Journal of Applied Fluid Mechanics, Vol. 7, No. 3, pp. 543-556, 2014. Available online at www.jafmonline.net, ISSN 1735-3572, EISSN 1735-3645.

Finite Element Simulation of Forced in a Flat Plate Solar Collector: Influence of Nanofluid with Double Nanoparticles

R. Nasrin† and M. A. Alim

Department of Mathematics, Bangladesh University of Engineering & Technology, Dhaka-1000, Bangladesh. † Corresponding Author Email: [email protected]

(Received August 21, 2013; accepted October 25, 2013)

ABSTRACT

This work compares heat loss characteristics across a riser pipe of a flat plate solar collector filled water based nanofluid of double nanoparticles (alumina and copper) with single nanoparticle (alumina). Also this study compares phenomena among four nanofluids namely water-copper oxide, water-alumina, water-copper and water-silver nanofluids. Comparisons are obtained by numerically solving assisted convective heat transfer problem of a cross section of flat plate solar collector. Governing partial differential equations are solved using the finite element simulation with Galerkin’s weighted residual technique. The average Nusselt number (Nu) at the top hot wall, average temperature (θav), mean velocity (Vav), percentage of collector efficiency (η), mid-height dimensional temperature (T) for both nanofluid and base fluid through the collector pipe are presented graphically. The results show that the better performance of heat loss through the riser pipe of the flat plate solar collector is found by using the double nanoparticles (alumina and copper) than single nanoparticle (only alumina). When comparing the four nanofluids considering the same solid volume fraction ( = 5%), this study claims that the average Nusselt number for water-Ag nanofluid is higher than others.

Keywords: Forced convection, Flat plate solar collector, Finite element simulation, Nanofluids, Nanoparticles, Solid volume fraction.

NOMENCLATURE

A surface area of the collector (m2) x, y dimensional coordinates (m) -1 -1 Cp specific heat at constant pressure (J kg K ) Greek Symbols h local heat transfer coefficient (W m-2 K-1) α fluid thermal diffusivity (m2 s-1) I intensity of solar radiation (W m-2), β thermal expansion coefficient (K-1) Archive-1 -1 of SID k thermal conductivity (W m K )  nanoparticles volume fraction L length of the riser pipe (m) ν kinematic viscosity (m2 s-1) m mass flow rate (Kg s-1) η collector efficiency Nu Nusselt number, Nu = hL/kf θ dimensionless temperature, Pr Prandtl number, ρ density (kg m-3) Re Reynolds number, μ dynamic viscosity (N s m-2) T dimensional temperature (K) V dimensionless velocity field Tin input temperature of fluid (K) Subscripts Tout output temperature of fluid (K) av average u, v dimensional x and y components of velocity col collector (m s-1) f fluid U, V dimensionless velocities nf nanofluid -1 Ui input velocity of fluid (ms ) s solid particle X, Y dimensionless coordinates 1 alumina nanoparticle 2 copper nanoparticle

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1. INTRODUCTION conventional fluids. Tyagi et al. (2009) investigated Predicted efficiency of a low-temperature The fluids with solid-sized nanoparticles suspended nanofluid- based direct absorption solar collector. It in them are called “nanofluids.” Applications of was observed that the presence of nanoparticles nanoparticles in thermal field are to enhance heat increased the absorption of incident radiation by transfer from solar collectors to storage tanks, to more than nine times over that of pure water. Azad improve efficiency of in transformers. The (2009) investigated interconnected solar flat-plate solar collector is commonly used today collector. Performance of a prototype of the heat for the collection of low temperature solar thermal pipe solar collector was experimentally examined energy. It is used for solar water-heating systems in and the results were compared with those obtained homes and solar space heating. Because of the through theoretical analysis. Iordanou (2009) desirable environmental and safety aspects it is investigated flat-plate solar collectors for water widely believed that solar energy should be utilized heating with improved heat Transfer for application instead of other alternative energy forms, even in climatic conditions of the mediterranean region. when the costs involved are slightly higher. Solar The aim of this research project was to improve the collectors are key elements in many applications, thermal performance of passive flat plate solar such as building heating systems, solar drying collectors using a novel cost effective enhanced devices, etc. Solar energy has the greatest potential heat transfer technique. of all the sources of renewable energy especially when other sources in the country have depleted. Álvarez et al. (2010) studied finite element Forced convection is a mechanism in which fluid modelling of a solar collector. A mathematical motion is generated by an external source (like a model of a serpentine flat-plate solar collector using pump, , suction device etc.). Significant amounts finite elements was presented. The numerical of heat energy can be transported very efficiently by simulations focused on the thermal and this system and it is found very commonly in hydrodynamic behavior of the collector. Otanicar et everyday life, including , air al. (2010) studied nanofluid-based direct absorption conditioning, steam turbines and in many other solar collector. They reported on the experimental machines results on solar collectors based on nanofluids made from a variety of nanoparticles carbon nanotubes, Lund (1986) analyzed general thermal behavior of graphite, and silver. They demonstrated efficiency parallel-flow flat-plate solar collector absorbers. improvements of up to 5% in solar thermal Nag et al. (1989) analyzed parametric study of collectors by utilizing nanofluids as the absorption parallel flow flat plate solar collector using finite mechanism. In addition the experimental data were element method. Piao et al. (1994) studied forced compared with a numerical model of a solar convective heat transfer in cross-corrugated solar collector with direct absorption nanofluids. Karanth air heaters. Kolb et al. (1999) experimentally et al. (2011) performed numerical simulation of a studied solar air collector with metal matrix solar flat plate collector using discrete transfer absorber. Tripanagnostopoulos et al. (2000) radiation model (DTRM)–a CFD Approach. investigated solar collectors with colored absorbers. Dynamics (CFD) by employing conjugate heat Kazeminejad (2002) numerically analyzed two transfer showed that the heat transfer simulation dimensional parallel flow flat-plate solar collectors. due to solar irradiation to the fluid medium, Temperature distribution over the absorber plate of increased with an increase in the mass flow rate. a parallel flow flat-plate solar collector was Zambolin (2011) theoretically and experimentally analyzed with one- and two-dimensional steady- performed systems and state conduction equations with heat generations. components. Testing of thermal efficiency and Generally a direct absorption solar collector (DAC) optimization of these solar thermal collectors were using nanofluids as the performs addressed and discussed in this work. Enhancement better than a flat-plate collector. Much better of flat-plate solar collector thermal performance designed flat-plate collectors might be able to with silver nano-fluid was conducted by Polvongsri match a nanofluid based DAC under certain and Kiatsiriroat (2011). With higher thermal conditions. ArchiveLambert et al. (2006) conducted conductivityof of theSID working fluid the solar collector Enhanced heat transfer using oscillatory flows in performance could be enhanced compared with that solar collectors. They proposed the use of of water. The solar collector efficiency with the oscillatory laminar flows to enhance the transfer of nano-fluid was still high even the inlet temperature heat from solar collectors. of the working fluid was increased. Martín et al.

Struckmann (2008) analyzed flat-plate solar (2011) also analyzed experimental heat transfer collector where efforts had been made to combine a research in enhanced flat-plate solar collectors. To number of the most important factors into a single test the enhanced solar collector and compare with a equation and thus formulate a mathematical model standard one, an experimental side-by-side solar which would describe the thermal performance of collector test bed was designed and constructed. the collector in a computationally efficient manner. Taylor et al. (2011) analyzed nanofluid optical Natarajan and Sathish (2009) studied role of property characterization: towards efficient direct nanofluids in solar water heater. Heat transfer absorption solar collectors. Their study compared enhancement in solar devices is one of the key model predictions to spectroscopic measurements issues of energy saving and compact designs. The of extinction coefficients over wavelengths that aim of this paper was to analyze and compare the were important for solar energy (0.25 to 2.5 μm). heat transfer properties of the nanofluids with the

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R.Nasrin and M. A. Alim / JAFM, Vol. 7, No. 3, pp. 543-556, 2014.

Modeling of flat-plate solar collector operation in designed and analyzed a thermal efficiency of flat- transient states was conducted by Saleh (2012). plate solar air heaters. This study presents a one-dimensional mathematical model for simulating the transient Nasrin and Alim (2013) investigated free processes which occur in liquid flat-plate solar convective analysis in a solar collector where the collectors. The proposed model simulated the numerical results showed that the highest heat complete solar collector system including the flat- transfer rate was observed for both the largest Pr plate and the storage tank. Karuppa et al. (2012) and Ra. Ghasemi and Razavi (2013) numerically experimentally investigated a new solar flat plate conducted nanofluid simulation with finite volume collector. Experiments had been carried out to test Lattice-Boltzmann enhanced approach. In this paper the performance of both the water heaters under the numerical approach was based on a modified water circulation with a small pump and the results and robust finite volume method. Kumar (2013) were compared. The results showed that the system studied radiative heat transfer with MHD free could reach satisfactory levels of efficiency. convection flow over a stretching porous sheet in Amrutkar et al. (2012) studied solar flat plate presence of heat source subjected to power law heat collector analysis. It was expected that with the flux. The author discussed the effects of the various same collector space higher thermal efficiency or parameters entering into the problem on the higher water temperature could be obtained. temperature distribution and wall temperature gradient. Sandhu (2013) experimentally studied temperature field in flat-plate collector and heat transfer In the light of above discussions, it is seen that there enhancement with the use of insert devices. Various has been a good number of works in the field of new configurations of the conventional insert heat loss system through a flat plate solar collector. devices were tested over a wide range of Reynolds In spite of that there is some scope to work with number (200-8000). Mahian et al. (2013) performed fluid flow, heat loss and enhancement of collector a review of the applications of nanofluids in solar efficiency using nanofluid. Also temperature, energy. The effects of nanofluids on the streamfunction and heatfunction profiles through performance of solar collectors and solar water the riser pipe of the collector can’t be shown in any heaters from the efficiency, economic and experimental works. In this paper, finite element environmental considerations viewpoints and the simulation of heat transfer by nanofluids through challenges of using nanofluids in solar energy the riser pipe of a flat plate solar collector is devices were discussed. Dara et al. (2013) performed. The objective of this paper is to present conducted evaluation of a passive flat-plate solar temperature, streamfunction and heatfunction collector. The research investigated the variations profile as well as heat loss system with the of top loss heat transfer coefficient with absorber comparison of nanofluid having double plate emittance; and air gap spacing between the nanoparticles with single nanoparticle and four absorber plate and the cover plate. Rao et al. (2013) different water based nanofluids. analyzed finite element technique of radiation and mass transfer flow past semi- infinite moving 2. PROBLEM FORMULATION vertical plate with viscous dissipation. Their result Flow Glass showed that increased cooling (Gr>0) of the plate Air gap passing and the Eckert number lead to a rise in the velocity. Solar cover pipe radiance Habib and El-Zahar (2013) mathematically modeled heat-transfer for a moving sheet in a moving fluid where the heat transfer depended on the relative velocity between the moving fluid and the moving sheet to a certain value after that value y the relative velocity had no effect. Effects of Inflow Absorber Out radiation and cold wall temperature boundary Insulation plate flow conditions on in a vertical x annular porousArchive medium were conducted by Patil et of SID al. (2013). The results revealed that the Nusselt Fig. 1. Schematic diagram of the solar number and Sherwood number at cold wall collector decreased with the increase in radius ratio, whereas they increased with the radius ratio at hot wall for A cross section of the system considered in the different temperature boundary conditions at the present study is shown in Fig. 1. The system cold wall. Singh et al. (2013) studied effect of consists of a flat plate solar collector. The fluid cooling system design on engine oil temperature. A through the copper riser pipe is water-based simple experimental setup was developed for nanofluids. The nanofluid is assumed optimization of the . It was observed incompressible and the flow is considered to be that the reduction in engine oil temperature could be laminar. It is taken that water and nanoparticles are achieved by systematic design changes. Chabane et in thermal equilibrium and no slip occurs between al. (2013) studied thermal performance them. The flat-plate solar collector is an insulated optimization of a flat plate solar air heater. metal box with a glass cover (called the glazing) Experimentally investigates of single pass solar air and a dark-colored absorber plate. A, L and D are heater without fins; present the aims to review of the surface area of the collector, length and inner diameter of the riser pipe. The density of the

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nanofluid is approximated by the Boussinesq mCp T out T in  model. Only steady state case is considered. The FR  (6) A I  h T  T  computation domain is a fluid passing copper riser    m amb  pipe which is attached ultrasonically to the absorber Tout  Tin plate. The fluid enters from the left inlet and getting where Tin, Tout and Tm  are inlet, outlet heat form upper and lower boundaries and finally 2 exits from the right inlet of the riser pipe of a flat and fluid mean temperatures, respectively. plate solar collector. The maximum possible useful energy gain in a solar collector occurs when the whole collector is at the 3. MATHEMATICAL inlet fluid temperature. The actual useful energy FORMULATION gain (Qusfl), is found by multiplying the collector heat removal factor (F ) by the maximum possible It is necessary to measure its thermal performance, R useful energy gain. This allows the rewriting of Eq i.e. the useful energy gain or the collector (4): efficiency. If I is the intensity of solar radiation, incident on the aperture plane of the solar collector Q F A  I   h T  T   (7) having a collector surface area of A, then the usfl R m amb amount of solar radiation received by the collector Equation (7) is a widely used relationship for is: measuring collector energy gain and is generally known as the “Hottel-Whillier-Bliss equation”. Qi  I.A (1) A measure of a flat plate collector performance is However, a part of this radiation is reflected back to the collector efficiency (η) defined as the ratio of the sky, another component is absorbed by the the useful energy gain (Qusfl) to the incident solar glazing and the rest is transmitted through the energy. glazing and reaches the absorber plate as short wave radiation. Therefore the conversion factor indicates useful gain mCp T out T in  the percentage of the solar rays penetrating the   (8) available energy AI transparent cover of the collector (transmission) and the percentage being absorbed. Basically, it is the The instantaneous thermal efficiency of the product of the rate of transmission of the cover (λ) collector is: and the absorption rate of the absorber (к). Thus: Q F A I   h T  T    usfl R m amb Qrecv  I A (2) AIAI As the collector absorbs heat its temperature is (9) TT getting higher than that of the surrounding and heat  m amb  FRR  F h is lost to the atmosphere by convection and I radiation. The rate of heat loss (Qloss) depends on where m is the mass flow rate of the fluid flowing the collector overall heat transfer coefficient (h) and through the collector; Cp is the specific heat at the collector temperature: constant pressure. Qloss  hATcol Tamb  (3) The governing equations for laminar forced convection through a solar collector filled with Thus, the rate of useful energy extracted by the water-alumina nanofluid in terms of the Navier- collector (Q ), expressed as a rate of extraction usfl Stokes and energy equation (dimensional form) are under steady state conditions, is proportional to the given as: rate of useful energy absorbed by the collector, less the amount lost by the collector to its surroundings. u v   0 (10) This is expressed as: x y

Qu sfl  Qrecv  Qloss  I  A  hATcol Tamb  (4) Archive ofu  uSID  p 22 u  u uv     (11) where T and T are collector temperature and nf nf 22 col amb x  y  x xy ambient temperature outside the collector respectively. It is also known that the rate of v  v  p 22 v  v extraction of heat from the collector may be uv     (12) nf nf 22 measured by means of the amount of heat carried x  y  y xy away in the fluid passed through it, which is: 22 Qusfl  mC p Tout Tin  (5) TTTT    uv    (13) nf 22 Equation (4) may be inconvenient because of the xy xy difficulty in defining the collector average temperature. It is convenient to define a quantity The thermal diffusivity: that relates the actual useful energy gain of a collector to the useful gain if the whole collector  kC (14) nf nf p nf surface were at the fluid mean temperature. This quantity is known as “the collector heat removal the density : factor (FR)” and is expressed as:

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R.Nasrin and M. A. Alim / JAFM, Vol. 7, No. 3, pp. 543-556, 2014. x y u v p XYUVP,,,,,     2 LLUUin in fU in nf1    f    s (15) T T k   in f the heat capacitance: qL Then the non-dimensional governing equations are CCC1       (16)  pnf p f p  s U V   0 (19) X Y the viscosity of the nanofluid is considered by the Pak and Cho correlation (1998). This correlation is UUPUU  1  22  UV  f  nf   (20) given as: 22 X  Ynf  X f Re XY 2 nf  f 1  39.11   533.9  (17)   VVPVV  1  22  UV  f  nf   (21) 22 the thermal conductivity of Maxwell Garnett (MG) X  Ynf  Y f Re XY model (1904) is :   1   22    UV nf   (22) k22 k  k  k 22 s f f s  X Y RePr  f XY kknf f (18) ks2 k f   k f  k s  ν UL where Pr  f is the Prandtl number, Re  in For water based nanofluid with double α f  f nanoparticles the modified properties of Eqs. (15 to is the Reynolds number.The corresponding 18) are as follows: boundary conditions take the following form: / nf1  1   2  f   1  s1   2  s 2  (15 ) At all solid boundaries:U = V = 0

 k f is the density: At the upper and lower walls:   Y knf CCCC1             pnf1 2 p f 1 p s12 2  p  s At the inlet boundary: θ = 0, U = 1 (16/) At the outlet boundary: convective boundary is the heat capacitance. condition P = 0 The effective viscosity of the nanofluid is considered by the Pak and Cho correlation (1998). 3.1 Mean Nusselt Number This correlation is given as modified form The average Nusselt number (Nu) is expected to depend on a number of factors such as thermal  1  39.11     533.9 22   (17/) nf f  12  12 conductivity, heat capacitance, viscosity, flow structure of nanofluids, volume fraction, Also the effective thermal conductivity (modified dimensions and fractal distributions of form) is used from Maxwell Garnett (1904) model nanoparticles. The rate of heat transfer along the upper heated wall of the collector is used by Saleh ks1 k s 2 2 k f  2 1 k f  k s 1  2 2 k f  k s 2  et al. (2011) as kknf f ks1 k s 2 2 k f  1 k f  k s 1  2 k f  k s 2  1 / (18 ) knf  Nu dX (23)  kYf  Where subscripts 1 and 2 represent alumina and 0 copper nanoparticles respectively. The boundaryArchive conditions are: 3.2of Mean Temperature SID and Velocity At all solid boundaries: u = v = 0 The mean bulk temperature and average sub domain velocity of the fluid inside the collector At the top and bottom surfaces of the pipe: heat flux may be written as  dV/ V and T av  per unit area k  q  I   h T  T  nf col amb VV/ dV V y av  , where V is the volume of the collector. At the inlet boundary: TT in , u = Uin At the outlet boundary: convective boundary 3.3 Streamfunction condition p = 0 Streamfunction  is obtained from velocity The above equations are non-dimensionalized by components U and V. The relationship between using the following dimensionless dependent and stream function and velocity components is independent variables:   U  , V   . Y X

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 2  2 U V  F dA  F n ds Thus    (24)   X 2 Y 2 Y X A c   N udA  N un ds     3.4 Heatfunction A c Heatfunction ξ is obtained from conductive heat   N  u dA  N u dA   N u n ds     fluxes  ,   as well as convective heat A A c  X Y  using  F   F  .F fluxes (Uθ, Vθ). It satisfies the steady energy balance equation such that Thus 2nd ordered terms in momentum and energy     U   , V    . Eqs (27) to (29) can be written as X Y Y X 22 UUUU NN   2 2 N  dA         XY22 XXYY    Thus   U  V  (25) AA X 2 Y 2 Y X   N Sx dS0 S0 4. NUMERICAL 22 VVVV NN   IMPLEMENTATION N  dA   dA 22 XXYY    XY  The governing equations along with the boundary AA conditions are solved numerically, employing   N Sx dS0 Galerkin weighted residual finite element S0 techniques. To derive the finite element equations, 22 the method of weighted residuals Zienkiewicz   NN     N  dA   dA (1991) is applied to the governing Eqs (19) to (22) XY22 XXYY    AA as   N qw dSw UV S N  dA 0 (26) w  XY where surface tractions (S , S ) along outflow A x y boundary S0 and velocity components and fluid UUP  f    temperature or heat flux (qw) that flows into or out N U V  dA   H   dA from domain along wall boundary S . XYX  nf    w AA (27) Applying Gaussian quadrature technique to 1  22UU nf N dA momentum and energy equations in order to  22 Re f  XY A  generate the boundary integral terms associated with the surface tractions and heat flux VVP  f    N U V  dA   H   dA UUP   f    XYX  nf    N U V  dA  H   dA  AAAAXYX   (28)  nf   1  22VV  nf N dA 1 nf NUNU     22 dA N Sx dS0 Re f  XY Re AS X  X  Y  Y A  f 0 (30) 22   nf      N U V dA  N  dA  X Y RePr 22 VVP  f    f XY N U V  dA  H   dA  AAAAXYY      (29) nf Archive of SID 1 nf NNVV where A is the element area, N ( α = 1, 2, … … , dA N Sy dS0 Re f AS X  X  Y  Y 0 6) are the element interpolation functions for the (31) velocity components and the temperature and H ( λ = 1, 2, 3) are the element interpolation functions TT 1 nf N U V dA for the pressure. A  X Y RePr  f Applying Gauss’s Divergence theorem to the 2nd NNTT ordered derivative part of the governing equations : dA N qww dS ASXXYY    w (32) The basic unknowns for the above differential equations are the velocity components U, V the temperature  and the pressure P. The six node triangular element is used in this work for the development of the finite element equations. All six

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nodes are associated with velocities as well as Qux N S dS0 , Qvy N S dS0 , temperature. Only the corner nodes are associated  S0  S0 with pressure. This means that a lower order polynomial is chosen for pressure and which is Q N qww dS  S satisfied through continuity equation. The Galerkin w finite element method Taylor and Hood (1973) and These coefficients are solved by Galerkin’s Dechaumphai (1999) is used to solve velocity weighted residual method. Substituting the element components and the temperature distribution and velocity components, the temperature and the linear interpolation for the pressure distribution pressure distributions from Eqs.(33 to 36), the according to their highest derivative orders in the linear algebraic equations are differential Eqs (26), (30 to 32) are as K  x U   K  y V  0 (37) UX ,Y   N  U  ,V X ,Y   N  V ,

TX ,Y   N  T and PX ,Y   H  P f KUUKVUMPx  y    x    nf  where β = 1, 2, … … , 6 and λ = 1, 2, 3. Thus (38) 1 nf  SSUQxx yy u Re f    U N N dA V N N dA 0   ,,xy    (33) AA  f KUVKVVMPx  y   y   nf  UU  NNN   ,,xy dAVU   NNN    dA (39)  1 nf  AA SSVQxx  yy  v Re  f    1 nf  U N ,,,,x N  x dA N  y N  y dA Re  f AA KUKV xy      f P H  H ,0xx dA N  S dS 1 nf  (40) nf S0 (34) SSQxx yy  A RePr     f The linear algebraic equations are solved by UV  NNN   ,,xy dAVV   NNN    dA  applying the Newton-Raphson iteration technique AA  FKUKV (41) 1 nf p  x  y V N ,,,,x N  x dA N  y N  y dA Re  f AA  f  FKUUKVUMP   f u  x   y    x  P H  H ,0yy dA N  S dS nf (42) nf  S0 (35) A 1 nf ()SSUQxx  yy  u Re  f   

U  NNN   ,,xy dAV   NNN    dA   f AA FKUVKVVMPv x   y    y    nf  1 nf  (43) N ,,,,x N  x dA N  y N  y dA  RePr f AA 1 nf ()SSVQxx  yy  v Re  f     N qww dS Sw FKUKVxy       (36)    (44) 1 nf  The coefficients in above governing equations are SSQxx yy  Archive ReProf f  SID   denoted as

K N N dA , K N N dA , This leads to a set of algebraic equations with the  xx ,  yy , A A incremental unknowns of the element nodal velocity components, temperatures, and pressures in Kxx N N  N  , dA  A the form,

F p KKpu pv 00u  K N N N dA , K N N dA ,   yy    ,     A A KKKK F u uu uv u up v   , Sxx N,, x N x dA KKKK  F v  A vu vv v vp   p F  KKKuv   0  S N N dA ,  yy ,, y y A where Δ represents the vector of nodal velocities, Mxx H H, dA , Myy H H, dA pressure and temperature.  A  A

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KKUKUKVuu x  x   y   Table 1 Grid Sensitivity Check at Pr = 6.6,  =    5% (water-alumina nanofluid) and Re = 600 1 nf  , Nodes Nu Nu Base Time (s) SS xx yy (elements) Nanofluid fluid Re  f   506 (60) 8.12945 6.52945 226.265 KKU , KKV , uv y  vu x  1788 (240) 9.29176 7.89976 312.594 KKKKKu0   p  p   pp  v  ,

 f 6692 (960) 10.37518 8.48701 398.157 KMup x , KKpv y , nf   25860 11.05698 9.02676 485.328 (3840)  f KMvp y KKvy  101636 11.05711 9.02688 979.377    nf (15360) KKUKVKV    vv x  x   y  An extensive mesh testing procedure is conducted 1 nf  , SSxx yy to guarantee a grid-independent solution for Re = Re  f   600 and Pr = 6.6 in a solar collector. In the present KKux  , KKpu x , work, we examine five different non-uniform grid   systems with the following number of elements within the resolution field: 60, 240, 960, 3840 and KKUKV   xy    15360. The numerical scheme is carried out for

1 nf highly precise key in the average Nusselt number ()SSxx yy for water-Al O nanofluid ( = 5%) as well as base RePr  f   2 3 fluid ( = 0%) for the aforesaid elements to develop an understanding of the grid fineness as shown in The iteration process is terminated if the percentage Table 1 and Fig. 3. The scale of the average Nusselt of the overall change compared to the previous numbers for 3840 elements shows a little difference iteration is less than the specified value. The with the results obtained for the other elements. convergence of solutions is assumed when the Hence, considering the non-uniform grid system of relative error for each variable between consecutive 3840 elements is preferred for the computation iterations is recorded below the convergence criterion ε such that n1  n   , where n is . number of iteration and UV,, . The convergence criterion was set to ε = 10-4.

4.1 Mesh Generation In the finite element method, the mesh generation is the technique to subdivide a domain into a set of sub-domains, called finite elements, control volume, etc. The discrete locations are defined by the numerical grid, at which the variables are to be calculated. It is basically a discrete representation of the geometric domain on which the problem is to be solved. The computational domains with irregular geometries by a collection of finite elements make the method a valuable practical tool for the solution Fig. 3. Grid test for riser pipe of the solar of boundary value problems arising in various fields collector Archive Tableof 2 Thermo SID physical properties of fluid and of engineering. Fig. 2 displays the finite element nanoparticles mesh of the present physical domain. Physical Fluid phase Ag Cu Al O CuO 2 3 Properties (Water)

Fig. 2. Mesh generation of the riser pipe of the solar collector Cp(J/kgK) 4179 235 385 765 535.6  (kg/m3) 997.1 10500 8933 3970 6500 4.2 Grid Independent Test k (W/mK) 0.613 429 400 40 20 2 α107 (m /s) 1.47 1738.6 1163.1 131.7 57.45

4.3 Thermo-physical Properties The thermo-physical properties of the nanoparticle are taken from Ogut (2009) and given in Table 2.

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4.4 Code Validation 5%, the temperature distributions become distorted resulting in an increase in the overall heat transfer. This result can be attributed to the dominance of the solid concentration. This is because the thermal conductivity of the solid particles is very high. This means that higher heat transfer rate is predicted by the nanofluid having two nanoparticles namely

Al2O3 and Cu. It is worth noting that as the solid volume fraction of Al2O3 and Cu nanoparticles increases, the thermal boundary layer near the top and bottom surfaces of the riser pipe becomes thick which indicates a steep temperature gradients and hence, an increase in the overall heat transfer from the absorber plate containing pipe to the outlet edge. But further increasing  to 10% (= 5% + 5%) there is no perturbation observed in the isothermal lines at all. Thus adding more solid volume fraction is not advantageous. Fig. 4. Comparison between present code and 2 Kalogirou (2004) at I = 1000 W/m The corresponding velocity field indicates that at  = 1% the velocity of nanofluid is high. Thus the The present numerical solution is validated by nanofluid quickly passes the pipe by getting heat comparing the current code results for collector from upper and lower walls as a result the streamlines appear the whole riser pipe. In the efficiency - temperature difference [Ti - Ta] profile of water with the graphical representation of velocity vector, initially the flow covers the entire Kalogirou (2004) for flat plate solar thermal domain of the pipe while it concentrates near the collector at irradiation level 1000 W/m2 and the middle of the pipe of flat plate solar collector due to mass flow rate per unit area was 0.015 (kg/s m2). increase solid volume fraction  from 1% (= 0.05% Solar thermal collectors and applications were + 0.05%) to 10% (= 5% + 5%) of water- reported by Kalogirou (2004). Figure 4 alumina/copper nanofluid. This happens because of demonstrates the above stated comparison. The escalating solid concentrations of flow. Nanofluid numerical solutions (present work and Kalogirou having larger density does not move freely. (2004)) are in good agreement. The heatlines are smooth and it is observed that the lines are perfectly perpendicular to the isothermal 5. RESULTS AND DISCUSSION lines and the upper and lower walls. This further indicates that the heat flow is conduction dominant. In this section, numerical results of isotherms, From the Fig. 5(c) it is clearly observed that the streamlines and heatlines for various values of solid heatlines with greater strength become smaller in volume fraction ( =  + ) of the water- 1 2 size at the middle of the flow pipe for  = 5% alumina/copper nanofluid and various nanofluids (2.5%+2.5%). This happens due to more thermal such as water-CuO, water-Al O , water-Cu and 2 3 conductive heat flux and as it is seen the case of the water-Ag with solid volume fraction ( = 5%) lowest solid volume fraction, the strength of through a riser pipe of flat plate solar collector are heatline goes to low. The heatlines remain constant displayed. The considered values of  (= 1+2) are for further increasing  from 5% to 10%. This  = (1%, 3%, 5%, 7% and 10%), while the means that major amount of heat flux or transport Reynolds number (Re = 600) and Prandtl number occurs for  = 5% of water-Al O /Cu nanofluid. (Pr = 6.6) are chosen. In addition the values of the 2 3 average Nusselt number, mean bulk temperature, mean sub domain velocity, percentage of collector 5.2 Effect of Different Nanofluids efficiency Archive and mid-height temperature Theof performance SID of water and four different water (dimensional) are shown. based nanofluids on the dimensionless temperature, streamfunction and heatfunction are presented in 5.1 Effect of Double Nanoparticles Fig. 6 (a) to (c) while solid volume fraction of nanoparticles  = 5%. The isotherms are smooth The effect of  (= 1 + 2) on the thermal, velocity monotonic curves symmetric to the mid-horizontal and heat flux fields are presented in Fig. 5 (a)-(c) axis. The temperature lines through the horizontal while Pr = 6.2 and Re = 600. The strength of the riser pipe become more heated for accordingly thermal current activities is more activated with water, water-copper oxide, water-alumina, water- escalating volume fraction of water-Al2O3/Cu copper and water-silver. The fluid enters from the nanofluid. Increasing  (solid volume fraction of left inlet and getting heat form upper and lower alumina and copper nanoparticles equally), the boundaries and finally exits from the right inlet of temperature lines near the upper and lower parts of the riser pipe of a flat plate solar collector. Initially the riser pipe become flatten whereas at the lower  (clear water) the isothermal lines are distinct (= 1% = 0.5% + 0.5%) they are bended due to through the pipe. Due to rising thermal conductivity concentration of solid particles is dominated across of the nanofluid they become more heated and try the pipe. With the rising values of  from 1% to to gather near the exit boundary. The thermal

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boundary layer becomes thick for water-Ag nanofluids respectively. In the velocity vector, the nanofluid than other nanofluids and water because flow covers the whole domain of the pipe for base Ag nanoparticle has more thermal conductivity than fluid (water) while it concentrates near the middle others. of the riser pipe due to rising density of the nanoparticles. Fluid with solid particles (nanofluid) has lower velocity than base fluid (without solid  = 10% particle).

Water-Ag nanofluid  = 7%

Water-Cu nanofluid

 = 5%

Water-alumina nanofluid

 = 3%

Water-CuO nanofluid  = 1%

(a) water (a)  = 10%

Water-Ag nanofluid  = 7% Water-Cu nanofluid  = 5%

Water-alumina nanofluid  = 3% Water-CuO nanofluid  = 1% (b) water (b)

 = 10%

Water-Ag nanofluid  = 7% Water-Cu nanofluid Archive = 5% of SID Water-alumina nanofluid  = 3% Water-CuO nanofluid  = 1% (c) water (c) Fig. 5. Effect of  of water-alumina/copper nanofluid on (a) temperature and (b) streamfunction and (c) heatfunction Fig. 6. Effects of various nanofluids as well as base fluid on (a) temperature and (b) streamfunction and (c) heat function The strength of the flow circulation is much more deactivated for water, water-aluminium oxide, In the heatfunction (Fig. 6 (c)) heatlines are smooth water-copper oxide, water-copper and water-silver and it is observed that the lines are perfectly

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perpendicular to the isotherm lines and the upper water-Cu, water-Al2O3, water-CuO nanofluids and lower walls. This further indicates that the heat respectively. Heat transfer rate increases by 33%, flow is conduction dominant. An important point to 30%, 22% and 20% with the variation of  from 1% note is that the heatlines with greater strength to 5% respectively for Ag, Cu, Al2O3 and CuO become smaller in size at the middle of the flow nanoparticles. Here Nu remains constant for water pipe. This happens due to more conductive heat with the variation of  . For all nanofluids mean flux and as we see the case of water, the strength of Nusselt number rises sharply from 0% to 5% and heatlines go to low. This means that major amount heat transfer rate remains nearly constant for of heat flux or transport occurs for water-silver escalating  from 5% to 10%. Thus, it is not always nanofluid. Thus, relatively less heat flow occurs for beneficial to introduce more solid volume fraction clear water. of nanoparticle with base fluid for a flow.

5.3 Mid-height Temperature The temperature (dimensional) of water- alumina/copper nanofluid and water-copper nanofluid at the middle height of the riser pipe with the influences of solid volume fraction are displayed in Fig. 7(i) and (ii) respectively. From the Fig. 7(i) it is shown that the inlet temperature of fluid is maintained at 300K and then it increases gradually with the contact of heated solid upper and lower boundaries of the riser pipe. And finally the output temperature of water-alumina/copper (i) (ii) nanofluid becomes 344K, 350K, 354K, 357K, 357K Fig. 8. Mean Nusselt number for the effect of (i) and 357K for  = 0%, 1%, 3%, 5%, 7% and 10% nanofluid with single and double nanoparticles respectively. and (i) various nanofluids

Similarly mid-height temperature increases with growing  upto 5% and then remains unchanged. 5.5 Mean Bulk Temperature The output temperature of water-Cu nanofluid becomes 344K, 350K, 355K, 360K, 360K and Figures 9(i) and (ii) display mean temperature (θav) 360K for  = 0%, 1%, 3%, 5%, 7% and 10% versus the nanofluid with single and double respectively. nanoparticles and various nanofluids. θav grows sequentially for  upto 5% for both figures. Mean temperature remains constant for further increasing values of solid volume fraction. It is well known that thermal conductivity of Ag nanoparticle is higher than others. Higher thermal conductivity is capable to carry more heat. Thus average bulk temperature of water-Al2O3/Cu and water-Ag nanofluids have found higher in Figs. 9(i) and 9(ii) respectively. There is no change of water ( = 0%) due to the deviation of nanoparticles volume fraction. (i) (ii)

Fig. 7. Mid-height temperature for the effect of (i) water-Al2O3/Cu nanofluid and (i) water-Cu nanofluid

5.4 Rate of Heat Transfer Archive of SID In Fig. 8(i) average Nusselt number at the upper hot surface with various solid volume fraction is accounted for nanofluid having double and single nanoparticle as well as clear water. Nu enhances sharply with growing  upto 5% and then remains (i) (ii) unchanged for advance mixture of solid volume faction for water based nanofluid having double as Fig. 9. Average temperature for the effect of well as single nanoparticles. Rate of heat transfer (i) nanofluid with single and double enhances by 27% and 22% with the variation of  nanoparticles and (i) various nanofluids from 0% to 5% for water-alumina/copper and water-alumina nanofluids respectively. 5.6 Magnitude of Average Velocity

From the plot of the average Nusselt number (Nu)- Magnitude of average velocity vector (Vav) for the solid volume fraction () of the Fig. 8(ii) it is nanofluid with single and double nanoparticles and observed that rate of heat transfer is maximum for various nanofluids are expressed in the Fig. 10(i) water-Ag nanofluid. And then Nu devalues for and (ii). Vav has notable changes with different

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R.Nasrin and M. A. Alim / JAFM, Vol. 7, No. 3, pp. 543-556, 2014.

values of solid concentration of different nanofluids. Growing  devalues mean velocity of the nanofluid through the riser pipe of the flat plate 6. Conclusion solar collector. Here water-alumina nanofluid has The finite element simulation of forced convection higher mean velocity than the water-alumina/copper heat transfer by a water based nanofluid containing nanofluid. Less solid concentrated nanofluid has double nanoparticles and various nanofluids inside greater velocity than highly concentrated nanofluid. the riser pipe of a flat plate solar collector is Also mean velocity is obtained maximum for water accounted. Various solid volume fraction ( = and then for water-alumina, water-copper oxide, 1+2) of water-Al2O3/Cu nanofluid and also water-copper and water-silver nanofluids different nanofluids have been considered for respectively. Water has lower density than all showing the temperature, flow and heat flux considered nanofluids. patterns. The results of the numerical analysis lead to the following conclusions:  The structure of the fluid isotherms, streamlines and heatlines through the solar collector is found to appreciably depend upon the  (= 1+2) and different nanofluids.  Adding two nanoparticles with base fluid is more effective in enhancing performance of heat loss rate than single nanoparticle.  Water-Ag nanofluid is better than other considered nanofluids for heat transfer (i) (ii) characteristics.

Fig. 10. Mean velocity for the effect of (i)  Percentage of collector efficiency is obtained maximum for 5% solid volume fraction of nanofluid with single and double nanoparticles and (i) various nanofluids water-silver nanofluid.  Mean temperature is higher for nanofluid with 5.7 Collector Efficiency double nanoparticles than nanofluid with Figures 11(i) and (ii) express the collector single nanoparticle. efficiency η(%)-solid volume fraction  (%) for the  Average velocity decreases due to growing  nanofluid with single and double nanoparticles and for all nanofluids. various nanofluids. Here  varies from 0% to 10%.  The mid height temperature of nanofluids From this figure it is observed that adding low increase steadily while passing through the quantities of nanoparticles leads to the remarkable riser pipe for all . enhancement of the efficiency until a volume fraction of approximately 5%. After a volume Thus water-Cu nanofluid is more effective in order fraction of 5%, the efficiency begins to level off to promote heat loss system through the riser pipe with increasing volume fraction. The authors of a flat plate solar collector for lower cost of Cu attribute this unchanging to the high increase of the nanoparticles than that of silver nanoparticles. fluid absorption at high particle loadings. The main difference in the steady-state efficiency occurs in REFERENCES water based nanofluid having alumina and copper nanoparticles. Consequently, percentage of solar Álvarez, A., M.C. Muñiz, L.M. Varela, O. Cabeza collector efficiency is obtained maximum for water- (2010), Finite element modelling of a solar silver nanofluid in Fig. 11(ii). Collector efficiency collector, Int. Conf. on Renew. Energies and rises from 65% to 89% with growing the solid Power Quality, Granada (Spain). volume fraction  from 0% to 5% for water-Ag nanofluid. Archive Amrutkar,of S.K. , SIDS. Ghodke, Dr.K.N. Patil, (2012), Solar flat plate collector analysis, IOSR J. of

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