# Investigation of Counterflow Microchannel Heat Exchanger with Hybrid Nanoparticles and PCM Suspension as a Coolant

Authors: Mushtaq I. Hasan; Mohammad J. Khafeef; Omid Mohammadi; Suvanjan Bhattacharyya; Alibek Issakhov
Journal: Mathematical Problems in Engineering
 (2021)

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## Abstract

The effect of the hybrid suspension on the intrinsic characteristics of microencapsulated phase change material (MEPCM) slurry used as a coolant in counterflow microchannel heat exchanger (CFMCHE) with different velocities is investigated numerically. The working fluid used in this paper is a hybrid suspension consisting of nanoparticles and MEPCM particles, in which the particles are suspended in pure water as a base fluid. Two types of hybrid suspension are used (Al2O3 + MEPCM and Cu + MEPCM), and the hydrodynamic and thermal characteristics of these suspensions flowing in a CFMCHE are numerically investigated. The results indicated that using hybrid suspension with high flow velocities improves the performance of the microchannel heat exchanger while resulting in a noticeable increase in pressure drop. Thereupon, it causes a decrease in the performance index. Moreover, it was found that the increment of the nanoparticles’ concentration can rise the low thermal conductivity of the MEPCM slurry, but it also leads to a noticeable increase in pressure drop. Furthermore, it was found that as the thermal conductivity of Cu is higher than that for Al2O3, the enhancement in heat transfer is higher in case of adding Cu particles compared with Al2O3 particles. Therefore, the effectiveness of these materials depends strongly on the application at which CFMCHE is employed.


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## Body

## 1. Introduction

The need for cooling devices in various industries such as building [1], electronic devices [2], and solar applications [3–6] has increased so that various researches have been conducted on this field. Thus, enhancing the performance of heat transfer and thermal storage systems is very important and has gained lots of interest [7]. The geometry and working flow are the most noteworthy methods for improvement. Using metal and carbon nanofluids, due to the high thermal conductivity of these materials, has intensified their application in modern heat transfer systems. Phase change materials (PCMs) could improve the heat storage capacity of the fluid and can enhance the heat storage and heat transfer potential of the working fluid by absorbing and releasing heat at a constant temperature. A point to be noted is that the weak thermal conductivity of PCM has limited severely the heat transfer of these materials during both discharging and charging processes in thermal storage systems. A wide range of investigations was conducted to enhance the thermal conductivity of PCMs. From these methods, the use of nanoparticles to increase the heat transfer rates is of high significance [8]. Kashani et al. [9] carried out a numerical investigation into the discharging of Nanoenhanced Phase Change Material (NEPCM) inside an enclosure. They used different types of nanofluids at concentrations of ϕ = 0%, 2.5%, and 5% in a cavity in which the left wall is under constant heat flux, and the other sides were thermally insulated. It was illustrated that the heat transfer rate of the enclosure improves, as the nanoparticles are added to the system. Gujarathi [10] studied the characteristics of PCM enriched by nanoparticles to be used in a data center cooling system. Thus, wide ranges of concentration of copper were added to the paraffin as the PCM. The dispersion of nanoparticles into the paraffin increased its thermal conductivity when compared with conventional PCM. As a result, the heat transfer and melting rate were improved in the presence of nanoparticles. A point to be mentioned is that since concentration is associated with viscosity increment, the lower concentrations of nanoparticles showed better heat transfer properties in comparison with higher concentrations. Using high latent heat capacity of PCM along with high thermal conductivity of nanoparticles was stated as a promising potential in data center cooling applications. Farsani et al. [11] compared the impacts using nanoalumina at the concentration of 0.01, 0.02, and 0.03 by volume on the melting and solidification of PCM. They employed the enthalpy-porosity method to predict the PCM behavior. It was found that the overall performance of the phase change exceeds at the concentration of 0.02, which is due to the dominance of conduction improvement over the convection weakening.In fact, dispersing carbon and metal nanoparticles into the base fluid could improve the thermal conductivity, and dispersing microencapsulated PCM (MEPCM) could enhance the heat storage capacity of the base fluid.There are numerous studies regarding the performance of microchannel heat exchangers by using MEPCM suspension, nanofluids, and hybrid suspensions. Hasan et al. [12] numerically studied the performance of a counterflow microchannel heat exchanger (CFMCHE) charged with nanofluid as a coolant fluid. Two types of nanofluids including Al2O3-water and Cu-water were studied at concentrations of 1% to 5% by volume. It was inferred that using the nanofluids as a coolant medium results in the enhancement of the thermal performance of CFMCHE, with no rise in pressure drop because of low concentrations and also the ultrafine solid particles. The effectiveness of nanoparticles was higher in lower concentrations than in high concentrations. In other words, the effectiveness decreased with increasing the concentration. They also concluded that the best nanoparticle to be used is the one with higher thermal conductivity. Hasan [13] numerically investigated a CFMCHE with MEPCM suspension as the working fluid. The MEPCM suspension used in his research was made of microcapsules constructed from n-octadecane and polymethylmethacrylate as the core and shell materials, respectively. These capsules were dispersed in pure water at a concentration range of 0 to 20%. From their results, it was found that using MEPCM suspension as a cooling medium results in improvement of thermal performance of the CFMCHE but increasing the pressure drop significantly. As well, in order to obtain the benefits of melting of phase change material (PCM) and releasing the latent heat, it is favorable to use the MEPCM suspension with low concentration. Ho et al. [14] employed a hybrid suspension as a working fluid, consisting of Al2O3 nanoparticles and MEPCM particles and water as the base fluid. The thermal properties of hybrid suspension, including the thermal conductivity, specific heat, dynamic viscosity, latent heat of fusion, and density, were experimentally examined. It was concluded that increasing the concentration of Al2O3 nanoparticles increases the thermal conductivity of the PCM suspension. Ho et al. [15] experimentally investigated the effect of using a hybrid nanofluid on the natural convection in a circular tube. They employed pure water, PCM suspension (wPCM = 2, 5, and 10 wt.%), and nanofluids (wnp = 2, 6, and 10 wt.%) as cooling fluids and investigated the convection in the tube. The nanofluid decreased the specific heat and increased the thermal conductivity while PCM suspension weakened the thermal conductivity and increased the specific heat. The dominance of the thermal conductivity over specific heat in nanofluid and also specific heat over thermal conductivity in PCM suspension led to the improvement of the heat transfer of the working fluid. Ho et al. [16] experimentally used a hybrid nanofluid containing Al2O3 nanoparticles along with MEPCM particles to investigate their effects on the laminar convective cooling performance in a circular tube. A significant enhancement in cooling was obtained by using the hybrid nanofluid compared with the pure PCM suspension, Al2O3 nanofluid, and water. However, as the concentration rose, because of viscosity increment, the pressure drop increased, and thus, the effect of utilizing hybrid suspension decreased. Meanwhile, the dependency of pressure drop on concentration was higher in case of hybrid suspension than the nanofluid or pure PCM suspension. Elbahjaoui and El Qarnia [17] studied a shell and tube thermal storage system. They used water as the heat transfer fluid and n-octadecane embedded in shell space as the PCM. They investigated two cases of stationary and pulsating heat transfer fluid (HTF) on the storage characteristics and, thus, used nanoparticles with concentrations ranging from 0 to 7% by volume and HTF with dimensionless frequency from 0.01 to 3. The best performance was obtained in a volume fraction of 7% and pulsating frequency of 1. In the optimum case, the melting time was reduced up to 14.4%.Augmenting convective heat transfer by using a swirl generator is one of the most popular techniques in the HVAC&R industry [18–23]. Hao and Tao [24] numerically investigated the mixed convective heat transfer. A square cavity with partial slip-filled kerosene–cobalt nanofluid is used for the study. The horizontal walls of the cavity are kept insulated while the vertical wall is partially heated. It was reported that heat flow was affected by the change in volume concentration of ferrofluid.Goel et al. [25] numerically investigated the free convective heat transfer and flow of MHD Alumina-Cu/water nanofluid filled in a square cavity. The cavity contains a corrugated conductive cylinder. The left wall of the cavity is given constant heat. Corcione correlation is used for determining the thermal conductivity and viscosity of the hybrid nanofluid. It was reported from the results that the presence of a wavy block in the cavity influences the flow and thermal characteristics. Local Thermal Nonequilibrium model has been utilized by Tsai and Chein [26] to investigate the heat transport through convection in a porous medium filled with Ag–MgO/H2O nanofluid. The influencing parameters investigated in the study are Rayleigh number, porosity, the volume fraction of nanoparticles, interface convective heat transfer coefficient, and thermal conductivity ratio. The study concluded that vortex strength is increased with an increase in Ra while the dispersion of combined Ag–MgO nanoparticles in the fluid reduces the flow and thermal transport in the cavity as compared with Ag and MgO nanoparticles individually. Lee and Mudawar [27] numerically inspected the effect of MHD flow of second-grade fluid on the convective heat transfer in a vertical channel filled with porous medium. The results are analyzed with respect to velocity, temperature, volume concentration, skin friction, and heat and mass flow rate. It was revealed that increasing the permeability results in an increase in skin friction.Manikandan and Rajan [28] experimentally investigated the double pipe HE, shell and tube HE, and plate HE for the same surface area under the same condition with the same nanofluids for thermal and flow characteristics. The results obtained from the experiments showed that minimum pressure drop was obtained with plate-type HE at 27% enhancement while maximum pressure drop was observed with double pipe HE with 85% enhancement in thermal transport. Sadeghi et al. [29] numerically revealed the benefits of using multilayer PCMs. 15 sets of experiments have been conducted to investigate the effect of various arrangements and thickness of the layer of phase change materials. It was revealed that the single layer saves 23% of inlet energy while three layers of PCM save 41% of inlet energy. Dogonchi et al. [30] utilize controlled volume-based FEM for investigating the presence of nanoparticles in a square cavity fitted with an elliptical cylinder for free convective heat transfer. The results obtained from the simulation show that, at a specific aspect ratio, enhancement in heat transfer and Nu was observed.Ghalambaz et al. [31] numerically investigated the impact of Ag–MgO/water hybrid nanofluid filled in a square cavity fitted with a solid conductive layer at a hot wall for free convection. The parameters used for the study are volume concentration of nanoparticles, Rayleigh number, and thermal conductivity ratio. The study concluded that adding the hybrid nanoparticles in the base fluid and increasing the Ra and thermal conductivity ratio lead to the enhancement of heat transport. Ishak et al. [32] investigated the effect of wall thickness on heat transfer and entropy production in a square cavity filled with Al2O3 nanofluid. A moving heat source is present at the lower wall, which allows partial isothermal heating while other walls remain insulated. It was revealed from the obtained results that thermal conductivity and thickness of the wall are key parameters to control the optimal heat transfer and pressure drop.Rejvani et al. [33] experimentally reveal the effect of the addition of SiO2, and MWCNT in 10 W 40 engine oil. The viscosity of the resulting hybrid nanofluid was tested for various concentrations at different temperature ranges. The results show a 35% increase in the viscosity of the hybrid nanofluid comparative to base fluid.Alsabery et al. [34] computationally studied the convective heat transfer and entropy production in a trapezoidal cavity filled with nanohomogenous Al2O3-water nanofluid under the influence of a magnetic field. The governing PDEs are solved using Galerkin weighted residual FEM. The parameters studied are Rayleigh No., the concentration of nanoparticles, Hartmann No., thermal conductivity, and height of the trapezoidal body. It was revealed that streamlines show more sensitive behavior for Hartmann as compared with the change in volume fraction.Mehryan et al. [35] revealed the impact of MWCNT-Fe2O3/H2O nanofluid on the convective heat transfer under the influence of an inclined magnetic field. The parameters that influence the thermal and flow characteristics are studied. An increase in average Nusselt’s number was up to Ra = 104 while an increase in viscosity due to the addition of nanoparticles decreases the average Nu. Hoseinzadeh et al. [36] numerically investigated porous rectangular fin and run the simulation for analyzing the thermal transport. The results obtained from Runge-Kutta numerical analysis are compared with results obtained through collocation method (CM), homotopy perturbation method (HPM), and homotopy analysis method (HAM). It was revealed from the study that on increasing the porosity, convection, and radiation; temperature gradient and heat flow increase along the fin length. Taamneh et al. [37] computationally investigated the thermal and flow behavior of Al2O3-H2O nanofluid in a triangular duct. The Reynolds number varied between 4000 and 10000. 20% increase in friction factor was observed with the addition of nanoparticles in comparison to base fluid while pressure drop was increased by 85% for Re = 10000. Besides this, a 40% increase in the production of entropy was also observed when varying the concentration of nanoparticles from 0.05 to 0.1%. Raza et al. [38] investigated the effect of MoS2–H2O nanofluid in a channel with different shapes of nanoparticles. A magnetic field influenced the flow. The results obtained from the analysis show that increasing the concentration of nanoparticles in the base fluid increases the Nu while increasing the value of wall expansion ratio results in augmentation of velocity profile between bottom wall and center.Giwa et al. [39] investigated the impact of ferrous hybrid nanofluid on the convective thermal and flow performance in the rectangular cavity under the influence of a magnetic field. The thermal properties of hybrid nanofluid are also analyzed for different particle concentrations. The magnetic field enhances the average Nu by 4.9% while increasing the strength of the magnetic field further enhances the thermal transport. The authors also noticed that the use of hybrid nanofluid shows better results in comparison to mono nanofluid. Giwa et al. [40] in another work investigated the thermal performance of Alumina-MWCNT/water nanofluid filled in a square enclosure. The nanofluid has been investigated for the different weight ratios of nanoparticles. It was revealed that nanofluid with a 60–40 weight ratio of Al2O3-MWCNT nanoparticles gives the best results. The hybrid nanofluid also promotes convective heat transfer with the cavity. Osman et al. [41] experimentally investigated a uniformly heated rectangular channel for convective heat transfer in a turbulent flow regime. Alumina-water nanofluid is used as a working fluid for the investigation. The Re varied from 200 to 7000. It was revealed from the results that a maximum heat transfer of 54% was observed in transition flow for nanofluids having 1% of nanoparticles. Mahadevi et al. [42] numerically investigated the effect of different inclination angles of the circular tube on the mixed convection heat transfer of Al2O3-water nanofluid. It was observed that maximum deposition of nanoparticles takes place at a 30o inclination angle for all concentrations. It was revealed that inclination angles have a little effect on HTC up to 35o. Further increase in the inclination angle decreases the HTC.Sharifpur et al. [43] optimized the concentration of TiO2-water nanofluid for maximum convective heat transfer in a square cavity. The upper and lower walls of the cavity are insulated while a temperature gradient exists between the left wall and right wall. It was found that the addition of TiO2 nanoparticles enhances the heat transport for all concentrations while the maximum heat transfer of 8.2% was observed at 0.05% concentration. Sharifpur et al. [44] experimentally investigate the impact of the size of Al2O3 nanoparticles on the thermal conductivity of Al2O3-glycerol nanofluid. The nanofluid prepared with 3 different sizes of nanoparticles for concentration varied between 0.5 and 4%. It was revealed from the experiments that maximum augmentation of thermal conductivity was observed at 4% concentration for 31 nm nanoparticles. It was also found that thermal conductivity is influenced by volume concentration and size of nanoparticles, while temperature variation shows negligible impact.After a wide review of previous research, the researcher did not find a previous study regarding the usage of hybrid suspension in the heat exchanger of microchannels. Thus, it is a source of modernity for this paper. In fact, by using the hybrid suspension, both advantages of nanoparticles and microcapsules are obtained. MEPCM can improve the heat capacity of the cooling fluids, and on the other hand, nanofluid can improve the thermal conductivity; thereupon, using a mixture of these materials may lead to a significant increase in heat transfer of microchannel heat exchanger.


## 2. Mathematical Model

Figure1 represents the schematic structure of CFMCHE used in this study with square channels carrying cold and hot fluids. To study the fully CFMCHE, numerically, a huge amount of time is required due to its complication. As shown in Figure 2, given that there is a symmetry between the cold and hot channel rows, geometrically and thermally, assuming a part of the geometry as the model studied is acceptable, since it gives an adequate indication for the whole heat exchanger performance. Hence, two channels in the cold and hot fluids flow, and the separating wall between them is considered as the studied cases and modeled numerically [18, 19].Figure 1
A schematic model of the counterflow MCHE.Figure 2
A schematic of the heat exchange unit.The assumptions used to solve this model are 3D, laminar, steady-state, incompressible fluid, continuum flow, constant properties, and thermally isolated from the ambient.


## 3. Governing Equations

The governing equations are continuity, momentum, and energy used for the flow of pure fluids, nanofluid, MEPCM suspension, and hybrid suspension as follows [13, 20, 21].


### 3.1. Governing Equations for Pure Water and Nanofluids

The continuity equation is(1)∂uj∂x+∂vj∂y+∂wj∂z=0.The momentum equations are(2)uj∂uj∂x+vj∂uj∂y+wj∂uj∂z=1ρj∂P∂x+μjρj∂2uj∂x2+∂2uj∂y2+∂2uj∂z2,(3)uj∂vj∂x+vj∂vj∂y+wj∂vj∂z=1ρj∂P∂y+μjρj∂2vj∂x2+∂2vj∂y2+∂2vj∂z2,(4)uj∂wj∂x+vj∂wj∂y+wj∂wj∂z=1ρj∂P∂z+μjρj∂2wj∂x2+∂2wj∂y2+∂2wj∂z2,wherej stands for h for the hot and c for the cold fluids, respectively.The energy equation for fluids in heat exchanger is(5)ρcu∂T∂x+v∂T∂y+w∂T∂z=Φ+k∂2T∂x2+∂2T∂y2+∂2T∂z2.The energy equation for solid walls in heat exchanger is(6)ks∇2Ts=0.


### 3.2. Governing Equations for MEPCM and Hybrid Suspensions

The governing equations used for pure fluid (equations1 to 4 and 6) are also used MEPCM and hybrid suspension.The enthalpy-based energy equation is written as follows:(7)∇·v⟶ρfHe=∇·kf∇Tf.It also can be defined as(8)ρfu∂He∂x+v∂He∂y+w∂He∂z=kf∂2Tf∂x2+∂2Tf∂y2+∂2Tf∂z2.The enthalpy of the slurry (He) is shown by equation (9) and computed as follows:(9)He=he+ΔH.The sensible heat is calculated by equation (10), in which href is the reference enthalpy at Tref [21].(10)he=href+∫TreftCpfdT.The slurry’s latent heat (ΔH) is calculated by equation (11), where (β) is the mass ratio of molten to the total PCM in the slurry, (Φ) is the MEPCM mass fraction, and (L) is the fusion latent heat. The PCM begins to melt at Tsolidus where the liquid fraction is zero and melting ends at Tlquidus. At this point, the liquid fraction reaches one.(11)ΔH=βϕL,where β = 0 if Tf < Tsolidus, and β = 1 if Tf > Tlquidus.(12)β=Tf−TsolidusTliquidus−Tsolidus,ifTsolidus<Tf<Tliquidus.


### 3.3. Model Boundary Conditions

The working fluids enter the channels at a defined velocity and temperature. Pure water is the hot fluid used in hot channels while the cold fluid in the cold channels is tested (pure water, Nanofluid, MEPCM suspension, and hybrid suspension). The boundary conditions of the model are given in Tables1–3.Table 1
Bottom channel (hot fluid) (0 ≤y ≤ Hh).
LocationBoundary conditionCommentsAtx = 0uh = uhi, vh = wh = 0, Th = ThiHot fluid inflowAtx = L∂uh/∂x=vh=wh=0,∂Th/∂x=0Hot fluid outflow (fully developed flow, end of the channel)Aty = 0uh = vh = wh = 0,∂Th/∂y=0No-slip, adiabatic wallAty = Hhuh = vh = wh = 0, −kh∂Th/∂y=−ks∂Ts/∂y,Th = TsFluid-solid interface (no-slip, conjugate heat transfer)Atz = 0uh = vh = wh = 0,∂Th/∂z=0No-slip, adiabatic wallAtz = Wchuh = vh = wh = 0,∂Th/∂z=0No-slip, adiabatic wallTable 2
Top channel (cold fluid) (Hh + t ≤ y ≤ Hh + t + Hc).
LocationBoundary conditionCommentsAtx = 0∂uc/∂x=vc=wc=0,∂Tc/∂x=0Cold fluid outflow (fully developed flow, end of the channelAtx = Luc = uci, vc = wc = 0, Tc = TciCold fluid inflowAty = Hh + tuc = vc = wc = 0, −kc∂Tc/∂y=−ks∂Ts/∂y,Tc = TsFluid-solid interface (no-slip, conjugate heat transfer)Aty = Hh + t + Hcuc = vc = wc = 0,∂Tc/∂y=0No-slip, adiabatic wallAtz = 0uc = vc = wc = 0,∂Tc/∂z=0No-slip, adiabatic wallAtz = Wchuc = vc = wc = 0,∂Tc/∂z=0No-slip, adiabatic wallTable 3
Solid wall separating two channels (Hh ≤ y ≤ Hh + t).
LocationBoundary conditionCommentsAtx = 0∂Ts/∂x=0Adiabatic wallAtx = L∂Ts/∂x=0Adiabatic wallAty = Hh−kh∂Th/∂y=−ks∂Ts/∂y,Th = TsFluid-solid interfaceAty = Hh + t−kc∂Tc/∂y=−ks∂Ts/∂y,Tc = TsFluid-solid interfaceAtz = 0∂Ts/∂z=0Adiabatic wallAtz = Wch∂Ts/∂z=0Adiabatic wallIn the present study, to solve the boundary conditions and also governing equations, the finite volume method (FVM) is employed. Computational fluid dynamics (CFD) is employed to solve the model and also determine the profile of the fluid flow, temperature, and pressure fields in the CFMCHE. Meanwhile, the dimensions of the square channel used in this model areW = 100 μm, H = 100 μm, L = 10 mm, and t = 50 μm. W, H, L, and t are width, channel height, length, and wall thickness, respectively.Performance parameters have been calculated as follows.The ratio of the experimental heat transfer to the maximum heat that is possible to be transferred is defined as heat exchanger effectiveness (Ɛ).(13)ε=chThi−ThocminThi−Tci−ccTco−TcicminThi−Tci,where Cc = mCpc and Ch = mCph.In the heat exchange cell, the total pressure drop is(14)ΔPt=ΔPh+ΔPc=Phi−Pho−Pci−Pco.In order to investigate the overall performance of the CFMCHE, both hydrodynamic and thermal performances must be taken into account. Thus, performance index is defined as the effectiveness of CFMCHE to the total pressure drop of heat exchanger [19]:(15)η=εΔpt.The input power required for the pump to circulate fluids in the microchannel heat exchanger is(16)PP=VΔPt.Flow rate (m3/s) is defined as follows:(17)V=vinA.There is another factor called performance factor defined as the heat transfer rate to the pumping power ratio and used to investigate the overall performance of the CFMCHE and also verify the obtained results of the performance index [19]:(18)η∗=qWP·PW.


## 3.1. Governing Equations for Pure Water and Nanofluids

The continuity equation is(1)∂uj∂x+∂vj∂y+∂wj∂z=0.The momentum equations are(2)uj∂uj∂x+vj∂uj∂y+wj∂uj∂z=1ρj∂P∂x+μjρj∂2uj∂x2+∂2uj∂y2+∂2uj∂z2,(3)uj∂vj∂x+vj∂vj∂y+wj∂vj∂z=1ρj∂P∂y+μjρj∂2vj∂x2+∂2vj∂y2+∂2vj∂z2,(4)uj∂wj∂x+vj∂wj∂y+wj∂wj∂z=1ρj∂P∂z+μjρj∂2wj∂x2+∂2wj∂y2+∂2wj∂z2,wherej stands for h for the hot and c for the cold fluids, respectively.The energy equation for fluids in heat exchanger is(5)ρcu∂T∂x+v∂T∂y+w∂T∂z=Φ+k∂2T∂x2+∂2T∂y2+∂2T∂z2.The energy equation for solid walls in heat exchanger is(6)ks∇2Ts=0.


## 3.2. Governing Equations for MEPCM and Hybrid Suspensions

The governing equations used for pure fluid (equations1 to 4 and 6) are also used MEPCM and hybrid suspension.The enthalpy-based energy equation is written as follows:(7)∇·v⟶ρfHe=∇·kf∇Tf.It also can be defined as(8)ρfu∂He∂x+v∂He∂y+w∂He∂z=kf∂2Tf∂x2+∂2Tf∂y2+∂2Tf∂z2.The enthalpy of the slurry (He) is shown by equation (9) and computed as follows:(9)He=he+ΔH.The sensible heat is calculated by equation (10), in which href is the reference enthalpy at Tref [21].(10)he=href+∫TreftCpfdT.The slurry’s latent heat (ΔH) is calculated by equation (11), where (β) is the mass ratio of molten to the total PCM in the slurry, (Φ) is the MEPCM mass fraction, and (L) is the fusion latent heat. The PCM begins to melt at Tsolidus where the liquid fraction is zero and melting ends at Tlquidus. At this point, the liquid fraction reaches one.(11)ΔH=βϕL,where β = 0 if Tf < Tsolidus, and β = 1 if Tf > Tlquidus.(12)β=Tf−TsolidusTliquidus−Tsolidus,ifTsolidus<Tf<Tliquidus.


## 3.3. Model Boundary Conditions

The working fluids enter the channels at a defined velocity and temperature. Pure water is the hot fluid used in hot channels while the cold fluid in the cold channels is tested (pure water, Nanofluid, MEPCM suspension, and hybrid suspension). The boundary conditions of the model are given in Tables1–3.Table 1
Bottom channel (hot fluid) (0 ≤y ≤ Hh).
LocationBoundary conditionCommentsAtx = 0uh = uhi, vh = wh = 0, Th = ThiHot fluid inflowAtx = L∂uh/∂x=vh=wh=0,∂Th/∂x=0Hot fluid outflow (fully developed flow, end of the channel)Aty = 0uh = vh = wh = 0,∂Th/∂y=0No-slip, adiabatic wallAty = Hhuh = vh = wh = 0, −kh∂Th/∂y=−ks∂Ts/∂y,Th = TsFluid-solid interface (no-slip, conjugate heat transfer)Atz = 0uh = vh = wh = 0,∂Th/∂z=0No-slip, adiabatic wallAtz = Wchuh = vh = wh = 0,∂Th/∂z=0No-slip, adiabatic wallTable 2
Top channel (cold fluid) (Hh + t ≤ y ≤ Hh + t + Hc).
LocationBoundary conditionCommentsAtx = 0∂uc/∂x=vc=wc=0,∂Tc/∂x=0Cold fluid outflow (fully developed flow, end of the channelAtx = Luc = uci, vc = wc = 0, Tc = TciCold fluid inflowAty = Hh + tuc = vc = wc = 0, −kc∂Tc/∂y=−ks∂Ts/∂y,Tc = TsFluid-solid interface (no-slip, conjugate heat transfer)Aty = Hh + t + Hcuc = vc = wc = 0,∂Tc/∂y=0No-slip, adiabatic wallAtz = 0uc = vc = wc = 0,∂Tc/∂z=0No-slip, adiabatic wallAtz = Wchuc = vc = wc = 0,∂Tc/∂z=0No-slip, adiabatic wallTable 3
Solid wall separating two channels (Hh ≤ y ≤ Hh + t).
LocationBoundary conditionCommentsAtx = 0∂Ts/∂x=0Adiabatic wallAtx = L∂Ts/∂x=0Adiabatic wallAty = Hh−kh∂Th/∂y=−ks∂Ts/∂y,Th = TsFluid-solid interfaceAty = Hh + t−kc∂Tc/∂y=−ks∂Ts/∂y,Tc = TsFluid-solid interfaceAtz = 0∂Ts/∂z=0Adiabatic wallAtz = Wch∂Ts/∂z=0Adiabatic wallIn the present study, to solve the boundary conditions and also governing equations, the finite volume method (FVM) is employed. Computational fluid dynamics (CFD) is employed to solve the model and also determine the profile of the fluid flow, temperature, and pressure fields in the CFMCHE. Meanwhile, the dimensions of the square channel used in this model areW = 100 μm, H = 100 μm, L = 10 mm, and t = 50 μm. W, H, L, and t are width, channel height, length, and wall thickness, respectively.Performance parameters have been calculated as follows.The ratio of the experimental heat transfer to the maximum heat that is possible to be transferred is defined as heat exchanger effectiveness (Ɛ).(13)ε=chThi−ThocminThi−Tci−ccTco−TcicminThi−Tci,where Cc = mCpc and Ch = mCph.In the heat exchange cell, the total pressure drop is(14)ΔPt=ΔPh+ΔPc=Phi−Pho−Pci−Pco.In order to investigate the overall performance of the CFMCHE, both hydrodynamic and thermal performances must be taken into account. Thus, performance index is defined as the effectiveness of CFMCHE to the total pressure drop of heat exchanger [19]:(15)η=εΔpt.The input power required for the pump to circulate fluids in the microchannel heat exchanger is(16)PP=VΔPt.Flow rate (m3/s) is defined as follows:(17)V=vinA.There is another factor called performance factor defined as the heat transfer rate to the pumping power ratio and used to investigate the overall performance of the CFMCHE and also verify the obtained results of the performance index [19]:(18)η∗=qWP·PW.


## 4. Properties of Fluids

### 4.1. Properties of MEPCM Suspension

MEPCM particles are made of a polymer shell surrounding a core of PCM, preventing PCM from leakage, and keeping the form during phase change. Figure3 represents a schematic of a microcapsule during the phase change process [13]. Herein, the average diameter of MEPCM particles is 5 μm. The selection of core and shell materials of the microcapsule corresponds to the transporter fluid. N-octadecane with a melting temperature of about 301 K is used as PCM in the core of the capsule, and the shell is made up of polymethylmethacrylate (PMMA) [22–24]. Given that the physical properties of the wall material and PCM affect the properties of the MEPCM particle, different components must be taken into account while calculating the properties of MPCM.Figure 3
Schematic diagram of single MEPCM particles during melting.The densities of solid and liquid PCM were assumed to be the same as the density of n-octadecane. Moreover, energy and mass balances were utilized to calculate the density and specific heat of the microcapsules, respectively [25].(19)CpPCM=7Cpc+3Cpwallpcpwall3pc+7pwallρPCM,(20)ρPCM=107dcdPCM3pc.The thermal conductivity of microcapsules is also represented as follows:(21)1kPCMdPCM=1kcdc+dPCM−dckwalldPCMdc.PCM stands for the whole (capsule = wall + core) and the wall is the wall of the capsule (polymer).C is the core material (PCM) and d is the diameter.The suspension properties are a function of the properties of water (base fluid) and properties of the microcapsules. Hence, the specific heat and density are determined using a mass and energy balance [22–25].(22)ρf=cρPCM+1−cρw,(23)Cρf=ϕcρPCM+1−ϕCρw.The viscosity of the suspension is also determined using(24)μf=μw1−c−1.16c2−2.5.The thermal conductivity of the suspension is calculated as(25)kf=2kw+kPCM+2ckPCM−kw2+kPCM/kw−ckPCM/kw−1.The mass fraction can be calculated from(26)ϕ=cρPCMρw+cρPCM−ρw.


### 4.2. Properties of Nanofluids

According to the previous studies [26, 27], the thermophysical properties of the nanofluids are a function of the properties of solid particles, the base fluid, particles shape, and volume fraction of the solid particles in the suspension. The properties of nanofluids are determined using the following relations:Thermal conductivity:(27)knf=kfkp+SH−1kfSH−1ckf−kpkp+SH−1kf+ckf−kp.Viscosity:(28)μnf=μf1+2.5c.Density:(29)ρnf=cρp+1−cρf.Specific heat:(30)Cρnf=cCρp+1−cCρf.In equation (27), SH indicates the solid particle shape factor.(31)SH=3ψ.ψ represents the ratio of the surface area of a sphere (with the same volume of the particle) to the surface area of the particle. Thus, for the spherical particles, SH is 3.kp, kf, and knf are thermal conductivities of the solid particles, base fluid, and nanofluid, respectively.


### 4.3. Properties of Hybrid Suspensions

To determine the viscosity and thermal conductivity properties of hybrid suspension, the following relations are used [28]:Thermal conductivity:(32)khs=knf1−3c2.Viscosity:(33)μhs=μnf1+7.85ϕ.To calculate the specific heat and density of the suspension, we use the following relations [14].Specific heat:(34)Cphs=cnpρnpcpnp+cMEPCMρMEPCMcpMEPCM+1−cnp−cMEPCMcρbfpbfphs.Density:(35)phs=cnpρnp+cMEPCMρMEPCM+1−cnp−cMEPCMpbf,where hs, np, MEPCM, and bf refer to hybrid suspension, nanoparticle, microencapsulated phase change material, and base fluid, respectively. In Table 4, the rheological and thermal properties of the materials employed are listed.Table 4
Properties of materials.
Materialp (kg/m3)Cp (J/kg.K)K (W/m.K)Μμ (kg/m.s)Pure water981.341890.6430.00059n-octadecane (MEPCM core)solid = 85020000.18—liquid = 780PMMA (MEPCM wall)119014700.21—MEPCM particles867.218990.1643—Cupper (cu)8930383.1386—Al2O3360076536—


## 4.1. Properties of MEPCM Suspension

MEPCM particles are made of a polymer shell surrounding a core of PCM, preventing PCM from leakage, and keeping the form during phase change. Figure3 represents a schematic of a microcapsule during the phase change process [13]. Herein, the average diameter of MEPCM particles is 5 μm. The selection of core and shell materials of the microcapsule corresponds to the transporter fluid. N-octadecane with a melting temperature of about 301 K is used as PCM in the core of the capsule, and the shell is made up of polymethylmethacrylate (PMMA) [22–24]. Given that the physical properties of the wall material and PCM affect the properties of the MEPCM particle, different components must be taken into account while calculating the properties of MPCM.Figure 3
Schematic diagram of single MEPCM particles during melting.The densities of solid and liquid PCM were assumed to be the same as the density of n-octadecane. Moreover, energy and mass balances were utilized to calculate the density and specific heat of the microcapsules, respectively [25].(19)CpPCM=7Cpc+3Cpwallpcpwall3pc+7pwallρPCM,(20)ρPCM=107dcdPCM3pc.The thermal conductivity of microcapsules is also represented as follows:(21)1kPCMdPCM=1kcdc+dPCM−dckwalldPCMdc.PCM stands for the whole (capsule = wall + core) and the wall is the wall of the capsule (polymer).C is the core material (PCM) and d is the diameter.The suspension properties are a function of the properties of water (base fluid) and properties of the microcapsules. Hence, the specific heat and density are determined using a mass and energy balance [22–25].(22)ρf=cρPCM+1−cρw,(23)Cρf=ϕcρPCM+1−ϕCρw.The viscosity of the suspension is also determined using(24)μf=μw1−c−1.16c2−2.5.The thermal conductivity of the suspension is calculated as(25)kf=2kw+kPCM+2ckPCM−kw2+kPCM/kw−ckPCM/kw−1.The mass fraction can be calculated from(26)ϕ=cρPCMρw+cρPCM−ρw.


## 4.2. Properties of Nanofluids

According to the previous studies [26, 27], the thermophysical properties of the nanofluids are a function of the properties of solid particles, the base fluid, particles shape, and volume fraction of the solid particles in the suspension. The properties of nanofluids are determined using the following relations:Thermal conductivity:(27)knf=kfkp+SH−1kfSH−1ckf−kpkp+SH−1kf+ckf−kp.Viscosity:(28)μnf=μf1+2.5c.Density:(29)ρnf=cρp+1−cρf.Specific heat:(30)Cρnf=cCρp+1−cCρf.In equation (27), SH indicates the solid particle shape factor.(31)SH=3ψ.ψ represents the ratio of the surface area of a sphere (with the same volume of the particle) to the surface area of the particle. Thus, for the spherical particles, SH is 3.kp, kf, and knf are thermal conductivities of the solid particles, base fluid, and nanofluid, respectively.


## 4.3. Properties of Hybrid Suspensions

To determine the viscosity and thermal conductivity properties of hybrid suspension, the following relations are used [28]:Thermal conductivity:(32)khs=knf1−3c2.Viscosity:(33)μhs=μnf1+7.85ϕ.To calculate the specific heat and density of the suspension, we use the following relations [14].Specific heat:(34)Cphs=cnpρnpcpnp+cMEPCMρMEPCMcpMEPCM+1−cnp−cMEPCMcρbfpbfphs.Density:(35)phs=cnpρnp+cMEPCMρMEPCM+1−cnp−cMEPCMpbf,where hs, np, MEPCM, and bf refer to hybrid suspension, nanoparticle, microencapsulated phase change material, and base fluid, respectively. In Table 4, the rheological and thermal properties of the materials employed are listed.Table 4
Properties of materials.
Materialp (kg/m3)Cp (J/kg.K)K (W/m.K)Μμ (kg/m.s)Pure water981.341890.6430.00059n-octadecane (MEPCM core)solid = 85020000.18—liquid = 780PMMA (MEPCM wall)119014700.21—MEPCM particles867.218990.1643—Cupper (cu)8930383.1386—Al2O3360076536—


## 5. Numerical Model

Governing equations were transformed into algebraic equations using the finite volume method. The SIMPLE algorithm was employed to handle the mass conservation equation and get the pressure field. Computational fluid dynamic software (FLUENT 19.1) was used to determine the fields of velocity, pressure, and temperature distribution along the CFMCHE. Afterward, all the computational domain (two channels and the separating wall) was meshed with suitable size, and then using a mesh refinement process, the generated mesh was refined.


## 6. Results and Discussion

In order to investigate the effectiveness of the nanofluids, the model was firstly operated with pure water. The inlet temperatures of cold and hot fluids flowing in the channels were set as the boundary conditions with values ofTci = 293 K and Thi = 373 K. Then, we repeated operating the model by using nanofluid and MEPCM suspensions with volume fractions of (2%, 4%, 6%, and 8%). Noting that a core material of PCM is n-octadecane which has Tsolidus = 297 K and Tliquidus = 302 K; also, latent heat ΔH = 245,000 (J/kg). And then, we repeated again operating the model by adding nanoparticles of (Cu and Al2O3) with volume fractions of (2% and 4%) to the MEPCM suspension to form the hybrid suspension.To examine the validity of the present model, the model presented by Kashani et al. [9] was solved, and a comparison was made between the obtained results and those presented by them. The numerical model that used them is a microchannel heat exchanger composed of rectangular microchannels with hydraulic diameter Dh = 100 μm, channel height H = 100 μm, channel width W = 100 μm, and length L = 10 mm. A silicon wall with a thickness of 50 μm separates the channels, and the inlet velocity of the fluid was chosen to be Vi = 1 m/s.Figure4 illustrates the heat transfer rate distribution in terms of volume concentration for two cases of the present study and the numerical model of [9]. According to the figure, it is evident that the two models are in good agreement with each other, and the average error is 1.16% which is attributed to the end effect. Thereupon, the present model has acceptable accuracy and could be used as a reliable model to examine the impact of different nanofluids, including MEPCM and hybrid suspension on the performance of CFMCHE.Figure 4
Variation of heat transfer rate distribution with concentration as a comparison between the present model and [5].The heat transfer rate versus inlet velocity for pure MEPCM suspension at a concentration of 4% and enhanced (hybrid) suspension with the addition of 2% and 4% of Cu and Al2O3 nanoparticles is shown in Figure 5.Figure 5
Variation of heat transfer rate with inlet velocity for different concentrations of nanoparticles at concentration 4% MEPCM suspension.It is inferred that, for all cases, the heat transfer rate rises with increasing the velocity, which is because of the increase in flow rate. Also, results reveal that the heat transfer rises with adding nanoparticles, due to enhancing the thermal properties of suspension, especially thermal conductivity which increases with the increment of the amount of nanoparticles volume concentration. Furthermore, it could be noted that the enhancement in heat transfer is higher in case of adding Cu particles compared with Al2O3 particles because of the higher value of thermal conductivity of Cu compared with that of Al2O3.The variation of pressure drop with inlet velocity for pure MEPCM suspension at a concentration of 4% and enhanced (hybrid) suspension with adding 2% and 4% of Cu and Al2O3 nanoparticles is portrayed in Figure 6.Figure 6
Variation of pressure drop with inlet velocity for different concentrations of nanoparticles at concentration 4% MEPCM suspension.From Figure6, it is found that the pressure drop increases with the increment of inlet velocity for all cases, which is attributed to the increase in the frictional and dynamic losses. Also, it is shown that adding nanoparticles to the fluid leads to a higher pressure drop due to an increase in the dynamic viscosity. This trend increased with the increment of concentration. A slight difference was discovered between pressure drop in case of adding Cu particles compared with Al2O3 particles resulting from the difference between the densities.Figure7 shows the effectiveness versus inlet velocity for pure MEPCM suspension (at a concentration of 4%) and enhanced (hybrid) suspension by adding 2% and 4% of Cu and Al2O3 nanoparticles, respectively.Figure 7
Variation of effectiveness with inlet velocity for different concentrations of nanoparticles at concentration 4% MEPCM suspension.As depicted in Figure7, for all cases, as the inlet velocity increased, the effectiveness decreased. In fact, in high velocities, there is not enough time for all the particles to melt completely. As a result, the thermal energy was absorbed during melting, and also the effectiveness of MEPCM decreases. It is also evident that the effectiveness rises slightly with adding nanoparticles due to the enhancement of the thermal properties of suspension, especially thermal conductivity. A point to be mentioned is that, in high flow rates, the impact of nanoparticles on the development of the boundary layer decreases, resulting in better heat transfer of the suspension in higher velocities. In fact, in high velocities, the volume flow rate is dominated, and the effect of nanoparticles is weakened.Figure8 represents the performance index in terms of inlet velocity for pure MEPCM suspension (at a concentration of 4%) and enhanced (hybrid) suspension by adding 2% and 4% of Cu and Al2O3 nanoparticles, respectively.Figure 8
Variation of performance index with inlet velocity for different concentrations of nanoparticles at concentration 4% MEPCM suspension.As shown in Figure8, the performance index (η) for all cases decreases with an increment of inlet velocity. It is due to the higher increment of pressure drop than effectiveness. Also, the increase in pressure drop for hybrid suspensions is higher in comparison with that of MEPCM suspension resulting in a higher performance index of MEPCM suspension than that of hybrid suspensions.Figure9 indicates the variation of pumping power with inlet velocity for pure MEPCM suspension at a concentration of 4% and enhanced (hybrid) suspension by adding 2% and 4% of Cu and Al2O3 nanoparticles, respectively.Figure 9
Variation of pumping power with inlet velocity for different concentrations of nanoparticles at concentration 4% MEPCM suspension.From Figure9, it is found that as the inlet velocity increases, pressure drop increases and thus pumping power rises. Also, the pumping power increases with adding nanoparticles because of the increase in dynamic viscosity that results in an increment of pressure drop. Moreover, the more the number of nanoparticles, the more pumping power. Since there is no noticeable difference between the density values of Cu and Al2O3, a slight difference was seen between pumping power in case of adding Cu particles compared with Al2O3 particles.The variation of performance factor in terms of inlet velocity for pure MEPCM suspension (at a concentration of 4%) and enhanced (hybrid) suspension with adding 2% and 4% of Cu and Al2O3 nanoparticles is depicted in Figure 10, respectively.Figure 10
Variation of performance factor with inlet velocity for different concentrations of nanoparticles at concentration 4% MEPCM suspension.It is inferred that the performance factor (Ƞ) for all cases decreases with the increment of inlet velocity since the effect of inlet velocity on the increment of pumping power is higher in comparison with that on heat transfer rate. Also, the performance factor of MEPCM suspension is higher than that of the hybrid suspensions. It is due to the higher increment of pumping power for hybrid suspensions than MEPCM suspensions.


## 7. Conclusions

The following conclusions are drawn:(1)
The MEPCM suspension can be enhanced by adding nanoparticles to obtain a hybrid suspension.(2)
Using higher thermal conductivity nanoparticles leads to obtaining extra enhancement in heat transfer rates for MEPCM suspension.(3)
Using hybrid suspension leads to the enhancement of heat transfer rates in CFMCHE.(4)
Also, the hybrid suspension causes an extra rise in pressure drop, which dominates the thermal performance.(5)
Using hybrid suspension with high velocities leads to an increase in heat transfer rates of the microchannel heat exchanger. On the other hand, it significantly raises the pressure drop and, hence, causes a decrease in the performance index.



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*Source: 6687064-2021-03-25.xml*