ARID ZONE JOURNAL OF ENGINEERING, TECHNOLOGY & ENVIRONMENT AZOJETE September 2020. Vol. 16(3):435-448 Published by the Faculty of Engineering, University of Maiduguri, Maiduguri, Nigeria. Print ISSN: 1596-2490, Electronic ISSN: 2545-5818 www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 435 ORIGINAL RESEARCH ARTICLE MATHEMATICAL MODELING OF A FLAT PLATE SOLAR COLLECTOR WITH EUTECTIC SALTS AS PHASE CHANGE MATERIAL O. F. Isamotu,* N. A. Musa, O. J. Okegbile, M. A. Oriaifo and A. O. Bakare (Mechanical Engineering, Engineering, Federal University of Technology, Minna, Nigeria) *Corresponding author’s email address: olakunleisamot@yahoo.com 1.0 Introduction The growing number of problems with the world’s dependence on fossil fuels continues to foster the public’s desire to pursue clean, renewable sources of energy. Due to environmental issues and limited fossil fuel resources, more priorities are being given to renewable energy sources (Goswami, 2004). The energy from the sun is one form of renewable energy sources. It can be used for water heating in hot water systems, swimming pools as well as a supporting energy sources for central heating installations. The energy from the solar radiation is used for aforementioned purposes via solar collectors. At present the most often used solar collectors are liquid flat-plate collectors working either in parallel or perpendicular tube arrangement as well as the vacuum based structures. The flat plate collector supplies heat below 80°C when not integrated with phase change materials for energy storage and conservation (Hassan, 2003), ARTICLE INFORMATION ABSTRACT Solar energy is the most promising heat source for meeting energy demand without having negative impact on the environment. Solar energy is, however, intermittent in nature and time dependent energy source. In order to mitigate the intermittent supply of solar energy for water heating, the use of phase change material (PCM) comes into play. The PCM acts as a heat source for the solar heating system when the intensity of the solar radiation is low or no longer active. Knowledge about the thermal effectiveness of solar collector with PCM is paramount. So, this study developed a mathematical model to evaluate the thermal behavior of a flat plate solar collector integrated with a phase change material (PCM). This mathematical model developed for the flat-plate with PCM was based upon the conservation and heat transfer equations and used to predict the thermal behavior of integrated phase change material in solar collector during thermal storage. The energy balance equations for the flat-plate heating components of the collector and PCM were formulated numerically. The model was used to investigate the effect of inlet water temperature, water mass flow rate, outlet water temperature and the melt fraction during charging and discharging modes at each of the respective nodes. A comparison was made with a collector with and without PCM. The results show that charging and discharging processes of PCM have multiple stages. The addition of PCM in the first stage causes a decrease in temperature during charging and an increase during discharging. The highest water temperatures reached for the collector without and with a phase change material were approximately 51 and 74°C respectively Comparisons were also made between the simulated and experimental data for the solar water heater without and with PCM. Minimum inlet water temperatures of 41.54 and 36°C were observed for the simulated and experimental model while, 42.69 and 74°C were both recorded for outlet temperatures respectively, for solar water heater without PCM. For the solar water heater with PCM, the inlet temperatures for the simulation and experimental model were found to be 42°C and 56°C respectively. A maximum outlet water temperature of 108°C was obtained from the experimental model compared to 45°C obtained from simulation. The temperature of the hot water obtained was remarkable and sufficiently enough for many domestic and industrial applications. Finally, the solar water heating system with phase change materials finds useful application and acts as a renewable energy resource in regions where there is inconsistent or poor sunlight. © 2020 Faculty of Engineering, University of Maiduguri, Nigeria. All rights reserved. Submitted 18 Dec., 2020 Revised 19 April, 2020 Accepted 26 April, 2020 Keywords: Thermal storage solar collector numerical model phase change material experimental validation mailto:olakunleisamot@yahoo.com http://www.azojete.com.ng mailto:olakunleisamot@yahoo.com Isamotu et al: Mathematical Modeling of a Flat Plate Solar Collector with Eutectic Salts as Phase Change Material. AZOJETE,16(3):435- 448. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 436 in reality,theindicative temperature range of operating fluid in flat plate collectors is between the range of 30-65°C (Kalogirou, 2004) and the system has an efficiency index higher than 0.5 typical for available flat plate collectors. Several studies have been carried out on the use of solar energy for heating purpose (Badescu, 2007). Notably, Nahar (2002) carried out studies on a solar water heater storage collector system and discovered that the system could generate about 50.6°C water at 4:00pm and 41.6°C water the next day with overall efficiency of about 47%. Similarly, Zerrouki et al. (2012), worked on a solar storage collector system in Algeria. The system achieved a maximum temperature of 53°C with an initial temperature of 17°C around 7:00am. A maximum flow rate occurred around 1:00pm. Kürklü et al. (2002), investigated a technique that could enhance the thermal performance of a flat-plate solar collector. It was found that the proposed design significantly improved the collector heat transfer characteristics in term of absorptivity and heat transfer coefficient. Rabin et al. (1995) developed a mathematical and experimental model for the charging process of a solar collector storage system, integrated with salt hydrate as a PCM. The proposed model showed high accurate validation with the experimental PCM temperature measurements. However, the neglect of the convection heat transfer in the stationary heat transfer reduced the accuracy of their mathematical predictions.Lin et al. (2012), proposed a comparative experimental study, under a typical sunny day in Malaysia, to investigate the possibility of enhancing the performance of a flat-plate solar collector by integrating paraffin wax with a melting temperature of 60.45°C directly in contact with the collector’s absorber plate. The proposed collector achieved an efficiency of 52% at an inclination angle of 100, which was better by 23% than the conventional collector. Naghavi et al. (2015), proposed a theoretical model based on a one phase Stefan problem to investigate the thermal performance of integrating PCM to the manifold of an evacuated tube heat pipe solar collector system. it was revealed that the hot water volume and thermal efficiency of the baseline system significantly decreased with increase in the water volume flow rate from 50 to 80 litres per hour. The usable volume and the thermal efficiency almost remain the same in the innovative system. Although a lot of work has been done on solar water heater (Lin et al, 2012) the need to device a means of obtaining optimum performance of flat plate solar collector cannot be overemphaised. In view of this, Isamotu (2019) developed four different types of eutectic salt mixtures and found that the mixture of 1.77g of LiNO3, 2.94g of NH4NO3, 1g of NaNO3 and 1g of NaCl with melting point of 84.4°C and latent heat of 119KJ/Kg has better energy storage capabilities. Therefore the aim of this work is to developed a mathematical model for solar collector with the eutectic salt mixture according to Isamotu (2019) as PCM 2.0 Materials and Method The following materials were used in this research work: fiber glass, glass cover, absorber, working fluid, pipes (headers/risers), PCM, XM1400 solar dual transmission meter and KM25O thermocouple 2.1 Description of the Flat Plate Collector System A flat plate collector consisting of a transparent cover, fluid, heat insulation, phase change materials, absorber plate, and collector casing were used. Figure 1 shows how the flat plate collector look likes. In line with the principle of operation, the sunlight passing through the glazing cover strikes the absorber plate and the solar radiation is converted into usable heat and transferred via its inner surface to the fluid passing through the respective nodes of the collector. Subsequently, the fluid carries the energy away from the collector for direct use or storage. The absorber plate is made of a thin (flat or grooved) high thermal conductivity metal sheet which could be steel, aluminum or copper. In order to maximize the efficiency of a solar collector, the surface of the absorber plate is painted with black colour pigment because of its high absorptivity property. The flow tubes in the collector are the integral parts of the absorber plate and these tubes are connected to the header tubes at both ends and either of http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 445-448. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 437 which could serve as a supply or return pipe (inlet, outlet). Some of the thermal energy is transferred via convection to the transfer fluid and the other is transferred by both conduction and convection to the phase change material beneath the absorber. When the absorbed temperature of the flat plate collector becomes higher than that of the PCM, the heat is first stored as a sensible heat until the PCM reaches its melting temperature. At this point, the PCM starts to melt and after complete melting, the released heat is stored back in the molten PCM as a sensible heat. When the sun was no longer active, all the solar components starts to cool down and the PCM at this point serves as the main heat source for the flat plate solar system. Figure 1: Cross sections of a flat plate collector (Alternative Energy Tutorials, 2012) 2.2 Mathematical model of a Flat plate collector with PCM A schematic system study is depicted in Figure 2. Figure 2: Schematic of a solar thermal system and setup (Badescu, 2007) file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng mailto:olakunleisamot@yahoo.com Isamotu et al: Mathematical Modeling of a Flat Plate Solar Collector with Eutectic Salts as Phase Change Material. AZOJETE,16(3):435- 448. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 438 The system consists of a thermal solar panel, thermal tank, eutectic phase change materials, piping as well as control valves.The PCM (eutectic salt mixture) used in this system has a good thermal energy storage density and low thermal conductivity. The PCM was then embedded in black colour pigment and used to coat the solar panelwhich was integrated into the heat-exchanger in the solar collector as shown in Figure 3. Figure 3: Solar tube heat exchanger finite-difference formulation (Badescu, 2007) In order to write the energy conservation and heat transfer equations of the eutectic salt, the heat exchanger should be considered at each of the respective node because of the non- uniformly temperature distribution across each section. However, the model proposed is based on the following seven assumptions: (i)The thermo-physical properties of the PCM are independent of temperature, but different for solid and liquid phases. (ii) The heat transfer fluid is incompressible and it can be considered as a Newtonian fluid. (iii) The PCM is in perfect contact with the absorber. (iv) The PCM is homogeneous and isotropic. (v) The inlet velocity and inlet temperature of the heat transfer fluid are constant. (vi) No thermal expansion during melting process and (vii) The heat transfer in the direction of the transfer fluid is ignored. The mathematical modeling of the heat transfer processes of a flat plate solar collector with PCM consist of both the solar radiation which is the source of the solar energy and the solar collector. The solar collector is further divided into seven sections has follows: The glass cover, absorber plate, air gap, transfer fluid, collector efficiency factor, collector heat removal factor and phase change materials. Some of the mention parameters will be discussed individually, Global solar radiation is the total amount of solar energy received by the earth's surface, usually expressed as W/m2. About 99 percent of global solar radiation has wavelengths between 300 and 3000 nm. This includes ultraviolet (300-400 nm), visible (400-700 nm), and infrared (700-3000 nm) radiation. Bekkouche(2008) proposed a theoretical model based on the following correlations. The solar irradiance are calculated as follows:           2sin 1expcos1 1 hB A  (1) where: h is the sun’s height and θ1 is the direct incident angle. http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 445-448. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 439 The diffuse irradiance is expressed as hh GDD                 2 cos1 2 cos1 (2) where: β the tilt is angle of the collector and ρ is the albedo Dh and ρGh are further expressed as:    4.0sin' hADh  (3)    ''sin'' B h hAG  (4) The constants B,A',A" and B" depends on atmospheric state with time. The energy balance equations for all of the seven components of the solar collectors mentioned earlier with temperature dependent is obtained for each of the components. i. Glass covering According to Zueva and Magiera (2001) the glass covering can be thus be written as: cgρgVg dTg dt = hg.am Tam − Tg + hr1 Tab − Tg + hc1 Ta − Tg + αG p∇Z (5) where: c = specific heat, ρ = density, V = volume, T = temperature, t = time, h = heat transfer coefficient, α = absorption coefficient, G = heat flux of solar radiation,p = tube pitch, ∆z = spatial size of control volume Subscripts notation:,am = ambient, g = glass cover, a = air gap,ab = absorber, r = radiation c = convection According to Duffie and Beckman (1974) the heat transfer coefficients by convection are calculated respectively as: hcv,am = 3.9vwind + 5.62 (6) hcv,a = Nuλa ea (7) vwind , λa , ea are the wind velocity, air thermal conductivity and the air gap thickness respectively. The Nusselt number is calculated as follows: Nu = (0.06 − 0.017 β 90 ))Gr0.33 (8) Gr is the Grashoof number expressed as:           a acabs Tv eTTgGr 2 3 (9) The heat transfer coefficient by radiation is expressed as: hr,c−as = εc σ (Tc2 + Tas2 )(Tc + Tas) (10) where: Tas is the temperature of the air-space file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng mailto:olakunleisamot@yahoo.com Isamotu et al: Mathematical Modeling of a Flat Plate Solar Collector with Eutectic Salts as Phase Change Material. AZOJETE,16(3):435- 448. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 440 The heat transfer coefficient by radiation on the absorber is expressed as:                   abc abcabc abcr TTTTh   11 22 , (11) According to Duffie and Beckman (1974) Tas is expressed as: Tas = 0.0553Tam 3 2 (12) ii. The absorber plate According to Shiv et al. (2010), the transient thermo-physical properties of the absorber material are considered when a heat energy balance is applied to the absorber zone. The solar irradiance on the absorber zone of the solar collector control volume, the radiation between the absorber and the glass cover, the conduction between the absorber and the insulation zone and the heat transfers by convection with the fluid flow need to beconsidered. The following relation gives: cab(Tab)ρab(Tab)Vab dTab dt = {G(τa) + hr1(Tg− Tab) + hc1(Ta−Tab) + ki δi (Ti-Tab)}p∆Z+πdinhf∆Z(Tf−Tab) (13) where: τa = Effective transmittance absorption coefficient, k = thermal conductivity, δ = thickness, d = diameter, Subscripts: i = insulation, f = working fluid, in = inner. iii. Air gap of the flat plate collector ρaVaCa dTa dt = hcv,c−aSc Tc− Ta + hcv,ab−aSab Tab− Ta + Uloss,eSa,e Tam− Ta (14) According to Ahmad (2012), the heat exchange coefficient by convection can be estimated using (7) Nu = 0.023Re0.8Pr0.4 (15) Based on Incropera et al. (2006), the bottom loss and side loss coefficient of the collector is given as:                             windcvsins sins sloss windcvbins bins bloss h U h U ,, , , ,, , , 1 1, 1 1     (16) The thermal heat exchange with the phase change materials during charging and discharging modes are expressed as follows: Qab, PCM = − λPCM,iSPCM δTPCM,i δx (17) Qab, PCM = λPCM,iSPCM δTPCM,i δx (18) http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 445-448. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 441 where: i = solid when the phase change material is in the solid state and i = liquid when the phase change material is in the liquid state. iv. Heat transfer fluid According to Klein et al. (1974), the heat exchange coefficient of the collector can be determine as putting the tube cross section of the solar collector into consideration Ahtf the conservation energy equation for the HTF becomes ρhtfchtf ∂Thtf ∂t =− chtfm� htf Ahtf ∂Thtf ∂x + hπDi Ahtf (Tw−Thtf) (19) The thermal resistance of the wall is assumed to be negligible, the conservation energy equation of the wall now becomes: ρwcw ∂Tw ∂t = hπD Aw Thtf − Tw + 1 sw ( kwAw 1 Aw + kpcmApcm1 Aw ) (Tpcm−Tw) (20) where: Aw = Cross sectional area of the wall kw and kpcmare the thermal conductivity of the wall and the PCM respectively The heat transfer conduction within the PCM in the axial direction is negligible, therefore the conservation energy equation in the first cell of the PCM alternate to the wall becomes: ρpcm ∂Hpcm ∂t = 1 sw kwAw1 Aw + kpcmApcm1 Aw Tpcm−Tw + 1 sw kpcm Apcm ( Hpcm J+1 Aw − Hpcm j Aw ) (21) The energy conservation equation for the generic cell of the PCM becomes: ρpcm ∂Hpcm ∂t = kpcm cpcm ( 1 r ∂ ∂r (r ∂Hpcm ∂r )) (22) Charging phase: During this phase the water mass flow rate can be calculated from the heat released through solar radiation. Mass flow rate of water is expressed as: mw = GAcollectors 1000×Cpw×∆Tw×n (23) where: mw , Water mass flow rate       s kg , G, Radiation       2m w , A, Area of the collector (m2), Cpw , Specific heat of water       kgK kJ , ∆Tw , The heat transfer fluid temperature difference, n , number of tubes in the solar collector. According to Laouadi and Lacroix, (1999) the finite-difference formulation of the time derivative can be written for the solid phase as follows; Solid phase: TPCMm+1 = TPCMm + mwCpw∆Tw ρsVPCMCps ∆t (24) file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng mailto:olakunleisamot@yahoo.com Isamotu et al: Mathematical Modeling of a Flat Plate Solar Collector with Eutectic Salts as Phase Change Material. AZOJETE,16(3):435- 448. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 442 where: TPCMm , Temperature of PCM at m element (℃) , ρs , Density of PCM at solid phase       3m kg , VPCM , PCM volume   sCpm3 , PCM specific heat at solid phase       kgK kJ , ∆t , time differential (s). The same finite-difference formulation of the time derivative can be applied to the mushy and liquid phase as follows; t hV Tcm LPCML mushywpww mm      , 1 (25) Heat along the tubes of the collector according to Senthilkumar et al. (2014) is expressed as Qtube = ρLVPCMhLγ∆t (26) where: γm , Liquid fraction at element hL , PCM latent heat kJ kg ,ρL , Density of PCM at liquid phase       3m kg , Qtube, Heat along each tube (kJ), The finite-difference formulation of the time derivative can be applied to the liquid PCM as follows; TPCMm+1 = TPCMm + mwCpw∆Tw ρLVPCMCpL ∆t (27) Discharging phase This is the stage when the phase change material experiences phase change from liquid to mushy and solid. The rate of useful energy gain in this stage is less than the rate of the thermal losses at the point where the PCM starts to solidify.The water mass flow rate of heat transfer fluid during the discharge process can be calculated as follows; mw = Qcharging Cpw×∆Tw×n (28) The total heat absorbed during the charging phase by the phase change materials in all of the three stages is expressed as: Qcharging = mPCM (Cps∆Ts + hL + CpL∆TL) × n (29) where: mPCM , is the mass of the phase change material per finite different element. 2.3 Experimental evaluation of the solar water heater with PCM based thermal storage The experimental setup of of the solar water heater with PCM based thermal storage is shown in Figure 4. http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 445-448. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 443 Figure 4: The Experimental setup of a solar water heater with PCM The experiments were carried out between the hours of 9:00AM and 20:00 PM every day for four consecutive days and the temperatures of the storage at every 6:30AM were carefully observed. The flow rate of the water was controlled and manipulated by a water regulator. Solar intensity was measured by solar dual transmission meter XM1400 (manufactured in USA by EDTM INC). The temperatures at the different points (inlet, outlet, glass, absorber, and storage tank) of the system were measured by digital thermocouples KM 250 (manufactured in Australia by ACKSEN INC.). 3. Results and Discussion The systems of Equation (1) through (29) has been numerically solved using the finite difference scheme for the adopted phase change materials (eutectic metallic salts) and the results shown in Figures 5 to 8 Global, ambient condition, glass condition, water inlet conditions, heat transfer fluid temperature with respect to time, solar insolation, and water outlet condition are shown in Figures 5 to 8 Figure 5: Global solar radiation against time Figure 5 presents the time variation of solar insolation (W/m2) measured at the site where the research was conducted .It is clear that the intensity of radiation depends upon the hour of the file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng mailto:olakunleisamot@yahoo.com Isamotu et al: Mathematical Modeling of a Flat Plate Solar Collector with Eutectic Salts as Phase Change Material. AZOJETE,16(3):435- 448. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 444 day and the period of the year. Additionally, it can be deduced that the solar irradiance at 9:30 Am was observed to be 690W/m2 and the intensity kept on increasing with time until it reaches its peak at 4:00 pm. At this time 1050W/m2 was recorded which can be said to be progressive with respect to the result obtained in heating the water. The solar intensity declined from the peak value of 1050W/m2 in the hour of 4.00pm to 0W/m2 in the hours of 6.30, 7.00, 7.30 and 8.00pm as evident in Figure 5. Figure 6: Hourly variations of outlet water temperature without and with PCM Figure 6 shows the temperature variations of outlet water temperature without and with PCM as a function of time. For both cases, the temperatures increased with time till it reached maximum values and then gardually decreased. The highest water temperatures reached for the collector without and with a phase change material were approximately 51 and 74°C respectively. This was as a result of the rise of solar intensity experienced during that day till 4.30 pm. It was observed that for the case without PCM, all the absorbed solar radiations were used to heat the transfer fluid, contrary to the case where the PCM was used. Figure 7: Effect of inlet temperature on outlet water temperature The effect of inlet water temperature on its outlet temperature was shown in Figure 7. The maximum inlet temperature of 63°C was observed around 4.pm. The temperature however was not steady, it fluctuated upward and backward, as a result of non-uniform temperature http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 445-448. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 445 distribution at each of the respective nodes of the collector. An increase in inlet temperature led to a rise in outlet water temperature. A maximum steady temperature of 74°C was recorded at the outlet. The rise was mostly enhanced at higher inlet water temperature. Figure 8 shows the variation of ambient, water inlet, water outlet and glass temperatures with respect to time. Figure 8:The variation of ambient, water inlet, water outlet and glass temperatures with time It was clear that the inlet water temperature was 27°C at 9:30am in the morning which also corresponded to the ambient temperature and glass temperature at that point. Figure 8 showed that the outlet temperature increases with time. At about 12:30 pm a temperature of 66°C was recorded at the inlet and 72°C at outlet. The glass maintained a temperature of 36°C, while the ambient at this time was 31°C. The temperature of the glass is higher than that of ambient air becuase of the green house effect exhibited by it.The storage tank which houses the water has a temperature of 39°C at the upper layer and 30°C at the lower layer indicating a non-uniform temperature distribution in each of the layers. The thermal gradient curve of the graph clearly showed that the temperature rises with height which is the factor responsible for the hot water to stay above the cold water layer as a result of difference in density. The glass and ambient air reached their peak temperatures of 46°C and 36°C at 3.30pm and 4.00pm respectively. Maximum water outlet temperature of 74°C was obtained at 4.00pm and 5.00pm . At 8.00pm, when the solar energy was no longer acessible, the glass, ambient air and outlet water temperatures dropped to 29°C, 27°C and 68°C respectively as seen in Figure 8. Figure 9 was constructed to compare experimental result with simulation result. file:///C:/Users/user/Downloads/azojete143/www.azojete.com.ng mailto:olakunleisamot@yahoo.com Isamotu et al: Mathematical Modeling of a Flat Plate Solar Collector with Eutectic Salts as Phase Change Material. AZOJETE,16(3):435- 448. ISSN 1596-2490; e-ISSN 2545-5818, www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 446 Figure 9: Comparison between the results obtained from simulation and experimental results Temperature is the most significant parameter in the solar water heating system used in validating the experimental result. Figure 9 showed both the inlet and outlet water temperatures of the simulated model as well as the experimental for solar water heater without PCM and with PCM. Inlet temperatures of 41.54 and 36°C were observed for both the simulated and experimental model for the solar water heater without PCM, while 42.69 and 74°C were recorded for the outlet temperatures respectively. It was observed that the data of the outlet temperatures of the experimental model outweighed the outlet temperature of the simulated model. Additionally, the solar water heater with PCM, the inlet temperatures for the simulation and experimental model were found to be 42°C and 56°C respectively . A maximum outlet water temperature of 108°C was obtained from the experimental model and 45°C was obtained from simulation model. The result of the simulation model fairly agrees with the ones obtained by Nahar (2002) whose experiment generated a maximum output temperature of 50.6°C at the solar peak period and 41.6°C the next morning and Akuffo and Jackson, (2008) whose experiments generated a maximum outlet temperature of 45°C at solar peak period. The overall progression of the graph confirmed the efficiency and heat retaining capacity of the adopted phase change materials used in the research work. 4.0 Conclusıon A one dimensional theoretical model for a flat plate solar collector with phase change material was developed to investigate the thermal performance of the system. It is noteworthy that the numerical model presented, predicted the heat transfer characteristics during phase change material and interactions between the heat transfer fluids. The experimental data was also http://www.azojete.com.ng Arid Zone Journal of Engineering, Technology and Environment, September, 2020; Vol. 16(3) 445-448. ISSN 1596-2490; e-ISSN 2545- 5818; www.azojete.com.ng Corresponding author’s e-mail address: olakunleisamot@yahoo.com 447 validated with the numerical model and simulation. The results presented shows that the heat absorbed during the charging process increases at higher water mass flow rates and decreases during discharging process at higher water mass flow rates while the time needed to complete melting and solidification modes are not linear with the mass flow rate and the PCM. This research work indicated that salt hydrates are the most energy intensive of the PCM possibilities when compared to paraffin for energy storage. This assessment shows that when PCM was used as a medium for energy storage, it significantly accumulates more energy than when water was used as a medium for energy storage. The temperature of the hot water obtained was remarkable and sufficiently enough for many domestic and industrial applications. Finally, the solar water heating system with phase change materials finds useful application and acts as a renewable energy resource in regions where there is inconsistent or poor sunlight. References Ahmad, MS. 2012. 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