Numerical study of the effect of nanoparticles on thermoeconomic improvement of a solar flat plate collector

Accepted Manuscript Research Paper Numerical Study of the Effect of Nanoparticles on Thermoeconomic Improvement of a Solar Flat Plate Collector Farzaneh Hajabdollahi, Kannan Premnath PII: DOI: Reference:

S1359-4311(17)30842-6 http://dx.doi.org/10.1016/j.applthermaleng.2017.08.058 ATE 10940

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

14 February 2017 26 May 2017 9 August 2017

Please cite this article as: F. Hajabdollahi, K. Premnath, Numerical Study of the Effect of Nanoparticles on Thermoeconomic Improvement of a Solar Flat Plate Collector, Applied Thermal Engineering (2017), doi: http:// dx.doi.org/10.1016/j.applthermaleng.2017.08.058

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Numerical Study of the Effect of Nanoparticles on Thermoeconomic Improvement of a Solar Flat Plate Collector Farzaneh Hajabdollahi *, Kannan Premnath Department of Mechanical Engineering, University of Colorado Denver, USA 1

Abstract The influence of the nanoparticle Al2O3 on the thermo-economic optimization of a solar flat plate collector system at different mass flow rates of the working fluid is studied. In particular, the effects of the nanoparticle on the simultaneous optimization of the total annual cost (TAC) and the collector efficiency are investigated. In order to perform multi-objective optimization with the TAC and efficiency as the two objective functions with seven decision variables, including various collector design parameters, mass flow rate and the nanoparticls volumetric concentration, a Particle Swarm Optimization algorithm (PSO) is used. The sensitivity of the various design parameters on the collector efficiency is determined and investigated. Analysis of results reveal that the Pareto front for the case with a mass flow rate of 0.2kg/s dominates over the case with a mass flow rate of

, and the differences are found to become more pronounced with the

addition of the nanoparticle, especially at higher efficiencies. It is also observed that the collector system efficiency increases further with the nanoparticle concentration. It is found that for the optimal performance of the system that simultaneously optimizes TAC and efficiency, all the collector design parameters, except for the number of tubes, can be selected at lower magnitudes when the nanoparticle additive is introduced into the working fluid. Overall, parameter optimization with the use of nanoparticle results in a

decreses in the TAC and *

increase in the efficiency of the flat plate collector.

Corresponding author: Farzaneh Hajabdollahi, Department of Mechanical Engineering, University of Colorado Denver, USA, E-mail address: [email protected]

Keywords: Solar flat plate; Efficiency; Total annual cost; Nanoparticle Al2O3; Multiobjective optimization;

Nomenclature

Ta ambient temperature (oC) Ti collector inlet temperature (oC)

a annualized factor () A surface area (m2) cp heat capacity (J/kg.K) Cb bond conductance

U collector loss coefficient (W/m2.K) U L collector overall loss coefficient

(W/m2.K) S net absorbed radiation (W/m2) W space between tubes (m) W p pump power (kW) y depreciation time (year)

Ccol collector investment cost ($) Cinv annual cost of investment ($/year) Cop annual cost of operation ($/year)

C pump pump investment cost ($)

Ctotal total annual cost($/year) 1 / Cb bond resistance (W/m2.K) Di tube inner diameter (m) Do tube outer diameter (m)

Greek abbreviation  emissivity ()  particle volumetric concentration (-)

 transmittance ()  absorptance () g ( ) effective product transmittance-

f friction factor () FR heat removal factor ()

hc convection heat transfer coefficient (W/m2.K) h fi tube side convection heat transfer coefficient (W/m2.K) hr equivalent radiation heat transfer coefficient (W/m2.K) hwind wind heat transfer coefficient (W/m2.K) I solar radiation intensity (W/m2) k conductivity (W/m.K)

k el price of electrical energy ($ / kWh)  mass flow rate (kg/s) m

N h hours of operation (hour/year) N p number of covers () Nu Nusselt number () i interest rate ()

Q useful heat energy gain (W) Ra Rayleigh number Rb ratio of total radiation on titled to horizontal surface () Re Reynolds number () 2

absorptance  col collector efficiency ()

 F fin efficiency ()  p pump efficiency ()  viscosity (Pa.s) P pressure drop ( pa)

 collector tilt (o)  assembly factor () insu insulation volume (m 3 )  plate thickness (m)  g reflectance from the surroundings () Subscrips a air b bottom c cover e edge f fluid insu insulation p absorber plate t top

t

thickness (m)

1. Introduction Flat plate collector (FPC) in the solar water heater (SWH) is the main part of an energy system. A flat plate solar collector is a special kind of heat exchanger which transforms solar radiant energy into heat [1]. Nanofluid is the nanoparticle suspension of particles with relatively small size and low concentration dispersed in a base fluid such as water and oil [2]. During the past decade, the technology to make particles in nanometer dimensions has been improved [3]. The effects of the nanoparticle Al2O3 on thermo-economic optimization of a shell and tube heat exchanger (STHE) were explored at different mass flow rates for the tube side by Hajabdollahi and Hajabdollahi [4]. This study showed that nanoparticle addition increased the system efficiency and reduced the cost. Exergy efficiency optimization of a flat-plate collector with Al2O3 nanofluid was studied by Shojaeizadeh and Veysi to present a suitable exponential correlation for the optimized exergy efficiency [5]. Recently, some experimental studies investigated the thermal performance of FPC using nanofluids as the working fluid. For example, an experimental study performed by Zamzamian et al. investigated the effect of Cu nanoparticle concentration on the efficiency of a flat plate collector (FPC) [6]. They found that by increasing the nanoparticle weight fraction, the efficiency of the collector was improved. Afterwards, He et al. prepared the Cu–H2O nanofluid to enhance the efficiency of a FPC experimentally [7]. From the analysis of their results, it was shown that adding the Cu– H2O nanofluids was suitable for improving the efficiency of flat-plate solar collector.

3

Then, Moghadam et al. investigated the effect of CuO–water nanofluid as the working fluid in a FPC to increase the collector efficiency experimentally [8]. Their experimental results demonstrated that adding the nanofluid increased the collector efficiency when compared to using water as the working fluid. Earlier, the effect of Al2O3–water nanofluid as the working fluid on the efficiency of a FPC experimentally was also investigated by Yousefi et al. [9]. The results put in evidence that the nanofluids as working fluid increased the efficiency as compared with water. In another research, the effects of CuO/Water nanofluid on the efficiency of a direct absorption parabolic trough collector (DAPTC) were investigated by Menbari et al. analytically and experimentally to highlight the improvements in the thermal efficiency of the collector [10]. The results showed that the thermal efficiency of the system could be enhanced as a result of increased nanoparticle volume fraction and nanofluid flow rate. Goudarzi et al. performed an experimental research in order to study the thermal performance of a solar collector utilizing distilled water and CuO–H2O nanofluid for the working fluids [11]. Their results also confirmed that using nanofluids can significantly enhance the efficiency compared with water. In a very recent research, Ahmadi Boyaghchi and Chavoshi performed the thermodynamic, economic and environmental analyses of a solar-geothermal combined cooling, heat and power, CCHP system with the flat plat collectors containing water-CuO nanofluid as the working fluid to investigate the thermal performance of a solar collector [12]. A SiO2-water nanofluid with a mass fraction of 1% was experimentally performed by Noghrehabadi et al. to demonstrate the changes on the performance of a square flat-plate solar collector [13]. Ahmadi et al. investigated the effect of Graphene nanofluid on thermal efficiency of the flat plate solar collectors to find the best working fluid [14]. They found that R134a was the best fluid

4

with 4.194% improvement in daily exergetic efficiency. The thermal performance of a flat-plate volumetric solar collector using a blended plasmonic nanofluid as the working fluid was investigated by Jeon et al. in a recent study to facilitate the development of highly efficient solar collectors [15]. The results of this study verified the enhancement of highly efficient solar thermal collectors using plasmonic nanofluids. In another research, Tomy et al. investigated the performance of a flat plate solar collector with silver/water nanofluid using Artificial Neural Network (ANN) to analyze thermal efficiency [16]. It was observed from this study that, the results agreed well with the experimental results with less than ±2% derivations. The effects of the silver and gold nanoparticle volume fraction on the collector efficiency were carried out by Chen et al. to investigate the optimum solutions for efficiency [17]. They showed that silver and gold nanofluids obtained higher thermal conversion efficiencies than the titanium dioxide nanofluid. However, to the best of our knowledge, prior studied have not yet considered thermo-economic modeling, analysis and optimization of multiple objective functions for a flat plate collector (FPC) using nanoparticles as an additive for the working fluid, which is addressed in the present investigation. In this regard, one of the main aims of the present study is to explore the influence of nanoparticle Al2O3 on the thermo-economic optimization of a flat plate collector at different mass flow rates of the working fluid. In particular, our goal is to optimize this FPC system by simultaneously maximizing the collector efficiency and minimizing the total annual cost (TAC) and determine the best mass flow rate of the working fluid from the viewpoint of thermodynamic efficiency and economics by considering two cases, i.e. with and without the nanoparticles in the FPC system. Since this requiring resolving conflicting multiple objectives subject to several design variables of the FPC, we consider a novel application of the Particle Swarm

5

Optimization (PSO) algorithm to provide a Pareto optimum front to study the sensitivity of introducing a nanoparticle into the working fluid of the FPC. To facilitate our analysis, we consider seven design variables that include various parameters of the FPC such as the (i) mass flow rate, (ii) number of tubes, (iii) collector length, (iv) collector width, (v) tube diameter, (vi) insulator thickness and (vii) volumetric concentration of the nanoparticle. The simultaneous optimization of the collector efficiency and TAC will be done at two different mass flow rates, viz., at 0.2 kg/s and 0.3 kg/s in order to generalize the results obtained using the PSO algorithm. The sensitivity and the effects of each decision variable including the various system parameters mentioned above and the nanoparticle volume concentration on the collector efficiency and TAC will be analyzed and the trends in our optimization study results will be discussed. A schematic of a flat plate collector in the solar water heater is shown in Fig.1, where Al2O3 nanoparticles are dispersed into water, which is used as the working fluid. Our main goal is to perform a thermo-economic modeling, analysis and multi-objective optimization of this system using the PSO algorithm. The paper is organized as follows. Section 2 presents the various elements of the thermal modeling of the solar flat plate collector. The thermo-economic analysis aspects will be discussed in Sec.3. This is followed by the introduction of the various objective functions, decision variables and constraints (Sec.4) and a brief description of the PSO algorithm for multi-objective optimization (Sec.5). Section 6 outlines the details of our case study. Results and discussion, beginning with a verification and validation of our approach, and followed by various optimization results and the effect of design parameters on the efficiency, with and without nanoparticles, will be presented in Sec.7. Finally, Sec.8 summarizes the present study and the main conclusion arising from our investigation.

6

tor co lle c pla te Fla t

Heat exchanger

Radiation Radiation

Covers

Tube

Pump

Absorber plate

Insulation

Cold fluid

Fig. 1. Schematic diagram of the studied solar heater system and flat plate collector

2. Thermal modeling of a solar flat plate collector 2. 1. Received radiation on a tilted surface The total received radiation on a tilted surface can be expressed as a function of the intensity of the diffuse beam (involving the product of sky area, horizon and circumsolar diffuse), direct beam and reflected radiation from the surroundings, which is calculated as follows [18]:

  I  1  cos   I   1  cos   3   I t   I b  I d b  Rb  I d 1  b  1  I b / I h sin     I h  g   , (1) Ih  2 2   2      I h  where I b , I d , I h , Rb ,  and  g represent the direct beam intensity, diffuse beam intensity, the sum of the direct beam and diffuse beam intensity, ratio of total radiation on the titled plane to that on a horizontal plane, surface angle and solar reflectance from the surroundings, respectively. Further details for computing diffuse and direct beam can be found in [19]. 2.2. Absorbed radiation by collector In the flat-plate solar collector, the net solar radiation absorbed by the absorber plate S is estimated according to the effective transmittance-absorptance product g ( ) as follows [19]: 7

S=g ( ) It , g ( ) 

(2)

   1.01   , 1  1   

(3)

where  ,  and  denote the cover transmittance, plate absorptance and cover reflectance, respectively. 2.3. Friction factor in tube side and heat transfer coefficient For increasing the rate of heat transfer, the nanoparticle is added in the working fluid. In this paper, the nanoparticle alumina Al2O3 is considered to be mixed with the tube side fluid to obtain a nanofluid. The nanofluid properties of Al2O3 are estimated as follows [21]:

nf  1   bf   np , c p , nf 

1   c p bf   c p np , 1   bf   np

keff  k f kf

(4) (5)

 0764  0.0187T  273.15  0.462 ,

eff  1  7.3  123 2 , f

(6)

(7)

where  represents the volumetric concentration of the nanoparticle and the subscripts nf, bf, np, f and eff denote the properties for the nanofluid, base fluid, nanoparticle, fluid, and effective property, respectively. In the nanofluid, the Nusselt number for the tube side, Nunf and Fanning friction factor, f nf depend on the type of nanoparticle. The Nusselt number and Fanning friction factor

for Al2 O3 nanofluid are estimated as [21]:

Nunf  0.065Re0nf.65  60.221  0.0169 0.15  Prnf0.542 ,

8

(8)

f nf  0.3164 Re

0.25 nf

  nf    bf

   

0.797

 nf    bf

   

0.108

,

(9)

 /(Di N ) , Re nf  4m

(10)

where Re , N, Di, Pr ,  and  denote the Reynolds number, number of parallel tubes in the solar collector, inner tube diameter, Prandtl number, density and viscosity, respectively. The above relations are valid for the ranges within 4000  Re nf  16000 and

0    0.1 with a maximum deviation of  10% [21]. The convective heat transfer coefficient is then evaluated by using Nusselt number as follows: hnf  Nunf  keff  / Di .

(11)

2.4. Heat transferred to fluid The heat transfer rate in the fluid by using the collector is obtained as: Q  Ac FR S  U L (Ti  Ta )  m c p T nf ,

(12)

where Ac , U L , Ti , Ta , m , c p and T are considered to be the effective surface area of the collector, collector overall loss coefficient, fluid inlet temperature of the collector, ambient temperature, mass flow rate, specific heat capacity and the fluid temperature difference at the inlet and outlet of the collector, respectively. It may be noted that FR represents the heat removal factor and is calculated as follows: FR 

 A U F   m c p  1  exp   c L  , AcU L  m c p  

(13)

where F  is defined as F 

1 / UL  1 1 1 W    U D  W  D   C D h o F b i nf  L o

   

.

(14)

9

Here, Di , Do , W and 1 / Cb are the inner tube diameter, outer tube diameter, space between tubes and the bonding resistance, respectively. Moreover,  F is the efficiency of a straight fin with a rectangular profile, which can be determined as follows:

F 

tanhmW  Do  / 2 , mW  Do  / 2

(15)

m  U L / k  ,

(16)

where k and  are the fin conductivity and thickness, respectively. The collector overall loss coefficient U L (represented in Eq. (17) below) is a function of the bottom, edge and top loss coefficients:

U L  Ub  Ue  Ut .

(17)

Here, the bottom and edge loss coefficients are estimated as a function of the insulation thickness t and conductivity k as follows: U b  k / t insu,b ,

(18)

U e  k / t insu,e  Ac / Ae  ,

(19)

where Ae is edge heat transfer surface area. The top loss coefficient from the collector plate to the ambient is given as: Nc   U t  1 / R1   R2,i  , i 1  

(20)

R1  1/ hr , c  a  hwind  ,

(21)

R2  1/ hr , pc  hc, p _ c  .

(22)

Here, N c , hr ,c a and hr , p  c are the number of covers, radiation coefficients for the coverambient and plate-cover, respectively as follows [19]:

10





hr ,c  a   c Tc2  Ta2 Tc  Ta  ,

(23)

 Tp2  Tc2 Tp  Tc  ,  1/  p  1/  c  1

hr , pc

(24)

where  c ,  p ,  , Tc and T p are the cover emissivity coefficient, absorber emissivity coefficient, the Stefan-Boltzmann constant, cover temperature and absorber temperature, respectively. The variable hwind presented in Eq. (21) is the convective heat transfer coefficient for the wind, which is calculated as follows [22]:

hwind

 V 0.6    max  5, 8.6 0.4  , l  

(25)

where V and l are collector structure volume and the third root of V, respectively. Furthermore, hc , p _ c denotes the convective heat transfer coefficient in the gap between the absorber plate and the cover, which is estimated as: hc , p _ c 

Nua ka . t p c

(26)

Here, k a and t p c are the air conductivity and the gap thickness of the space between plate and cover, respectively. The variable Nua in the above represents the Nusselt number for tilt angles between 0 and 75o and is based on [23]: 

1/ 3   1708sin 1.8 1.6   1708   Ra cos   Nua  1  1.441    1     ,  1   Ra cos     Ra cos    5830   

(27)

where  and Ra are collector angle and Rayleigh number, respectively. The meaning of the + exponent is that only positive values of the terms in the bracket can be used. Finally, the collector efficiency can be estimated by:

 col 

Q . I t Ac

(28)

11

2. 5. Trend of solution Since the radiation resistance is a function of the absorber plate and cover temperature, the solution method requires a process of trial-and-error, which can be outlined as follows: 1- The absorber plate temperature is guesstimated. 2- The cover temperature is also guesstimated. 3- Then the heat transfer rate is obtained (Eq. (12)) using the definition of the absorbed radiation, collector overall loss coefficient and physical specification of the solar collector such as the tube number, tube diameter, fluid mass flow rate, etc. 4- Then, the cover temperature is modified using the relation given as follows: Tc  Tp  R2U t (Tp  Ta ) .

(29)

5- The old cover temperature should be replaced by the new cover temperature and the above steps from the step 3 are repeated until a convergence is met. 6- Afterwards, the plate temperature is modified using the equation given as follows:

Tp  Ta  (S  Q / Ac ) / U L .

(30)

7- Like the cover temperature, the old plate temperature should be replaced with the new one, and this process is repeated from the step 2 till the convergence is met. 8- Once the plate and cover temperatures are obtained, the heat transfer rate and collector efficiency can be calculated.

12

A flowchart, which summarizes the modeling performed in this study, is presented in Fig. 2.

Start

Tp1

Absorber plate temperature is estimated

Tc1

Cover temperature is estimated

Calculating the rate of heat transfer using Eq. 12

Tc2

Cover temperature is modified using Eq. 29

|Tc2-Tc1|<0.001

No

Tc2

Tc1

Yes

Tp2

Tp1

Absorber plate temperature is modified using Eq. 30

No

Tp2

|Tp2-Tp1|<0.001

Yes

Rate of heat transfer and collector efficiency are evaluated using Eqs. 12 and 28 Calculating the Efficiency and TAC

Finish

Fig. 2. Flowchart of the thermo-economic modeling of a solar flat plate collector

3. Thermoeconomic analysis To optimize the system from the economic aspect, the total annual cost (TAC) should be selected for analysis. The TAC consists of the operating and investment costs. The investment cost includes the capital cost of collector (including the absorber plate, 13

tubes, insulator, cover and assembly cost) as well as the pump and nanoparticle price, which is evaluated based on the market available prices as follows:





b b b b b Cinv  Ccol  C pump   a1 Ap  1  a2  Atube  2  a3 insu  3  a4  Ac  4  a5W p 5  Cnp ,

where

(31)

 , Ap , Atube , insu , Ac and W p are collector assembly factor, absorber surface area,

tube outside surface area, insulator volume, cover surface area and power for the pump, respectively. Furthermore,

and

where

are constants based on the

available market price of equipment. In addition, Cnp is the price of the nanoparticle and which is estimated as follows: Cnp  mnp ,

(32)

where mnp is required nanoparticle mass, which is estimated as





mnp  Nt L1 np Di2 / 4 .

(33)

Here Nt and L1 are tube number and tube length, respectively. The required pump power in Eq.(31) is obtained as follows:  P m . W p 

(34)

p

Here,

 and  p are fluid density and the efficiency of pump, respectively, and P is the

pressure drop which can be estimated as P 

2 f L1 / Di V 2 1000

,

(35)

where V and f are the velocity in the tube and the friction factor, respectively. The operating cost consists of the cost for pumping power to overcome the pressure drop through the collector tubes, which is obtained as Cop  k el N hW p .

(36)

14

Here, k el and N h are the electricity unit price and operating hours of the system per year. Finally, the total annual cost, Ctotal is defined as follows: Ctotal  aCinv  Cop ,

(37)

where a expresses the annual cost coefficient which is given as: a

i . 1  (1  i)  y

(38)

Here, i and y are defined as the interest rate and the life of the system, respectively.

4. Objective functions, decision variables and constraints In this section, both the collector efficiency and the TAC, determined form Eqs. (28) and (37), respectively, are chosen as the objective functions, which are optimized simultaneously. Furthermore, the mass flow rate, tube number, collector length, collector width, tube diameter, insulator thickness and the particle volumetric concentration are considered as the seven design parameters. The other required parameters are assumed as the input parameters. The constraint is set to insure that the collector transfers a desirable amount of heat rate in each case.

5. Multi-Objective Particle Swarm Optimization (MOPSO) Algorithm In the multi-objective optimization methods, several conflicting objectives are identified to be optimized simultaneously. Typically, the weighted summation of the objectives can be considered; however an optimal Pareto front is desirable, where a set of non-dominated points create a large part of the objective space. To find out the optimal Pareto front, the Multi-Objective Particle Swarm Optimization (MOPSO) algorithm is implemented. This algorithm was inspired by the behaviour of birds during immigration for exploring the best place using their swarm intelligence [20]. The position of each bird, which represents the decision variables, will be generated in the first iteration randomly.

15

Based on the formulations which are given below, in order to find the best global solution as well as the best location of each individual particle over time, the location of each bird will be updated as [20] v ij 1  wv ij  c1rand ( p i  x ij )  c2 rand ( p gj  x ij ) ,

(39)

xij 1  xij  vij 1 .

(40)

Here, i and j represent the ith particle in the swarm and the number of iterations, respectively. The terms p i and p gj indicate the best location of each individual particle over time and the best global solution in the swarm. In addition, w, c1 and c 2 represent the inertia weight, self-confidence factor and swarm confidence factor, respectively. Furthermore, rand is a random number generated within a range between 0 and 1. The details of the MOPSO algorithm are presented in detail in reference [21]. Designers are interested in finding a single optimum point among a set of optimum points in the Pareto front. One of the common strategies to select the final optimized point is the LINMAP method and the determination of the ideal point [21]. For this purpose, each objective can be non-dimensionalized using the equation given below: Fij

Fijn  2

i1 ( Fij ) 2 m

,

(41)

where i, j and m denote the index of each optimum solution on the Pareto front, the index for each objective and the number of optimum solutions on the Pareto front, respectively. Afterwards, the nearest point to the ideal point is obtained by the following relation and introduced as the final optimum point. di 

 F 2

j 1

n ij

n  Fideal ,j



2

.

(42)

16

6. Case study A case study is considered for a flat plate solar water heater in a city named Rafsanjan with the latitude of North 30o and located in Kerman, which is the biggest province of Iran. Hourly variations for the received radiation on the tilt surface for Rafsanjan city is obtained by Eq. (1). In order to reduce the computational complexity, the average amount of the received radiation is considered during a year, which is 253 W/m2. In addition, the average magnitude of wind velocity and ambient temperature are also considered for the thermo-economic optimization in this study. To receive the highest radiation, the collector angle is also supposed to be a constant and equal to the latitude during the year [21]. Water is considered as the working fluid with temperature dependent properties, and inlet temperature of 10oC. Copper material with a thermal conductivity of 385 W/(m.K) and emissivity of 0.92 is consider for the absorber plate. The constants

,

and the collector assembly factor in relation (31) are taken to be [120

60 220 4.5 3500], [0.9 0.8 1 1 0.47] and 1.5, respectively, according to the market available price. The life time for the system is considered to be 15 years. The rate of inflation and the cost of electricity needed by the pump are considered to be 12% and 0.1 $/kWh, respectively. The system is operated during a year with all hours of solar radiation, which is approximately equal to 365×24/2=4380 hours. In addition, about 1kW rate of heat transfer should be provided by the panel. To generalize the optimized results, the optimization process will also be carried out for different values of the mass flow rate, including 0.2 and 0.3 kg/s. In addition, based on the MOPSO algorithm discussed earlier, optimum results will be obtained for both with/without nanoparticle additive, and then compared with each other. The other remaining input data for thermal analysis are listed in Table 1.

17

Table.1. The operating conditions and input parameters for studied case Parameter Value Transmittance absorptance product (-) 0. 84 Space between cover and absorber plate (m) 0.025 Absorber emissivity (-) 0.92 Cover emissivity (-) 0.88 Insulator conductivity (W/m.K) 0.045 Absorber plate thickness (m) 0.0005 Ambient temperature (oC) 10 Wind velocity (m/s) 5

7. Results and discussion 7.1. Verification of modeling First, in order to verify and validate our modeling approach, the results are evaluated by comparing with the corresponding results in the literature. For the same input values listed in Table 2, the results are compared with those from reference [1], which are presented in Table 3.

Table. 2. Specification of studied solar collector in Ref [1] Parameter Value Panel surface area (m2) 9.14 Water mass flow rate (kg/s) 0.0087 Length of collector (m) 1 Wind speed (m/s) 25 Collector tilt (degree) 20 Fluid inlet and ambient temperature (K) 300 Plate thickness (mm) 2 Effective product transmittance–absorptance (-) 0.84 Emissivity of the absorber plate (-) 0.92 Emissivity of the cover (-) 0.88 Thickness of the back insulation (m) 0.08 Thickness of the sides’ insulation (m) 0.04 Thermal conductivity of the absorber plate (W/m K) 384 Thermal conductivity of the insulation (W/m K) 0.05 Incident solar energy per unit area of the absorber plate ( W/m 2) 500 Tubes’ centre to centre distance (m) 0.15 Inner diameter of pipes (m) 0.04

18

The results show that for the overall heat loss coefficient, useful heat gain, collector efficiency, and absorber plate temperature, the difference of percentage points for two mentioned modeling output results are acceptable.

Table. 3. The comparison of modeling output and the corresponding results from Ref. [1] Output parameters Ref [1] This work Difference (%) Overall heat loss coefficient (W/m2 K ) 4.6797 4.8809 +4.3 Useful heat gain (W) 2139.4 2064.3 -3.51 Collector efficiency (-) 0.468 0.452 -3.51 Absorber plate temperature (K) 339.43 330.27 -2.7%

7.2. Optimization results In this section, the result of the thermoeconomic modeling of a solar flat plate collector system used for water heating applications, in which Al2O3 nanoparticle is injected through the pure water as the working fluid, are presented and discussed. Thus, the multi-objective optimization for the solar flat plate collector is applied to optimize both efficiency and TAC as the two objective functions using the PSO algorithm. Mass flow rate, tube number, tube diameter, collector length, collector width, insulator thickness and the particle volumetric concentration are assumed as the design parameters, which are listed in Table 4. Also, the upper and lower range of variations for the decision variables are listed in this table. Afterwards the effect of nanoparticles injection is studied on both objective functions for the mass flow rates of 0.2 kg/s and 0.3 kg/s. In the next step, the influence of the design variables on the efficiency are obtained in both cases of nanofluid and pure fluid, and the results are compared. In addition, the effect of nanoparticle concentration on the efficiency is investigated for the above values of the mass flow rates.

Table.4. The design parameters and their lower and upper range of variation Variables From To Mass flow rate (kg/s) 0.2 2 19

Tube number (-) Tube diameter (mm) Collector length (m) Collector width (m) Insulator thickness (mm) Particle volumetric concentration (%)

3 5 0.5 0.5 20 0

10 30 4 4 150 0.1

The variation of the TAC versus the efficiency is shown in the Fig. 3 for different mass flow rates for the cases with and without nanoparticles. As it can be seen, these two objective functions are in conflict with each other. That is, by improving the efficiency, the TAC is decreased and vice versa. Pareto front for the case with nanoparticle overcomes the case without nanoparticles for the mass flow rate of 0.2 kg/s. In fact, at higher values of efficiency, the influence of nanoparticle is more obvious. In the same way, the case with nanoparticle is dominated over the case without nanoparticles for the mass flow rate of 0.3 kg/s. It can be demonstrated that at the mass flow rate of 0.3 kg/s, the effect of the nanoparticle additive is more apparent at lower efficiencies as compared with the mass flow rate of 0.2 kg/s. It can also be concluded that a lesser thermoeconomic improvement is observed for the higher mass flow rate. It is predicted that no significant thermo-economic improvement can be observed for the typical higher mass flow rate of 0.5 kg/s.

(a)

(b) 20

Ctotal ($/year)

Ctotal ($/year)

col ()

col ()

Fig. 3. Optimum Pareto fronts with/without nanoparticle additive for different mass flow rates a. w=0.2 kg/s, b. w=0.3 kg/s

Optimum Pareto fronts for the cases with and without nanoparticle additive are shown in Fig. 4 for the mass flow rates of 0.2 and 0.3 kg/s. Again, it is evident from this figure that the Pareto front at the lower mass flow rate dominates over the other Pareto for both the cases, i.e. with and without nanoparticle.

Ctotal ($/year)

(b)

Ctotal ($/year)

(a)

col ()

col ()

Fig. 4. Optimum Pareto fronts for different mass flow rates and in the both cases of with/without nanoparticle additive, a. Without nanoparticle additive, b. With nanoparticle additive

7.3. Effects of design parameters on the efficiency in the case without nanoparticles 21

Figure 5 shows the efficiency versus the solar flat plate collector specifications for the optimum points for the case without the nanoparticle additive. As it can be observed, the efficiency is significantly dependent on the number of tubes at both mass flow rates of 0.2 and 0.3 kg/s (see Fig.5a). In fact, the efficiency is varied between 0.49 and 0.57 at 0.2 kg/s mass flow rate when the number of tubes increases from 3 to 10, and these values are around 0.46 and 0.58 for the case with 0.3 kg/s as the mass flow rate. It is also seen that when the number of tubes is 5, the efficiency is higher for the mass flow rate of 0.3 kg/s. On the other hand, the efficiency remains generally constant when the number of tubes is selected to be more than 5 for the mass flow rate of 0.3 kg/s. Generally, it can be concluded that the number of tubes is selected to be mostly between 3 and 5. However, by an increase of the mass flow rate, the efficiency increases and this improvement is more obvious at greater sizes of the tube diameter as shown in Fig. 5b. On the other hand, for a fixed mass flow rate, increasing the size of tube diameter reduces the collector efficiency. In the graph related to the collector length shown in Fig. 5c, the relatively similar results for both mass flow rates can be observed. In fact, at a fixed value of the collector length, which is around 0.94 m, the efficiency changes between 0.5 and 0.57 at 0.2 and 0.3 kg/s mass flow rates. Another point which can be deduced from this figure is that at the lower value of the collector width, the efficiency is higher at 0.2 kg/s mass flow rate as compared with the mass flow rate of 0.3 kg/s (see Fig.5d). The efficiency versus the bottom insulator thickness is shown in the Fig. 5e. It is clearly seen that the efficiency improves by an increase of the bottom insulator thickness for different values of the mass flow rates. It is also evident that the points related to the case with mass flow rate of 0.2 kg/s totally dominates over the case with mass flow of 0.3

22

kg/s. Thus, as a key observation, we find that at the fixed value of bottom insulator thickness, the efficiency is higher at 0.2 kg/s mass flow rate as compared the 0.3 kg/s. 7.4. Effects of design parameters on the efficiency in the case with nanoparticles The efficiency versus the solar flat plate collector specifications for the optimum points for the case of with the additional of the nanoparticle is depicted in Fig. 6. Like the case without nanoparticle, the tube number has a positive impact on the efficiency, but the number of tubes is considered to be more in the case with nanoparticle (shown in Fig. 6a). In addition, for a fixed size of the tube diameter, higher efficiency is obtained at 0.3 kg/s mass flow rate as compared with 0.2 kg/s (Fig. 6b). For the sizes of the tube diameter greater than 10 mm, similar diameter size is selected in the case without nanoparticles and with nanoparticles. Efficiency versus the collector length variation is demonstrated in Fig. 6c. It can be seen that the collector length is considered to be in the range of 0.83 to 0.95 m, and at some values the efficiency is greater at the 0.2 kg/s mass flow rate as compared with that of 0.3 kg/s. As before, the points with the mass flow rate of 0.2 kg/s dominates over the points with the mass flow rate of 0.3 kg/s, where for a fixed collector width, efficiency is higher at 0.2 kg/s mass flow rate (shown in Fig. 6d). Furthermore, it is also evident that the points in the mass flow of 0.2 kg/s are almost dominating over the points at 0.3 kg/s mass flow in the analysis of the sensitivity to the bottom insulator thickness as shown in Fig. 6e. In fact, the efficiency is more at 0.2 kg/s as compared with 0.3 kg/s at a constant bottom insulator thickness. In this study, the particle volumetric concentration

is considered to be varying the

range between 0 and 0.1. The distribution of the efficiency versus the particle volume concentration is illustrated in Fig. 6f.

23

ηcol (-)

(b)

ηcol (-)

(a)

Di (mm) (d)

ηcol (-)

ηcol (-)

Nt (-) (c)

L1 (m)

L2 (m)

ηcol (-)

(e)

tinsu,b (m) Fig. 5. Scattering distribution of efficiency versus design parameters for the optimum points in the case of without nanoparticle additive ( Fig. 4a)

It can be concluded that the efficiency is more dependent on the particle volume concentration at the higher mass flow rate. In fact, at the mass flow rate of 3 kg/s, the

24

efficiency is improved by an increase of the particle concentration, while at the mass flow rate of 2 kg/s, the efficiency changes are less apparent. Scattering distributions of the collector efficiency versus the design parameters for the mass flow rate

kg/s with and without nanoparticle additive are shown in Fig.

7. The efficiency for the case with nanoparticles is higher than the case without nanoparticles, and this difference is more obvious in the tube number between 5 and 8 as shown in Fig. 7a. On the other hand, the efficiency decreases by an increase of the size of the tube diameter in nanofluid (Fig. 7b). It can be seen from the this figure that for the nanofluid with the diameters less than 10 mm, the efficiency is higher than for the case without nanoparticles. By adding nanoparticles to the water, shorter collector length is required as depicted in Fig. 7c. It should be also noted that larger collector width is required by adding nanoparticles in the mass flow rate of 0.3 kg/s as shown in Fig. 7d as compared with the pure water. In the case of bottom insulator thickness shown in Fig. 7e, it can be said that almost the same thickness can be selected for both nanofluid and pure fluid.

Table.5. Optimum values of the design parameters and objective functions for the final optimum solution in Fig. 3a Parameters With nanoparticle Without nanoparticle Tube number (-) 5 4 Tube diameter (mm) 15.5 18.7 Collector length (m) 0.8614 0.9378 Collector width (m) 0.5516 0.5168 Insulator thickness (mm) 109.2 111.3 Particle volumetric concentration (-) 0.0058 Efficiency (-) 0.5269 0.5161 Total annual cost ($/year) 23.9054 24.7853

Finally, the optimum values of the design parameters and the resulting objective functions values for the final optimum points are summarized and listed in Table 5. It

25

can be seen that the efficiency is equal to 52.69% in the case of including the nanoparticle. As

(b)

ηcol (-)

ηcol (-)

(a)

Di (mm) (d)

ηcol (-)

ηcol (-)

Nt (-) (c)

L2 (m) (f)

ηcol (-)

ηcol (-)

L1 (m) (e)

ϕ (-)

tinsu,b (m)

Fig. 6. Scattering distribution of efficiency versus design parameters for the optimum points in the case of with nanoparticle additive ( Fig. 4b)

26

a key observation, in particular, 3.5% decrease in the total annual cost (TAC) and 2% increase in the collector efficiency is observed in the case of using the nanoparticle additive when compared with the case of without nanoparticle additive in the final optimum solution. Thus, the TAC incurred in the case of nanofluid is lower than that of the pure liquid for the solar flat plate collector which is our desired goal. Finally, it is evident from our analysis results that all the other design parameters in the flat plate collector specification are selected to be at lower values for the case of using the nanoparticle except for the number of tubes, which is chosen to be at a higher value.

27

ηcol (-)

(b)

ηcol (-)

(a)

Di (mm) (d)

ηcol (-)

ηcol (-)

Nt (-) (c)

L1 (m)

L2 (m)

ηcol (-)

(e)

tinsu,b (m) Fig. 7. Scattering distribution of efficiency versus design parameters for w =0.3 kg/s and in the both cases of with/without nanoparticle additive ( Fig. 3b)

28

8. Summary and Conclusions In this study, we have performed thermo-economic modeling of a solar flat plate collector in which we introduced Al2O3 nanoparticles as an additive to water, which is used as a working fluid. Our goal was to carry out a multi-objective optimization of the collector efficiency and the total annual cost (TAC) using the Particle Swarm algorithm in order to study their sensitivity to adding nanoparticles and various associated collector design variables. In this regard, the mass flow rate of the working fluid, number of tubes, collector length, collector width, insulator thickness and the nanoparticles volumetric concentration were chosen as the design parameters. It was found from our thermo-economic optimization study that the Pareto front for the case with nanoparticles dominates over the case with pure water (i.e. no nanoparticles) at lower mass flow rates and the beneficial effect of adding Al2O3 was seen to be more pronounced at higher collector efficiencies. Also, the effects of various design parameters changes on the efficiency were investigated for both the case, i.e. with or without nanoparticles at a mass flow rate of 0.3kg/s in the optimum Pareto fronts. The analysis revealed that all the collector design parameters, except for the number of tubes, need to be selected at lower magnitudes for the nanoparticles-laden flat plate collector to achieve optimal system performance. In particular, it was found that for the case with nanoparticles, higher efficiencies were achieved when the number of tubes is between 5 and 8, and the tube diameter is less than 10 mm. In addition, our thermo-economic modeling showed that the collector system efficiency can be improved with an increase

29

in the nanoparticle volume concentration at higher mass flow rates. Overall, it was found that the use of Al2O3 nanoparticles reduces the total annual cost by the flat plate collector efficiency by

and increases

. In general, the thermo-economic optimization of

flat plate collector using nanoparticles via the Particle Swarm Optimization algorithm is found to be a promising approach, and complementing the associated observation from recent experimental studies. Such methodology can be used to perform multi-objective optimization-based comparative studies involving various types of nanoparticles in solar flat plate collector systems.

30

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[8] Moghadam J, Gord Mahmood F, Sajadi M, Hoseyn Zadeh M, ”Effects of CuO/water nanofluid on the efficiency of a flat-plate solar collector”, Exp Thermal Fluid Sci, 58 (2014), pp. 9–14. [9] Tooraj Yousefi, Farzad Veysi, Ehsan Shojaeizadeh, Sirus Zinadini, "An experimental investigation on the effect of Al2O3– H 2O nanofluid on the efficiency of flat-plate solar collectors", Renewable Energy, 2012: 39, 293-298. [10] Menbari A, Alemrajabi AA, Rezaei A. "Heat transfer analysis and the effect of CuO/Water nanofluid on direct absorption concentrating solar collector." Applied Thermal Engineering 104 (2016): 176-183. [11] Goudarzi K, Shojaeizadeh E, Nejati F. "An experimental investigation on the simultaneous effect of CuO–H2O nanofluid and receiver helical pipe on the thermal efficiency of a cylindrical solar collector." Applied Thermal Engineering 73, no. 1 (2014): 1236-1243. [12] Boyaghchi FA, Chavoshi M. "Multi-criteria optimization of a micro solargeothermal

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[15] Jeon J, Park S, Lee BJ. "Analysis on the performance of a flat-plate volumetric solar collector using blended plasmonic nanofluid." Solar Energy 132 (2016): 247-256. [16] Tomy AM, Ahammed N, Subathra MS, Asirvatham LG. "Analysing the Performance of a Flat Plate Solar Collector with Silver/Water Nanofluid Using Artificial Neural Network."Procedia Computer Science 93 (2016): 33-40. [17] Chen M, He Y, Zhu J, Wen D. "Investigating the collector efficiency of silver nanofluids based direct absorption solar collectors." Applied Energy 181 (2016): 65-74. [18] J. E. Hay, J.A. Davies. Calculation of the solar radiation on an inclined surface. Proceedings of the first Canadian Solar Radiation Data Workshop, p. 59, 1980 [19] Duffy J, Beckman W. Solar Engineering of Thermal Processes. Wiley&Sons, New York, 1991. [20] Kennedy J, Eberhart R. Particle Swarm Optimization. in: IEEE International Conference Neural Networks 1995: 1942–48. [21] Sepehr Sanaye, Hassan Hajabdollahi, "4E analysis and Multi-objective Optimization of CCHP Using MOPSOA". Proceedings of the Institution of Mechanical Engineers, Part E: Journal of Process Mechanical Engineering. 2013 doi: 0954408912471001. [22] J. W. Mitchell,. "Heat transfer from spheres and other animal forms". Biophysical Journal 16, 561, 1976. [23] K. G. T. Hollands, T. E. Unny, G. D. Raithby, L. Konicek, "Free convection heat transfer across inclined air layers". ASME, Journal of heat transfer, 98, 189, 1976.

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Table captions: Table.1. The operating conditions and input parameters for studied case Table. 2. Specification of studied solar collector in Ref [1] Table. 3. The comparison of modeling output and the corresponding results from Ref. [1] Table.4. The design parameters and their lower and upper range of variation Table.5. Optimum values of the design parameters and objective functions for the final optimum solution in Fig. 4a

34

Figure captions: Fig. 1. Schematic diagram of the studied solar heater system and flat plate collector Fig. 2. Flowchart of the thermo-economic modeling of a solar flat plate collector Fig. 3. Optimum Pareto fronts in the cases with/without nanoparticle. Fig. 4. Optimum Pareto fronts for different mass flow rates. Fig. 5. Scattering distribution of efficiency versus design parameters for the optimum points in the case of without nanoparticle additive (Fig. 4a). Fig. 6. Scattering distribution of efficiency versus design parameters for the optimum points in the case of with nanoparticle additive (Fig. 4b). Fig. 7. Scattering distribution of efficiency versus design parameters for mw=0.3 kg/s and in the both cases of with/without nanoparticle additive (Fig. 3b).

35

Highlights: 

Thermoeconomic modeling of a solar flat plate collector (FPC) system by suspending Al2O3 nanoparticle



Multi-objective optimization of total annual cost (TAC) and collector efficiency using Particle Swarm Optimization algorithm



Sensitivity study of various collector design parameters and nanoparticle concentration on thermo-economic collector system improvement



Optimal parametric design conditions determined with and without nanoparticles for FPC system

36