1.Introduction

Corresponding to different applications,solar collectors can be categorized into three main types by the operating temperatures[1].They are,A)Low-temperature collectors(T ＜ 100°C)such as solar flat plate collectors,B)Mediumtemperature collectors(T～400°C)such as the Parabolic collectors [2-5] and C) High-temperature collectors(T＞400°C)such as the dish collectors and Fresnel reflectors with Parabolic Trough collector(PTC).Geometrically,a parabolic collector contains a straight tube in one dimension with parabola curve in the other two sides.The absorber tube is generally straight along the length of collector on which solar energy or sunlight is focused on through the around parabolic mirrors.Due to the high efficiency and relatively low cost for such types of collectors,a large amount of studies have been devoted to their development and optimization.Among them,some of the work are introduced below.

Unsteady conjugate natural convection of hybrid water based nanofluid in a semicircular cavity has been numerically studied by Chamkha et al.[2].The environmental impact of nanofluid-based concentrating solar water heating system was studied by Khullar et al.[3].Many studies,both experimentally and/or numerically,were performed for using nanofluids in different solar collectors.For instance,Gorji et al.employed nano fluid in a flat solar collector[6],Nasrin and Alim[7]used the nanofluids in a wavy solar collector.Based on their study,researchers have tried to optimize the wavy solar collectors by using different nanofluids[8,9].Also,the thermal performance of alumina-water nanofluid in an inclined direct absorption solar collector(IDASC)has been evaluated using efficient analytical methods[10].

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Using the extended surfaces or porous media is another way to increase the heat transfer in solar parabolic collectors.For instance,Jamal-Abad et al.experimentally investigated the thermal performance of solar parabolic collector with the absorber tube filled by the porous copper foam[11].Increase in Nusselt number,friction factor and collector efficiency was found for such design.Using a two phase modeling,Kaloudis et al.investigated the effect of Al2O3nanoparticles concentration on the thermal efficiency of solar parabolic collector and found that a 10%boost in efficiency was possible for Al concentration of 4%[12].In another interesting design of the absorber tube,Bellos et al.proposed a convergent/divergent tube for the absorber and found that the use of thermal oil with nanoparticles as working fluid increases the collector efficiency by 4.25%while the geometry improvement increases the efficiency by 4.55%[13].More designs of these types of collectors can be found in the comprehensive review from Wang et al.[14].

Nanoparticle behavior in working fluid filled in various cavities of solar collectors has been paid special attention.For example,the effect of heated cylinder on a wavy cavity has been studied[15]and a circular-wavy cavity which is optimized using response surface method(RSM)[16].Kefayati et al.studied the non-Newtonian nanofluids in cavities and performed entropy generation study under various conditions[17-20].In fact,nanofluids has also been investigated for micro-channel heat sink cooling[21,22].More studies in the field of nanofluids and particles motion characteristics can be found in the literatures[23-32].For instance,a onedimensional mathematical model is proposed by Allouhi et al.[33]to investigate the effect of various nanoparticles suspended in the working fluid for medium and high temperature PTCs[12,34-39].

The following dimensionless variables are introduced:

The corresponding dimensionless parameters are as follows,

2.Problem description

The thermo-physical properties of nanoparticles are presented in Table 1.Boundary conditions are:

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K is the permeability of porous medium and knfis nanofluid thermal conductivity,g is the gravitate acceleration vector,μnf nanofluid dynamic viscosity,P is the pressure,ρnfis the nanofluid density,αnfis the thermal diffusivity,βnfis the coefficient of thermal expansion of the nanofluid and （Cp）nfis the heat capacitance of the nanofluid.Here,ρnf,(ρCp)nf,αnf,βnf,μnf,knf,σnfcan be de fined,respectively,as below,

The stream function and vorticity are de fined as follows to eliminate pressure source terms:

Fig.1.Geometry[1],boundary conditions and generated mesh considered in this study.

Table 1 Thermal properties of different nanoparticles.

Properties Symbol Unit Fe3O4 Al2O3 Cu TiO2 Heat capacitance cp Jkg-1K-1 670 765 385 686.2 Density ρ kg m-3 5200 3970 8933 4250 Thermal conductivity k Wm-1K-1 6 25 401 8.95 Thermal expansion coefficient β K-1 1.3×10-5 0.85×10-5 1.67×10-5 0.9×10-5

Based on the above short review of the existing literatures,one can note that there is not a suitable reference for the study of the effect of porous media on the heat transfer in such applications especially for solar collectors.So,the main purpose of the present study is to investigate the effects of porous material filled by nano fluid on the absorber tube heat transfer in a parabolic solar collector.Furthermore different types of nanoparticles and volume fractions will be examined to find the larger Nusselt number conditions.

Using(12),Eqs,(1)-(4)can be written in dimensionless form as[32].

A finite element method(FEM)was employed for solution of the problem.In the finite element method,the solution region is considered as being built up of many small,interconnected sub-regions called finite elements.The solution of a general continuum problem by the finite element method always follows an orderly step-by-step process.It is characterized by a variational formulation,a discretization strategy,one or more solution algorithms and post-processing procedures.A typical work out of this method involves(1)dividing the domain of the problem into a collection of subdomains,and(2)systematically recombining all sets of element equations into a global system of equations for the final calculation[15,16].Before the numerical simulation,mesh dependency has been investigated.As shown in Table 2.

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In this study,as shown in Fig.1,a nanofluid-based Concentrating Parabolic Solar Collector(CPSC)was considered under the constant heat flux and absorber tube was considered to be filled by porous material based on study of Jamal-Abad et al.[11].The boundary condition of the outer wall is constant solar heat flux,the inner wall inside which is filled by air is in constant low temperature Tcand two above side walls are insulated due to symmetric condition.The nanofluid used in this analysis is water based with the nano particles thermal properties listed in Table 1 and assumed to be Newtonian,incompressible and laminar flow.Using the Boussinesq approximation the governing equations for a steady incompressible two-dimensional laminar nanofluid flow are[32],

3.Numerical method

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4.Results and discussions

Based on previous studies,using nanofluids and porous media are two efficient methods for increasing the heat transfer in solar applications.In our study,a Concentrating Parabolic Solar Collector(CPSC)using various nanofluid filled in a porous absorber tube has been considered,as is also shown in Fig.1.It is tried to investigate the effect of these two methods on the Nusselt number.Methodology of analysis in this study is the finite element method(FEM)from FlexPDE software.The accuracy of our methodology was examined by comparing our results of temperatures lines with that of Chamkha et al.obtained by a finite difference method(FDM)[2].The comparison results are shown in Fig.2.The similar temperatures patterns obtained by our method and that of Chamkha et al.indicate the good accuracy of our method.For this geometry and mesh independency study,Table 2 is presented for different grid numbers and the obtained Nusselt Numbers.As is seen,the results con firm that 40×62 grid number has a reliable result.After applying the boundary conditions introduced in Section 3 in Eq.(17),the results for temperature contours,stream lines and local and average Nusselt number on the outer wall of tube,have been derived.To find the effect of different nanoparticles,Fe3O4,Al2O3,TiO2and Cu are chosen from Table 1 and th4e results of temperature/streamline contours when Ra=10,φ=0.08,Da=50 are depicted in Fig.3.As can be seen from Fig.3,under the proposed operation conditions,the Cu addition leads to the smallest temperature gradient distribution in the semi-annulus tube and the TiO2addition resulted in the largest one.While both Cu and TiO2additions lead to the smaller vortices compared to Fe3O4,Al2O3by notice from the streamlines in Fig.3.The data in Figs.3 and 4 is presented to show the local and average Nusselt number when different fluids containing different nanoparticles are introduced in the porous tubular absorber.It can be found that from the heat transfer view point,Cu and Al2O3are more appropriate nanoparticles due to their larger thermal conductivities.Cu has a significant difference among other nanoparticles in the average Nusselt number,so it is chosen for next steps to find the effect of porosity on the heat transfer in prius solar tube.

Table 2 Mesh independency study.

Starting Mesh Number 20×32 30×48 40×62 50×78 Nusselt Number 6.304816 6.433254 6.458288 6.458565

Fig.2.Validation the code for temperatures lines compared to Chamkha et al.[2].

Fig.5 shows the effect of Cu nanoparticles volume fraction on the temperatures and streamline contours when Ra=104,Da=50.It can be observed that the larger nanoparticles volume fraction φ leads to the shifting downward of the streamline loop center and from Fig.6 it can be easily concluded that the larger φ leads to larger Nusselt number and therefore the enhanced heat transfer performances for the designed case.

To find the effect of porosity on the efficiency of this type of solar tube,effect of Darcy number on the Nusselt numbers are discussed as shown in Fig.7.It reveals the effect of Darcy number on the temperatures and streamline contours of Cuwater when Ra=104and φ=0.08.As seen in these contours,increasing the Da number will lead to the increase in streamline values and decrease on the temperature values contours and from the Nusselt definition,by decreasing the temperature on outer surface,Nusselt number is increased,so increasing the Da are considered to be important driving force of the increase in both local and average Nusselt numbers,as is also presented in Fig.8.

Finally,the effects of Rayleigh number on the temperatures and streamline contours of Cu-water when Da=50 and φ=0.08 are demonstrated by Figs.9 and 10,respectively.From Fig.9 it can be seen that Rayleigh number variations has the most significant impact on the temperature and streamline patterns among all other parameters discussed before.Increasing the Ra number will lead to the shifting downward of the streamline centers until it breaks into two center loops when Ra=105and 106.It can be also noticed that the temperature contours of natural convection below the cool surface will be thinner by moving down and flow patterns moves up from its besides(left and right).Fig.10 for this situation confirm the Nusselt number increase by increasing the Ra numbers.Also the peak of local Nu is due to temperature contours behavior below the cool surface(inner curve or surface)as described above.

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Fig.3.Effect of nanoparticles type on the temperatures and streamline contours when Ra=104,φ=0.08,Da=50.

Fig.4.Local and average Nusselt number for different nanoparticles.

Fig.5.Effect of Cunanoparticles volume fraction on the temperatures and streamline contours when Ra=104,Da=50.

Fig.6.Local and average Nusselt number for different Cu nanoparticles volume fraction.

Fig.7.Effect of Darcy number on the temperatures and streamline contours of Cu-water when Ra=104and φ=0.08.

Fig.8.Local and average Nusselt number for different Darcy numbers of Cu-water nanofluid.

Fig.9.Effect of Rayleigh number on the temperatures and streamline contours of Cu-water when Da=50 and φ=0.08.

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It can be found from our above study that the main reason for the better performance from Cu nanoparticle is its higher thermal conductivity compared to other nanoparticles.Although the larger density and lower Cphas some effects in the governing equations but as shown by our study,thermal conductivity is a more effective parameter.It is believed that the addition of Cu nanoparticle would not obviously increase the cost of the fluid considering that its addition amount is very low and the price for copper itself is not high and often be used as the material for finned tube or as heat sink.

5.Conclusions

In this study,FlexPDE FEM numerical code have been applied to find the solution of 2D modeling of heat transfer for a nanofluid-based Concentrating Parabolic Solar Collector(CPSC)while the absorber tube is filled by porous material.Results of analysis con firmed that maximum Nusselt numbers occurs when nanoparticles volume fraction(φ)and Rayleigh numbers are in largest possible values.Also,Cunanoparticles shows the most significant increase in Nusselt number than Fe3O4,Al2O3and TiO2nanoparticles when they are employed in our solar collector design.Furthermore outcomes con firm that increasing the Darcy number is considered to be important driving force to increase in both local and average Nusselt numbers.

Fig.10.Local and average Nusselt number for different Rayleigh numbers of Cu-water nanofluid.

Conflict of interest

There is no conflict of interest.

Acknowledgments

The authors gratefully acknowledge the financial support of the National Natural Science Foundation of China(No.51422604,51776165)and China Postdoctoral Science Foundation(No.2017M610638).

References

[1]K.S.Reddy,N.R.Kamnapure,S.Srivastava,Int.J.Low Carbon Technol.12(2016)1-23.

[2]A.J.Chamkha,I.V.Miroshnichenko,M.A.Sheremet,J.Therm.Sci.Eng.Appl.9(2017)41001-41004.

[3]V.Khullar,H.Tyagi,Int.J.Environ.Stud.69(2012)220-232.

[4]A.Kasaeian,S.Daviran,R.D.Azarian,A.Rashidi,Energy Convers.Manag.89(2015)368-375.

[5]T.Sokhansefat,A.B.Kasaeian,F.Kowsary,Renew.Sustain.Energy Rev.33(2014)636-644.

[6]T.B.Gorji,A.A.Ranjbar,Sol.Energy 122(2015)314-325.

[7]R.Nasrin,M.A.Alim,Int.J.Eng.Sci.Technol.5(2013)58-77.

[8]M.Hatami,D.Jing,Appl.Therm.Eng.121(2017)1040-1050.

[9]M.Hatami,D.Jing,J.Mol.Liq.229(2017)203-211.

[10]M.Hatami,S.Mosayebidorcheh,D.Jing,J.Mol.Liq.231(2017)632-639.

[11]M.T.Jamal-Abad,S.Saedodin,M.Aminy,Renew.Energy 107(2017)156-163.

[12]E.Kaloudis,E.Papanicolaou,V.Belessiotis,Renew.Energy 97(2016)218-229.

[13]E.Bellos,C.Tzivanidis,K.A.Antonopoulos,G.Gkinis,Renew.Energy 94(2016)213-222.

[14]F.Wang,Z.Cheng,J.Tan,L.H.Liu,Renew.Sustain.Energy Rev.79(2017)1314-1328.

[15]M.Hatami,Adv.Powder Technol.3(2016)890-899.

[16]M.Hatami,D.Song,D.Jing,Int.J.Heat Mass Tran.98(2016)758-767.

[17]G.H.R.Kefayati,Powder Technol.299(2016)127-149.

[18]G.H.R.Kefayati,Int.J.Heat Mass Tran.108(2017)1481-1500.

[19]G.R.Kefayati,Int.J.Heat Mass Tran.94(2016)582-624.

[20]G.R.Kefayati,Int.J.Heat Mass Tran.94(2016)539-581.

[21]J.Zhou,M.Hatami,D.Song,D.Jing,Int.J.Heat Mass Tran.103(2016)715-724.

[22]O.Pourmehran,M.Rahimi-Gorji,M.Hatami,S.A.R.Sahebi,G.Domairry,J.Taiwan Inst.Chem.E.55(2015)49-68.

[23]M.Hatami,D.D.Ganji,Powder Technol.258(2014)94-98.

[24]P.Tazraei,A.Riasi,J.Fluid Eng.138(2016).

[25]M.Hatami,G.D D,Particuology 16(2014)206-212.

[26]A.S.Dogonchi,M.Hatami,G.Domairry,Powder Technol.274(2015)186-192.

[27]M.Hatami,M.Sheikholeslami,G.Domairry,Powder Technol.260(2014)59-67.

[28]M.Sheikholeslami,M.Hatami,D.D.Ganji,J.Mol.Liq.211(2015)577-583.

[29]D.Song,M.Hatami,Y.Wang,D.Jing,Y.Yang,Int.J.Heat Mass Tran.92(2016)864-876.

[30]W.Tang,M.Hatami,J.Zhou,D.Jing,Int.J.Heat Mass Tran.115(2017)430-440.

[31]M.Hatami,J.Zhou,J.Geng,D.Song,D.Jing,J.Mol.Liq.231(2017)620-631.

[32]M.Sheikholeslami,H.B.Rokni,Chem.Eng.Process Process Intensif.120(2017)93-104.

[33]A.Allouhi,M.B.Amine,R.Saidur,T.Kousksou,A.Jamil,Energy Convers.Manag.155(2018)201-217.

[34]A.Mwesigye,J.P.Meyer,Appl.Energy 193(2017)393-413.

[35]A.Mwesigye,.I.H.Yılmaz,J.P.Meyer,Renew.Energy(2017),https://doi.org/10.1016/j.renene.2017.10.047.

[36]E.Bellos,C.Tzivanidis,Therm.Sci.Eng.Prog.2(2017)71-79.

[37]A.Mwesigye,Z.Huan,J.P.Meyer,Energy Convers.Manag.120(2016)449-465.

[38]S.E.Ghasemi,A.A.Ranjbar,Appl.Therm.Eng.118(2017)807-816.

[39]E.Bellos,C.Tzivanidis,Sustain.Energy Technol.(2017),https://doi.org/10.1016/j.seta.2017.10.005.