝐷 , 𝐿≫𝐷 2𝜋𝐿
𝑙𝑛 4𝑧 𝐷 , 𝑧>3𝐷 2 𝐿≫𝐷 [7] (6)
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TABLEI. THERMO-PHYSICAL PROPERTIES CORRELATIONS OF WATER (BASEFLUID)
Thermo-physical property Correlation Error
Density [10] 𝜌 = 1000 − 0.0178 𝑇 − 4 1.7
0 ≤ T ≤ 100 ᵒC
± 0.2 %
Viscosity [10] ln𝜇
𝜇0= −1.94 − 4.80 𝑧 + 6.74 𝑧2 𝑧 =273 .16
T , 𝜇0= 1.792 × 10−3 kg/ m.s
±1 %
Specific heat 𝐶𝑃 𝑏𝑓 = −1 × 10−4𝑇3+ 0.029𝑇2− 1.7926𝑇 + 4209.6 0 ≤ T ≤ 100 ᵒC
R2 = 0.99
Thermal conductivity 𝑘𝑏𝑓 = −8 × 10−6T2+ 0.0019T + 0.5689 0 ≤ T ≤ 100 ᵒC
R2 = 0.99
C. Basefluid and basefluid correlations
In Western countries, freezing of basefliud is a primary problem as the temperature goes below 0ᵒC (273 K). But in India this will be limited for some places like Himalayan cities.Except these places the average temperature is more than the freezing temperature even in winter. So we have taken water as the basefluid as it is widely available and cheap. New correlations are developed for different thermo-physical properties with respect to temperature. Water properties are taken from Wiley [22] and NIST Chemistry Webbook [21] and curve were fitted to generate the basefluid correlations which are given in Table I.
White’s [10] viscosity correlation is taken to estimate viscosity of the basefluid (water).
D. Correlations for nanofluids
Nanofluids are prepared by adding nanoparticles with different volumetric concentration ratio with the base fluid.
Water-based nanofluids are quite common. Three different nanofluids [Al2O3,CuO,SiO2] have been considered with five different volumetric concentration (ϕ = Vp
Vtotal ), such as 0%, 1%, 2%, 3% and 4%, in order to study the performance of the GSHP. Various correlations are taken from different
Fig.1. Schematic diagram of GSHP system
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31 researchers. Also nanomaterial properties are taken from
handbook [23] in order to make this analysis based on reliable values.
(a) Density of Nanofluid
Density equation for nanofluid is given by Pak & Cho [3]
which is best suited for variable volumetric concentrations.
𝜌𝑛𝑓 = 𝜙𝜌𝑛𝑝+ 1 − 𝜙 𝜌𝑏𝑓 (7) where 𝜌𝑛𝑓,𝜌𝑛𝑝 and 𝜌𝑏𝑓 are the densities of nanofluid, nanoparticle and basefluid respectively and ϕ is the volumetric concentration of nanoparticle.
(b) Viscosity of Nanofluid
Viscosity correlation is given by Vajjha and Das [11] for nanofluid. This viscosity correlation is also concentration dependent, i.e, vary with change in concentration.
𝜇𝑛𝑓 = 𝐴1𝑒𝐴2𝜙 (8)
where𝐴1 and 𝐴2 are curve-fit constants.
(c) Specific heat of Nanofluid
Correlation for specific heat is given by Xuan &Roetzel [12] which is very effective for calculation of specific heat for nanofluid. This is also a concentration-dependent correlation.
𝐶𝑝𝑛𝑓 =𝜙 𝜌𝑛𝑝𝐶𝑝𝑛𝑝+(1−𝜙)𝜌𝑏𝑓𝐶𝑝𝑏𝑓
𝜌𝑛𝑓 (9) where 𝐶𝑝𝑛𝑓,𝐶𝑝𝑛𝑝 and 𝐶𝑝𝑏𝑓 are the specific heat of nanofluid, nanoparticle and basefluid respectively.
(d) Thermal conductivity of Nanofluid
Thermal conductivity correlation is based on two phenomena, i.e., thermal conductivity due to static and due to Brownian motion. Combining these two phenomena thermal conductivity can be obtainable for nanofluid. At first, this correlation (Eq (10)) was proposed by Koo &Kleinstreuer later modified by Vajjha and Das [11].
𝑘𝑠𝑡𝑎𝑡𝑖𝑐 =𝑘𝑛𝑝+(𝑛−1)𝑘𝑏𝑓− 𝑛−1 𝜙 (𝑘𝑏𝑓−𝑘𝑛𝑝)
𝑘𝑛𝑝+(𝑛−1)𝑘𝑏𝑓+𝜙 (𝑘𝑏𝑓−𝑘𝑛𝑝) (10a) where n = shape factor, for spherical shape particle n = 3 and 𝑘𝑛𝑝 and 𝑘𝑏𝑓 are the thermal conductivities of nanoparticle and basefluid respectively.
𝑘𝐵𝑟 = 5 × 104𝛽𝜙𝜌𝑏𝑓𝐶𝑝𝑏𝑓 𝑘𝐵𝑇
𝜌𝑛𝑝𝑑𝑝𝑓(𝑇, 𝜙) (10b)
where, 𝑘𝐵 = 1.38 × 10−23 = Boltzman constant
TABLE II. MATERIAL PROPERTIES OF DIFFERENT NANOPARTICLES
Material Density (kg/m3)
Specific heat (J/kgK)
Thermal Conductivity
(W/mK)
Al2O3 3600 765 36
CuO 6500 533 17.65
SiO2 2220 745 1.4
𝛽 = 𝐴1(100𝜙)−𝐴2 , values of 𝐴1 and 𝐴2 are given in Table 3 below.
𝑓 𝑇, 𝜙 = 2.8217 × 10−2𝜙 + 3.917 × 10−3 𝑇 𝑇0
+ (−3.0669 × 10−2𝜙 − 3.91123 × 10−3)
𝑑𝑝 and𝜌𝑛𝑝 are the nanoparticle diameter and density respectively.
T = absolute temperature and ϕ = volumetric concentration
𝑘𝑛𝑓 = 𝑘𝑠𝑡𝑎𝑡𝑖𝑐 + 𝑘𝐵𝑟 (10)
where𝑘𝑠𝑡𝑎𝑡𝑖𝑐 and 𝑘𝐵𝑟 are given in Eq (10a) and Eq (10b) respectively.
E. Nusselt number and convective heat transfer coefficient Nusselt number is the non-dimensional number which evaluates the convective heat transfer coefficient of the basefluid as well as nanofluid. Many researchers proposed new Nusselt number correlation for different nanofluids. For water, well known Dittus-Bolter correlation [7], which is shown in Eq.
(11). Gnielinski correlation is an alternate correlation to establish the Nusselt number for water, which is presented in Eq. (12). So the present study includes this correlation to establish convective heat transfer coefficient for water. Vajjha and Das [17] proposed a new correlation for Nusselt number of nanofluids, shown in Eq. (13).
For basefluid,
𝑁𝑢𝑏𝑓 = 0.023𝑅𝑒0.8𝑃𝑟0.3 (11)
𝑁𝑢𝑏𝑓 = 0.012(𝑅𝑒0.87− 280)𝑃𝑟0.4 (12)
For nanofluids,
𝑁𝑢𝑛𝑓 = 0.023𝑅𝑒0.8𝑃𝑟0.3 1 + 0.1771𝜙0.1465 (13)
Eq. (13) is valid in the range of :
1.988 <Pr< 13.44, 3000 < Re < 8000, 0 < ϕ < 0.06
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Convective heat transfer coefficient, ℎ =𝑁𝑢 ×𝑘
𝐷ℎ (14)
F. GSHP at CCHRC and parameters for Indian climate For the theoretical analysis, we have taken GSHP specification from GSHP tested at CCHRC, Fairbanks [1].
Indian climate conditions and soil conditions are adopted from the published data for the theoretical study. Soil thermal conductivities are found from literature for India [17]. Soil thermal conductivity is assumed to be 2 W/m-K [17] for the present study. Specifications of GSHP system, CCHRC is given in Table IV. Schematic view of GSHP at CCHRC is shown in Fig.2.Sivasaktivelet. al. [20] performed an experimental study on GSHP system and found that the water inlet temperature to the GHX was 38.4 ⁰C and outlet temperature from the GHX was 33.1 ⁰C. So the present study assumed the mean inlet temperature is to be 38 ⁰C and outlet temperature is to be 33 ⁰C. All thermo-physical properties were evaluated at fluid mean temperature, i.e. at 35.5 ⁰C.
G. Pumping power calculation
To circulate the working fluid in the GHX and as it is a Liquid-to-solid heat exchanger a pump is required. Estimation for pumping power, pressure drop and friction factor can be done by using the following correlations.
Pumping power, 𝑊𝑝 = 𝑚𝐿
𝜂 𝜌𝐿∆𝑃 (15) Where, 𝑚𝐿= mass flow rate of working fluid
𝜂 =pump efficiency
𝜌𝐿=density of the working fluid
∆𝑃 = Pressure drop Pressure drop,
∆𝑃 = 𝑓𝜌𝐿 𝑉2
2𝐷ℎ (16)
where, 𝑓 = Darcy friction factor 𝑉 = Fluid velocity
𝐷ℎ= Hydraluic diameter
Friction factor,
𝑓𝑏𝑓 = 0.3164 × 𝑅𝑒−0.25 , [10] (17) for(2 × 104< 𝑅𝑒 < 106)
For nanofluids, Vajjha and Das [12] proposed a new friction factor correlation which is a modified version of Blasius correlation given in Eq. (14).
𝑓𝑛𝑓 = 0.3164 × 𝑅𝑒−0.25 𝜌𝑛𝑓
𝜌𝑏𝑓 0.707
𝜇𝑛𝑓 𝜇𝑛𝑓
0.108
[12]
(18)
TABLE IV. SPECIFICATION OF GSHP AT CCHRC
Specifications Values
Depth of coil below surface [m] 2.9 Flow rate in the loop [L/min] 62.9
Pipe inner diameter [cm] 1.905
Pipe outer diameter [cm] 2.54
Pumping power [W] 750
No. of GHX loops 6
Compressor work [kW] 6
TABLEIII. CURVE FIT CONSTANTS (𝐴1,𝐴2) FOR 𝛽 FROM VAJJHA AND DAS [12]
Particle 𝑨𝟏 𝑨𝟐 Concentration
(ϕ)
Avg. Particle size(nm)
Temperature (K)
Al2O3 8.4407 1.07304 1% ≤ ϕ ≤ 10% 53 298 ≤ T ≤ 363
CuO 9.881 0.9446 1% ≤ ϕ ≤ 6% 29 298 ≤ T ≤ 363
SiO2 1.9526 1.4594 1% ≤ ϕ ≤ 10% 30 298 ≤ T ≤ 363
ZnO 8.4407 1.07304 1% ≤ ϕ ≤ 7% 29 & 77 298 ≤ T ≤ 363
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33 Fig.2 Schematic diagram of GSHP at C
CHRC [1]
III. RESULTS AND DISCUSSION A. Density
Due to the addition of nanoparticle into basefluid, the density of nanofluid is increasing with volumetric concentration, while increase in temperature results in decrease in density. A plot has been drawn to show the density of nanofluids and basefluid at various volumetric concentrations while the mean fluid temperature is at 35.5 ⁰C presented in Fig.3. From Fig.3 it is clear that, increase in volumetric concentration increases density.
Fig.3 Density of nanofluids at various volumetric concentrations at Tmean=35.5 ⁰C
CuO nanofluid shows the highest density over all other nanofluids and basefluid whereas SiO2 nanofluid shows lower density among all nanofluids. This is due to lower density of SiO2 nanoparticles as compared to that of CuO nanoparticles.
B. Viscosity
Viscosity is the most important parameter which affects the fluid flow mechanism of nanofluids.
Fig.4 Viscosity of nanofluids at various volumetric concentrations at Tmean=35.5 ⁰C
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Addition of nanoparticles increases the viscosity at a greater rate that leads to higher pumping power requirement. So it is important to study the viscosity increase of nanofluids over basefluid for heat transfer application to accurately determine the COP of the system. A plot has been drawn for the viscosity of nanofluids and basefluid at a mean fluid temperature and presented in Fig.4. Increase in particle volumetric concentration results in an increment in viscosity of the fluid. CuO nanofluids show the highest viscosity among all other nanofluids and basefluid.
Fig.5 Specific heat of nanofluids at various volumetric concentrations at Tmean=35.5 ⁰C
C. Specific heat
Specific heat has a greater importance in case of thermal energy storage. High specific heat capacity results in high heat accumulation. Coolants having higher specific heat results in better thermal performance. But the addition of nanoparticle may result in a decrease in specific heat. At higher temperature nanofluids show higher specific heat capacity than the basefluid. A plot has been generated at mean fluid temperature for the specific heat of basefluid and nanofluids at various volumetric concentrations shown in Fig.5. Specific heat diminishes with an increase in volumetric concentration and SiO2 nanofluid possesses the least specific heat in this group.
D. Thermal Conductivity
Thermal conductivity increases with increase in particle volume concentration.
Fig.6 Thermal conductivity of nanofluids at various volumetric conc. at Tmean=35.5 ⁰C
Due to the addition of nanoparticle its thermal conductivity increases over the basefluid. A plot has been generated to compare the thermal conductivity of nanofluids at various concentration and the basefluid shown in Fig.6. It is observed that CuO nanofluid possesses highest thermal conductivity among all other nanofluids and basefluid. The rate of increment in thermal conductivity due to increase in volumetric concentration is high in case of CuO and Al2O3 as compared to SiO2.
E. Fluid outlet temperature
Heat transfer fluid is entering into the GHX at 38 ⁰C and will exit at a lower temperature by rejecting the heat into the ground. A plot is generated for 3 nanofluids having 2%
volumetric concentration at different ground temperature by keeping volume flow rate constant and presented in Fig.7.
Outlet temperature for CuO nanofluid is high whereas water is having lower outlet temperature.
Fig.7 Fluid outlet temperature from GHX at various ground temperatures
F. Thermal resistance
Thermal resistance plays the most important role in heat transfer analysis. It is inversely proportional to the rate of heat transfer. In the present study, three thermal resistances are present across the heat transfer process from the heat transfer fluid (HTF) to the ground.Fig.8 shows the plot between the soil thermal resistance and soil thermal conductivity. The more is the soil thermal conductivity, the lower is the soil thermal resistance.
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35 Fig.8 Soil resistance versus Soil thermal conductivity
G. Pipe length
Pipe length is dependent on the thermal load on the GHX. If the space conditioning thermal load is more, then it requires longer pipe to reject heat. Fig.9 shows the plot between pipe length required to reject each kilowatt of heat to particle volumetric concentrations at constant volume flow rate and ground temperature. Below a volumetric concentration of 2%
all nanofluids analyzed have been proven to require lower pipe length than the basefluid. It is observed that increase in particle volume concentration results in higher length requirement after ϕ = 2%.This occurs, because of the limitation of the constant flow rate of nanofluids. At higher concentrations viscosity increases. For the same velocity, Re goes down, Nu and h go down. So to reject the same amount of heat, it requires more loop length.
Fig.9 GHX pipe length required at a constant flow rate and Tground =27 ⁰C
H. Pumping Power
Pumping power is dependent upon the ground temperature.
Increase in ground temperature results in an increase in GHE pipe length, so as to reject the same amount of heat. As pumping power is directly proportional to pipe length, increase in pipe length will require higher pumping power.
Fig.10 Pumping power variation for various ground temperature for discharging 1 kW of heat
Fig.11 Pumping power required for various volumetric concentrations and ground temperature
A plot has been drawn to show pumping power to reject each kilowatt of heat versus ground temperature in Fig.10 to see the variation. Increase in ground temperature results in more pumping power requirement to reject the same amount of heat.
Another plot is shown in Fig.11 shows the pumping power increment due to increase in particle volume concentrations of nanofluids. Due to increase in particle volume concentration the viscosity is increasing, so the pumping power is increasing.
CuO nanofluid requires highest pumping power among all nanofluids and basefluid, due to its high value of viscosity.
I. Heat Rejection
In order to compare the cooling effect, the amount of heat rejected to the ground per unit length of GHX is calculated.
Amount of heat rejection will vary if the ground temperature will vary.It is clear that heat rejection is inversely proportional to ground temperature. Fig.12 shows the bar graph of heat rejected to the ground per unit length of GHX for varying the ground temperature.It shows that ground temperature affects the heat transfer rate significantly. At lower ground temperature nanofluid heat rejection rate is more as compared to higher ground temperature for different heat transfer fluids.Here CuO nanofluid is the best performer. Another bar graph, Fig.13 is shown to compare the heat rejection to the ground by various nanofluids at different concentrations by keeping the ground temperature constant.
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Fig.12 Heat rejected per unit length of GHX at various ground temperature
CuO nanofluid rejects the highest amount of heat to the ground. In case of SiO2 nanofluid, increase in volumetric concentration to 4% is not increasing the heat transfer rate, much more than the basefluid, water.
Fig.13 Heat rejected per unit length of GHX by various nanofluids at Tground =27 ⁰C
J. COP of the GSHP system
COP of the system is the most important parameter to evaluate the system’s feasibility.
Fig.14 COP with basefluid and nanofluids in the GHX for the same ground temperature of 27 ⁰C
Fig.15 COP with basefluid and nanofluids n GHX for two ground temperatures
Fig.14 shows the bar graph for the COP of the GSHP system for several nanofluids of 2% and 4% concentration, at a constant ground temperature. for various nanofluid.The 4%
CuO nanofluid possess highest COP index, about 3.58 and proves that it is useful to implement nanofluid to increase the performance of GSHP system.All nanofluids give higher COP as compared to the basefluid. Another bar graph, Fig.15 is generated between COP of the system to two ground temperatures by keeping volumetric concentration constant at 2%.It confirms that increase in ground temperature results in a decrease in COP of the system due to a decrease in heat rejection rate.
IV. CONCLUSION
A theoretical analysis was performed to study the GSHP viability and application in order to go for further experimental and numerical analysis in this field. Data and specifications were taken from an actual operating system at CCHRC and from different literatures. Some important results we have found from this analysis are summarized below.
If ground temperature is higher, longer length of GHX pipe will be required. At lower concentration, around 2% and lower all nanofluids studied here require less length as compared to basefluid.
Pumping power increases with an increase in particle volume concentration and ground temperature. The 4% CuO nanofluid requires highest pumping power among all other nanofluid due to increase in viscosity.
But it also promises the highest COP.
Heat rejection per unit length decreases with increase in the ground temperature. The 4% CuO nanofluid shows maximum heat rejection per unit length of GHX pipe due to its higher thermal conductivity and higher convective heat transfer coefficient.
Soil thermal conductivity plays a major role in GSHP system performance. It offers the highest thermal resistance among the three thermal resistances to the heat transfer process. Heat rejection will be more if thermal conductivity of soil will be higher. So it is advisable to use a filler material of high thermal conductivity around the GHX coil.
The COP of a GSHP system decreases with an increase in ground temperature. By employing nanofluid it can be improved. A 4% CuO nanofluid gives highest COP as compared to other nanofluids and basefluid. So nanofluids will be a good heat transfer fluid for GSHP system.
In future, numerical simulations should be performed to corroborate the theoretical results. Using their results a demonstration GSHP should be designed and experiments be conducted to optimize the system.
ACKNOWLEDGMENT
Authors are thankful to CCHRC, Fairbanks, AK, USA for their data and reports on GSHP system for cold climates.
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