Thermal and hydrodynamic performances of MHD ferrofluid flow inside a porous channel

Accepted Manuscript Thermal and hydrodynamic performances of MHD ferrofluid flow inside a porous channel Ali Salehpour, Saeed Salehi, Samaneh Salehpour, Mehdi Ashjaee PII: DOI: Reference:

S0894-1777(17)30264-9 http://dx.doi.org/10.1016/j.expthermflusci.2017.08.032 ETF 9200

To appear in:

Experimental Thermal and Fluid Science

Received Date: Revised Date: Accepted Date:

27 December 2016 15 August 2017 30 August 2017

Please cite this article as: A. Salehpour, S. Salehi, S. Salehpour, M. Ashjaee, Thermal and hydrodynamic performances of MHD ferrofluid flow inside a porous channel, Experimental Thermal and Fluid Science (2017), doi: http://dx.doi.org/10.1016/j.expthermflusci.2017.08.032

This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain.

Thermal and hydrodynamic performances of MHD ferrofluid flow inside a porous channel Ali Salehpoura,*, Saeed Salehia, Samaneh Salehpourb, Mehdi Ashjaeea a

Department of Mechanical Engineering, College of Engineering, University of Tehran, P.O. Box: 111554563,Tehran, Iran. b

Department of Mechanical Engineering, K.N. Toosi University of Technology, Tehran, Iran.

Abstract MHD mixed convection heat transfer inside a rectangular porous channel under the effects of constant and alternating magnetic fields has been experimentally investigated. Deionized water containing magnetite particles flows through the channel filled with copper foam as a porous media. A constant heat flux condition is imposed on the top and bottom plates of the channel, while the side walls are adiabatic. Experiments were carried out at Gr=7.31×10 6 and 373≤Re≤1186. Influence of porous media, volume fraction of ferrofluid ( =0.5%, 1%, 1.5%), Reynolds number and magnetic field intensities and frequencies (B=250, 450 G and f=5, 10 Hz) on the characteristics of heat transfer and hydrodynamic are studied. The experimental results revealed that the copper foam has a significant effect on the thermal and hydrodynamic performances of the channel due to heat spreading through the copper matrix, better mixing of the fluid and extending the heat transfer area. It was observed that employing ferrofluid with different volume fractions increases both heat transfer rate and pressure drop because of thermal conductivity and viscosity increment, respectively. Applying constant magnetic field causes aggregation of nanoparticles in the area where the magnetic field is applied and consequently, heat transfer and pressure drop increase. Moreover employing alternating magnetic field further increased the heat transfer rate due to more intensified disturbance of the thermal boundary layer and improvement of the nanoparticles migrations. The alternating magnetic field reduced

*

Corresponding Author: [email protected]

1

pressure drop because of the periodic magnetic forces, leading to enhanced overall performance of the channel. Keywords: MHD Flow; Ferrofluid; Mixed convection heat transfer; Porous media; Constant and alternating magnetic fields Nomenclature A

Area [m2]

X

Cp

Specific heat [J/kg·K]

Greek

D

Diameter [m]

Β

Thermal expansion coefficient [1/K]

F

Frequency [Hz]

Ε

Porosity

fi

Inertia factor [-]

η1

Thermal performance

η2

Overall performance

µ

Dynamic viscosity [kg/m·s]

Gr g

4

Grashof number [-], gβq''H /kν

2

2

Gravitational acceleration [m/s ] 2

Entrance length [m]

h

Convective heat transfer coefficient [W/m ·K]

ν

Kinematic viscosity [m2/s]

H

Height of channel [m]

ρ

Density [kg/m3]

I

Electric current [A]

Volume concentration

2

K

Permeability [m ]

Subscript

K

Thermal conductivity [W/m·K]

avg

Average

L

Channel length [m]

B

Bottom

l

Length of the cell [m]

CS

Cross Section

M

Mass [kg]

exp

Experimental

Mass flow rate [kg/s]

F

Force convection

P

Pressure [Pa]

ff

Ferrofluid

Pr

Prandtl number [-],µCp/k

h

Hydraulic

q

Total heat flow [W]

m

Mean

2

q''

Heat flux [W/m ]

i

Inlet

Ra

Rayleigh number [-], GrPr

N

Natural convection

Re

Reynolds number [-],

o

Outlet

h/ACSµ 2

Ri

Richardson number [-], Gr/Re

p

Nanoparticles

t

Thickness of the cell [m]

R

Relative

u

Velocity [m/s]

s

Surface

V

Electric voltage [V]

w

DI Water

W

Channel width [m]

2

1. Introduction Cooling systems are being widely used in engineering applications, i.e., from large industrial systems such as boilers, heat exchangers, solar collectors to small devices, e.g., electronic microchips. Therefore efficiency enhancement of such systems have received a lot of attentions in the recent years. Active and passive methods are employed to increase the thermal performance of heat exchanging systems. Increasing thermal conductivity of the working fluid and extending the heat transfer area are a few examples of passive methods, while mechanical agitator, inducing electrostatic and magnetic fields, which demand external power sources, are considered as active methods [1-2]. In order to enhance the thermal efficiency using passive methods, many researchers have studied increasing thermal conductivity of working fluid employing nanofluids, in which the base fluid contains metallic or nonmetallic nanoparticles with diameters less than 100 nm. Many researchers have reported thermal conductivity enhancement due to the dispersion of nanoparticles within the base fluid [3-7]. Ferrofluid is a specific type of nanofluids which several numerical and experimental studies have been performed on its transport and heat transfer characteristics [8-15]. A ferrofluid is a stable synthesized mixture of a nonmagnetic fluid such as Deionized (DI) water or oil containing dispersed magnetized nanoparticles, for example magnetite, ferric oxide and iron nickel oxide [16]. In the absence of magnetic field, ferrofluid thermal conductivity and viscosity can be described similar to other nanofluids. Applying magnetic field changes the thermal conductivity and viscosity of the solution due to the formation of chain-like structures and consequently growth in the aggregation of the magnetic particles [17]. Li et al. [18] experimentally investigated the effects of magnetic field, volume fraction and different surfactants on the thermal conductivity and viscosity of the ferrofluids and observed thermal conductivity and viscosity increment in the presence of magnetic fields. Gavili et al. [19] studied thermal conductivity and time saturation of ferrofluid under different magnetic field intensities and obtained the required time for ferrofluid to reach its saturation state. It was seen that the magnetic field can increase thermal conductivity up to 200%. Numerous experimental studies on the ferrofluid convective heat transfer have been carried out and effects of different parameters such as volume fraction, Reynolds number, magnetic field and surfactants were examined [20-27]. Motozawa et al. [22] investigated the effect of the 3

constant magnetic field on the ferrofluid heat transfer performance within a rectangular channel. The local convective heat transfer coefficients, in the area affected by the magnetic field, increased up to 20%. Laminar ferroconvection of a copper tube under constant magnetic field was assessed by Lajvardi et al. [24]. Applying magnetic field improved thermophysical properties of ferrofluid and heat transfer rate of the copper tube. In the recent years, some researchers employed alternating magnetic field as an active method to increase thermal performance. Ghofrani et al. [28] investigated the effect of the alternating magnetic field with different frequencies on the convective heat transfer of a ferrofluid inside a copper tube. It was observed that the alternating magnetic field has a significant effect on the heat transfer rate in low Reynolds numbers and a 27.6% maximum enhancement for heat transfer rate was achieved. Goharkhah et al. [26] studied the effect of constant and alternating magnetic fields on the thermal and hydrodynamic characteristics of a rectangular copper channel and presented an efficient arrangement for the electromagnets. Results showed that the heat transfer rate enhanced about 37.3% under the effect of alternating magnetic field. The staggered layout was shown to be an appropriate arrangement for the electromagnets in order to increase the effectiveness of magnetized area. As mentioned before, passive methods such as extending heat transfer area using fins or porous medium can be employed to enhance the heat transfer performance. Metal foams with open cell structures are a type of porous media, which their properties such as high thermal conductivity, heat transfer area to volume ratio and mechanical stability make them an appropriate choice for heat transfer applications. Effects of the porous media on the characteristics of heat transfer have been vastly studied [28-31]. A few researchers have experimentally examined the heat transfer rate of nanofluids in porous media. For instance, Hajipour and Molaei Dehkordi [37] investigated mixed convective heat transfer of a vertical rectangular porous channel. The heat transfer and pressure drop were increased employing aluminum porous in the channel filled with Al2O3-water nanofluid. The force convection heat transfer of Al2O3-water nanofluid in a horizontal pipe with constant surface temperature filled with aluminum porous media was studied by Nazari et al. [38]. Results revealed that porous media significantly increased both heat transfer rate and pressure drop. The experimental investigation of ferroconvection of a tube partially filled with copper foam under the effect of permanent magnets was performed by

4

Sheikhnejad et al. [39]. Maximum heat transfer enhancement was about 140% due to the presence of the permanent magnet and porous medium. Based on recent researches, MHD ferrofluid flow through the porous medium has not been experimentally studied well and further studies are required to have a more profound insight into the fluid flow and heat transfer phenomena. In this research a rectangular channel with uniformly heated top and bottom plates filled with copper foam is employed. Two electromagnets are utilized to produce constant and alternating magnetic fields. Our specific focus is to explore the effects of constant and alternating magnetic fields with different intensities and frequencies on the ferrofluid heat transfer and hydrodynamic characteristics in porous media. Local convective heat transfer coefficient and pressure drop along the channel are measured for different volume fractions of ferrofluid, Reynolds numbers, intensities and frequencies of constant and alternating magnetic fields. The remainder of the paper is organized as follows. The detailed explanation of experimental setup, including the setup structure, the procedure of ferrofluid preparation and metal foam properties is presented in Section 2. The data reduction process and thermophysical properties of the employed ferrofluid are brought in Sections 3 and 4, respectively. Section 5 along with Appendix A describes the uncertainty analysis of the measured and calculated quantities. In Section 6, the experimental results are presented and discussed. Firstly, the experimental setup is verified using theoretical correlations and then the effects of metal foam, ferrofluid volume fraction, constant and alternating magnetic fields on the thermal and hydrodynamic performances of the channel are presented. Finally, the main findings of the present work are summarized and concluded in Section 7.

2. Experimental setup 2.1. Setup Structure The main components of the experimental setup include a constant temperature bath at the upstream of the loop to provide constant temperature inlet flow, a 24 V DC pump to circulate fluid through the closed loop, a rectangular porous channel, a magnetic field generator system, a

5

Lutron data acquisition system to record temperatures, an Endress Hauser pressure transmitter, 12 K-type thermocouples and a calibrated flowmeter. Schematic of experimental apparatus is shown in Fig. 1(a). Width (W), height (H) and length (L) of the rectangular channel are 50 mm, 20 mm and 430 mm, respectively. The constant heat flux condition is imposed on the top and bottom copper plates of the channel using two planar heaters. The channel is insulated by two Polyurethane (PU) plates on top and bottom of the copper plates pressing the heaters to the channel. In addition, PU is used to build up the side walls, inlet and outlet parts of the channel in order to reduce heat losses and ensure minimizing axial conduction. To record surface temperatures, 10 holes are drilled on the side walls of the top and bottom copper plates using a super drill machine. 12 calibrated K-type thermocouples are used to measure the surface, inlet and outlet temperatures. Thermocouples are connected to the data acquisition device and the temperature can be recorded continuously. The constant temperature bath keeps the inlet temperature (Tm,i) fixed and a thermocouple is installed before the inlet part to ensure that the inlet temperature does not change. A 0.1 ºC difference is observed between the measured inlet temperature and the set value of constant temperature bath. The outlet temperature (Tm,o) is measured right after the outlet part. Pressure drop along the channel is measured using a pressure transmitter with operating range of 0-250 kPa. The flow rate of ferrofluid is measured by an accurately calibrated flowmeter. Variation of the flow rate is set through the input voltage of the DC supplier connected to the pump. The system of magnetic field generator (Fig. 1(b)) includes 8 DC power supply channels, two electromagnets, a signal generator, an oscilloscope and an HT201 Teslameter. The Teslameter is placed between the plates and electromagnets to measure the intensity of magnetic field. Each branch of electromagnets connects to one channel of the DC power supply. In order to produce alternating magnetic field, the DC power supply connects to the signal generator with a microcontroller to convert the DC electric current into a rectangular pulses current. The oscilloscope is used to demonstrate the shape of the generated pulse wave.

6

Figure 1. (a) Schematic of experimental setup diagram, (b) Test rig and experimental apparatus, (c) heated test section in close view.

7

2.2. Ferrofluid Preparation Procedure Samples of ferrofluid are produced based on the coprecipitation method [43]. The production process is initiated with degassed DI water in a purged enclosed area. The air is extracted from the enclosed area by blowing a Noble gas such as Argon. Then, the DI water is degassed by injecting Argon into it. Specific amounts of FeCl2·4H2O and FeCl3·6H2O based on the stoichiometric proportional of ferrofluid (Fe3O4) chemical composition are dissolved in the degassed DI water. A mechanical agitator is used to mix the solution. In a time-consuming but accurate process, NH4OH droplets are added using a Burette into the swirling solution. The process of adding droplets of NH4OH is stopped when the pH reaches 12. Then, the solution is placed in a centrifugal device with a powerful permanent magnet to detach the black dough from the original solution. The dried out obtained black product is solved again in the degassed DI water using the mechanical agitator. To increase the stability of the ferrofluid, Tetra Methyl Ammonium Hydroxide (TMAH, (CH3)4NOH) is used as a surfactant [43]. After about 90 minutes of mixing the solution, the ferrofluid is placed in a Heichler homogenizer device. The sonication of the solution is repeated three times for 10 minutes. To provide three solutions with different volume fractions ( =0.5%, 1.0%, 1.5%) the above procedure is carried out identically for specific stoichiometric values proportional to assumed volume fractions. The scanning electron microscope (SEM) image of the final produced ferrofluid is shown in Fig. 2. The mean diameter of particles is 20 nm.

Figure 2. The SEM image of the ferrofluid.

8

2.3. Copper Foam Sample A copper foam sample, shown in Fig. 3(a), with dimensions equal to the channel (20mm(H)×50mm(W)×430mm(L)), is brazed to the top and bottom plates. The sandwich-like arrangement process is used to produce the copper foam [40]. In order to characterize a metal foam two parameters should be specified, namely, PPI and Porosity (ε). PPI is the number of pores per inch which can be obtained by counting the number of pores in 25.4 mm and porosity is the ratio of void volume to the total volume of metal foam, which consists of the void and solid volumes. Tetrakaidecahedron structure proposed by Gibson and Ashby [40] can be used to characterize the geometric features of the metal foam pores. One easy way to measure the porosity is the method presented by Mancin [41], using high-resolution image from the surface of the metal foam. A similarity between the SEM image and tetrakaidecahedron physical structure can be observed in Fig. 3(a) and (b). By measuring the length and thickness of the hexagonal window of the cells and substituting in the below equation, relative density and porosity are calculated [40]: t  R  1    1.06   l 

2

(1)

where ρR, t and l are relative density, thickness and length of the cell, respectively. Geometrical properties of the copper foam are reported in Table 1. Table 1. Properties of copper foam. Geometrical property

Value -1

Number pores per inch PPI (in )

15

Relative density, ρR

0.0987

Porosity, ε

0.9013

Cell thickness, t (mm)

0.501

Cell length, l (mm)

1.642

2

Permeability, K (m )

1.774×10-7

Inertia factor, fi

0.05524

9

Figure 3. Copper foam structure, (a) high resolution and (b) SEM images.

Measured pressure gradient for different mass flow rates of DI water in the rectangular channel filled with copper foam (shown in Fig. 4) can be related to the velocity according to the following equation [41]:

dp   2  u  fi u  au  bu 2 dz K K

(2)

The first term of the right-hand side is Darcy term which represents the linear dependence of pressure gradient to velocity for low mass flow rates. The second term is a quadratic dependence of pressure drop to velocity within the porous medium. In the above equation K and fi factors are permeability and inertia factors, respectively and can be obtained through a curve fitting to the measured data using least square error regression. Results are presented in Table 1.

10

400 350

dp/dz (Pa/m)

300 250 200 150 100 50 0

0.01

0.02

u (m/s)

0.03

0.04

Figure 4. The pressure gradient as a function of velocity for DI water through copper foam.

3. Data Reduction The local convective heat transfer coefficient h(x), along the channel, is calculated using

q  (3) T s  x  T m  x  Where q'' is the constant heat flux imposed on each copper plate, Ts(x) is the surface temperature h

which is measured by five thermocouples on each plate and Tm(x) is the bulk temperature which is calculated using energy balance

T m  x   T m ,i 

qx LmC p

(4)

Tm,i is the inlet temperature, q is the total imposed heat on the system (q= q''A), L is the length of the channel and m is the mass flow rate. The imposed constant heat flux q'' is obtained through VI (5) A A, V and I are the area of the plates, voltage and electric current, respectively. To assess the q  

reliability of thermal insulation of the heated test section using PU plates, Eq. (6) is used to evaluate the leaked heat flux to the environment.

11

q  

mC p T m ,i T m ,o 

where, Tm,i

(6)

A and Tm,o are inlet and outlet temperature, respectively. The Maximum difference

between two values of q'' which is due to heat leakage through thermal insulation is obtained 9.18%. The average convective heat transfer coefficient is calculated as 1 L h( x)dx (7) L 0 In order to determine the thermal performance of the channel and taking into account havg 

simultaneous effects of pressure drop and heat transfer enhancement, the below parameters are defined

1 

hff hw

(8)

h ff 2  h w (9) Pff Pw where η1 and η2 are thermal and overall performance ratios of the channel, respectively. DI water

flowing through the plain channel (without metal foam) is considered as the base case and assigned with subscript “w”, while “ff” stands for ferrofluid flowing inside the porous channel.

4. Thermophysical properties of the ferrofluid Volume fraction, specific heat and density of the ferrofluid can be obtained from below equations [3]:

 mp     p    mp   mw        p   w 

(10)

ff  1    w  p

(11)

 C 

p ff

 1     C p     C p  w

(12) p

12

In the above equations  , m, ρ and Cp are volume fraction, mass, density and specific heat and subscripts “p”, “w” and “ff” stand for nanoparticles, water and ferrofluid, respectively. Viscosity and thermal conductivity of the ferrofluid for different volume fractions are measured using viscometer (Anton Paar Lovis 2000 M) and KD2 pro (Decagon Devices Inc.) devices in the temperature range of 20C-60C. Primary tests for transport properties measurements of DI water are carried out to ensure the validity of the devices. The obtained results are compared with Ref. [42] in Fig. 5.

0.9

0.9

0.8

0.8

X

X

0.6

X

X X

X

0.7

X

X

0.6

0.5

0.5 Ref [42]- Exp. Data- Ref [42]-k Exp. Data-k

0.4 X

0.3 20

X

k(W/m.K)

.103 (Pa.s)

0.7

30

40

0.4

o

T ( C)

50

60

0.3 70

Figure 5. Comparison of the measured viscosity and thermal conductivity of DI water with Ref. [42].

5. Uncertainty analysis Uncertainties in the measured parameters such as thermal conductivity include two different errors, namely, a fixed error ef provided by the manufacturer (calibration uncertainty) and a random estimated error er (resolution uncertainty). Total uncertainty is calculated by the rootsum-squares method [52].

   e f2  e r2 (13) For example uncertainty of thermal conductivity measurement contains a fixed error of ef=5% and a random estimated error of ef=3.64%. Therefore, the total uncertainty in the thermal 13

conductivity is δ=±6.18%. Total uncertainties of all measured parameters are presented in Table 2. The effect of uncertainty of each measured parameters on the derived ones are assessed using the error propagation method [50, 51]. If {x1,x2,…,xn} are measured parameters and {δx1, δx2,…, δxn} are their corresponding uncertainties, respectively; the uncertainty of f which is a function of {x1,x2,…,xn}, f = f (x1,x2,…,xn), can be compute from:

 f   f i    xi  i 1  x i  n

2

(14)

For instance, the uncertainty in the local convective coefficient h, is a contribution of heat flux, surface temperature and bulk temperature uncertainties. The uncertainty of h is computed as: 2

2

  h   h   h h     q     T s    T m   q    T s    T m

2

(15)

where h 1 h q h q  ,  ,  q (Ts  Tm ) Ts (Ts  Tm ) Tm (Ts  Tm ) Hence, relative uncertainty of Eq. (15) can be obtain by 2

2

(16)

2

  q    T s   T m    (17)      h  q    (T s T m )   (T s T m )  The same procedure is performed on other calculated parameters and results are presented in

h

Table 2 and their corresponding uncertainty formulas can be found in Appendix A. Maximum uncertainty for h occurred at the first thermocouple, for Re=1186, ϕ=1.5%, B=450 G and f=10 Hz is ±4.2%.

14

Table 2. Uncertainty of all measured and derived parameters. Parameter Temperature Voltage Current W, L, H Thermal Conductivity Dynamic Viscosity Pressure Drop Mass Flow Area Cross Section Area Hydraulic Diameter Reynolds Number Total heat Heat Flux Heat Transfer Coefficient Average Heat Transfer Coefficient Thermal performance ratio Overall performance ratio

Uncertainty ±0.51K ±0.51V ±0.005A ±0.0005m ±6.2% ±2.8% ±3.3% ±1.7% ±1.0% ±2.7% ±3.1% ±5.2% ±0.4% ±1.1% ±4.2% ±2.7% ±3.4% ±5.3%

6. Results and discussion Experimental investigation of MHD mixed convective heat transfer through a rectangular porous channel with uniformly heated top and bottom plates, under constant and alternating magnetic fields, is conducted in this paper. The experiments were carried out at Gr=7.31×106 and 373≤Re≤1186. Therefore, the Richardson number Ri=Gr/Re2 varies between 5.20 and 52.56. Table 3 presents the Reynolds and Richardson numbers of all investigated cases. It is seen that minimum Richardson number is above the unity, which indicates the significant effects of natural convection on the heat transfer characteristics and presence of mixed convection flow regime. Table 3. Reynolds and Richardson numbers of all investigated cases at Gr=7.31×106 Reynolds number 373 539 701 862 1024 1186

Richardson number 52.56 25.17 14.88 9.84 6.97 5.20

The effect of metal foam, ferrofluid volume fraction, constant and alternating magnetic fields on the thermal and hydrodynamic performances of the channel are presented and discussed. Results are compared with the case of DI water in the plain channel (without metal foam).

15

6.1. Setup Verification The validity of experimental results is examined using comparisons of local convective coefficients, h, with theoretical correlations. For mixed convection heat transfer in a horizontal channel some correlations were proposed [45-48], based on a superposition of results for pure force convection (F) and natural convection (N):

Nu n  Nu Fn  Nu Nn

(20)

Osborne and Incropera [45] found Eq. (20) yields most accurate results for n=3. The Nusselt number of natural convection (NuN), based on Rayleigh number is proposed as 1

Nu N  0.229Ra 4

(21)

On the other hand, the well-known Shah formulation [44] for laminar flow between parallel plates under constant heat flux boundary condition is used to calculate the force convection Nusselt number (NuF). 1  1.490  x   3  1  Nu F   1.490  x   3  0.4  0.506 164 x  8.235  8.68 103 x   e 

x   0.0002 0.0002  x   0.001

(23)

0.001  x 

where,

x 

x Re Pr H

(24)

Figure 6 compares the local convective coefficients, h, for DI water flowing through a plain channel under constant heat flux boundary condition with the theoretical correlations at Re=373 and 701. While the force convection correlation are in acceptable agreement with the present experimental data for the top plate, it significantly underestimates the convective coefficient of the bottom plate. The figure clearly indicates the importance of the buoyancy effects and presence of the mixed flow regime for the bottom plate.

16

1400 1200 X

h (W/m2.K)

1000 800

Y

X X

600

Mixed convection-Re=373 Mixed convection-Re=701 Force convection-Re=373 Force convection-Re=701 Experimental-Bottom plate-Re=373 Experimental-Bottom plate-Re=701 Experimental-Top plate-Re=373 Experimental-Top plate-Re=701

X

X

X

Y

Y

Y

Y

400 Y

200 0

0.1

0.2

0.3

0.4

x (m)

Figure 6. Experimental and theoretical local convective coefficients of the top and bottom plates for Re=373 and Re=701

6.2. Effect of copper foam Figure 7 shows the effect of the presence of the copper foam on the temperature distribution of the top and bottom plates for DI water at Re=373. A significant difference is observed between top and bottom plates temperatures in the case of the plain channel. This temperature difference is due to the buoyant effects in the mixed convection regime. Previous studies [45, 49] have shown that the buoyant force induced by the heated bottom plate causes secondary flows in the form of longitudinal rolls. Although the buoyancy induced secondary flows cause heat transfer enhancement of the bottom plate, penetration to the top plate is suppressed by the thermal stratification in the top boundary layer. While the bottom plate flow regime is characterized by mixed convection, the top plate heat transfer is dominated by force convection. Therefore, an asymmetrical temperature distribution between top and bottom plate is observed even with the symmetrical thermal boundary condition. As shown in Fig. 7 the copper foam enhances the heat transfer and reduces the temperature asymmetry of the top and bottom plates, due to the heat spreading through the copper matrix, significant increment of momentum and energy transport and increase in the specific area of heat transfer (area to volume ratio).

17

390 380 370

T (K)

360 Top plate Top plate-Cu foam Bottom plate Bottom plate-Cu foam

350 340 330 320 310 300

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

0.35

Figure 7. Effect of copper foam on the surface temperature of top and bottom plates for DI water at Re=373

Local and average convective coefficients of the top and bottom plates for porous and plain channels are illustrated in Figs. 8(a) and (b), respectively. This figure shows that the copper foam significantly increases the local convective coefficient. It is also observed by Fig. 8(b), the heat transfer enhancement due to the copper foam grows with Reynolds number. In Fig. 9 thermal performance ratio (η1), defined in Eq. (8), is shown and maximum increase for the top and bottom plates at the highest Reynolds number are 269% and 107%, respectively. The heat transfer enhancement due to the metal foam on the top plate is about 2.5 times more than the bottom plate.

18

2500

2000

(a) 2000

(b)

Top plate Top plate-Cu foam Bottom plate Bottom plate-Cu foam

Top plate Top plate-Cu foam Bottom plate Bottom plate-Cu foam

h (W/m .K)

havg (W/m .K)

1500

2

2

1500

1000

1000

500 500

0

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

0

0.35

400

600

800 Re

1000

1200

Figure 8. Effect of copper foam on (a) local convective coefficient at Re=1186 and (b) average convective coefficient for DI Water.

4 Top plate Bottom plate

3.5

1

3 2.5 2 1.5 1

400

600

800 Re

1000

1200

Figure 9. Thermal performance of the top and bottom plates of porous channel for DI water.

6.3. Effect of ferrofluid volume fraction In the absence of magnetic field, ferrofluid with volume fractions ϕ=0.5%, 1.0% and 1.5% is used in the experimental setup to examine the effect of Fe3O4 volume fraction variation on the heat transfer characteristics. Figures 10 and 11 present the surface temperatures and local convective coefficients of channel plates for different volume fractions. As expected using ferrofluid increases thermal conductivity and disturbs thermal boundary layer, leading to heat 19

transfer enhancement. Viscosity gradient, Brownian motion and particles migration are reasons of thermal conductivity enhancement [53, 54]. It should be noted that similar trends were observed for all investigated Reynolds numbers, but the extreme cases correspond to the largest variations are presented in Figs. 10 and 11.

335

325

(a)

DI Water =0.5% =1.0% =1.5%

330

(b)

DI Water =0.5% =1.0% =1.5%

320

T (K)

T (K)

325 320

315

315 310 310 305

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

305

0.35

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

0.35

Figure 10. Effect of volume fraction of Fe3O4 on the surface temperature of (a) top and (b) bottom plates at Re=373

Variations of the thermal performance ratio in Fig. 12 shows that increasing Reynolds number and volume fraction result in heat transfer improvement. The maximum enhancement of heat transfer rate for the top and bottom plates with ϕ=1.5% and Re=1186 are 309% and 124%, respectively in comparison with the reference case (DI water in the plain channel).

20

2500

(a)

(b)

2000

h (W/m2.K)

h (W/m2.K)

2000 1500

1500 1000

DI Water =0.5% =1.0% =1.5%

DI Water =0.5% =1.0% =1.5%

500

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

1000

0.35

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

0.35

Figure 11. The effect of volume fraction of Fe3O4 on the local convective coefficient of (a) top and (b) bottom plates at Re=1186

4.5 4 Y

3.5

Y

Y

1

Y

3

DI Water-Top plate =0.5%-Top plate =1.0%-Top plate =1.5%-Top plate DI Water-Bottom plate =0.5%-Bottom plate =1.0%-Bottom plate =1.5%-Bottom plate

Y

Y

X O

2.5 2 1.5

O X

400

O X

O X

O X

600

Y

800 Re

O X

1000

O X

1200

Figure 12. Effect of different volume fraction of Fe3O4 on thermal performance ratios of top and bottom plates.

6.4. Effect of constant and alternating magnetic field To investigate the effect of the magnetic field on the heat transfer, constant fields with intensities B=250 G and 450 G and alternating fields with intensity B=450 G and frequencies f=5 Hz and 10 Hz are applied. The alternating magnetic field was generated by converting the DC current to pulsating current using the signal generator system (Fig. 1(b)). For this purpose, a rectangular 21

pulses wave with equal connection and disconnection time, shown in Fig. 13, is employed. Period (T) is the sum of connection and disconnection times and the frequency is the inverse of period f=1/T.

Magnetic field intensity

t1:Connection time t2:Disconnection time

Bmax

t1

t2

2T

T

Time

Figure 13. Rectangular pulses wave used to generate alternating magnetic field

An appropriate arrangement of electromagnets is staggered layout [26]. Therefore, the center of the first electromagnet is located under the bottom plate at distance of 90 mm from the entry and the second one is placed on the top plate with an axial distance of 160 mm from the first electromagnet. The effect of constant and alternating magnetic fields with different intensities and frequencies on the surface temperatures and local convective coefficients of the top and bottom plates are illustrated in Figs. 14 and 15. These figures show inducing constant and alternating magnetic fields improve the cooling effect of the heated channel. Heat transfer enhancement due to the magnetic fields is higher in the vicinity of electromagnets for the top and bottom plates. For instance, in Figs. 14(a) and 15(a) the temperature reduction is more significant near the upper electromagnet (x=0.25 m).

22

335

325 Y

330

X

DI Water =1.5%-B=0 G-f =0Hz =1.5%-B=250 G-f=0 Hz =1.5%-B=450 G-f=0 Hz =1.5%-B=450 G-f=5 Hz =1.5%-B=450 G-f=10 Hz

Y

320

X

Y X

325

DI Water =1.5%-B=0 G-f=0 Hz =1.5%-B=250 G-f=0 Hz =1.5%-B=450 G-f=0 Hz =1.5%-B=450 G-f=5 Hz =1.5%-B=450 G-f=10 Hz

Y X Y

Y

320 Y

315

T (K)

T (K)

Y X

X

315

Y X

X

Y

X

310 310

(a)

Y X

X

(b)

Y X

305

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

305

0.35

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

0.35

Figure 14. Effect of constant and alternating magnetic field on the surface temperature of the (a) top and (b) bottom plates for ϕ=1.5% and Re=373.

Heat transfer enhancement is improved by increasing magnetic field intensity. This improvement can be related to the absorption of magnetite particles to the magnetized area. This aggregation disturbs and diminishes the growth of boundary layer and consequently increases the mixing and heat transfer of ferrofluid. On the other hand, the magnetite particles stick together due to magnetic forces and form a chain-like strings which increases the thermal conductivity of ferrofluid. In the case of the alternating magnetic field, the induced magnetic force absorbs and releases the bulk of passing nanoparticles. This mechanism augments the effect of particles migration and boundary layer disturbance, which results in more intensified mixing and further enhancement of heat transfer.

23

3000

3000

2500

Y

Y

h (W/m .K)

X

2000

(b)

DI Water =1.5%-B=0 G-f=0 Hz =1.5%-B=250 G-f=0 Hz =1.5%-B=450 G-f=0 Hz =1.5%-B=450 G-f=5 Hz =1.5%-B=450 G-f=10 Hz

X

2500

X

Y

Y

X

2000

X

1500

X

Y

X Y

Y Y

X Y

1000

500

0.05

0.1

DI Water =1.5%-B=0 G-f=0 Hz =1.5%-B=250 G-f=0 Hz =1.5%-B=450 G-f=0 Hz =1.5%-B=450 G-f=5 Hz =1.5%-B=450 G-f=10 Hz

2

X

2

Y

h (W/m .K)

(a) X

0.15

0.2 0.25 x (m)

0.3

X Y

1500

1000

0.35

0.05

0.1

0.15

0.2 0.25 x (m)

0.3

X Y

0.35

Figure 15. Distribution of local convective coefficients of (a) top and (b) bottom plates for different magnetic field intensities and frequencies (ϕ=1.5% and Re=1186).

Figure 16 depicts thermal performance ratio for different magnetic field intensities and frequencies. Heat transfer improves with increasing Reynolds number, magnetic field intensity and frequency. Maximum heat transfer enhancement observed for the alternating magnetic field with f=10Hz, ϕ=1.5% and Re=1186 are 361% and 160% for top and bottom plates, respectively.

5.5

3 X

5 Y

4.5

DI water =0.5%-B=250 G-f=0Hz =0.5%-B=450 G-f=0Hz =0.5%-B=450 G-f=10Hz =1.5%-B=250 G-f=0Hz =1.5%-B=450 G-f=0Hz =1.5%-B=450 G-f=10Hz

X Y

2.5

DI water =0.5%-B=250 G-f=0Hz =0.5%-B=450 G-f=0Hz =0.5%-B=450 G-f=10Hz =1.5%-B=250 G-f=0Hz =1.5%-B=450 G-f=0Hz =1.5%-B=450 G-f=10Hz

Y

Y

Y

Y Y

3.5 Y

3 2.5

X

X

X

Y

X

2

X

Y Y

(a) 600

800 Re

1000

Y X

Y

X

X

X

X

400

1

1

Y

4

X

(a)

X

1.5

1200

400

600

800 Re

1000

1200

Figure 16. Variation of thermal performance ratio of (a) top and (b) bottom plates with Reynolds number for different magnetic field intensities and frequencies (ϕ=0.5% and 1.5%).

24

6.5. Pressure drop In order to study the hydrodynamic performance of the channel, pressure drop has been measured between inlet and outlet. Figure 17 signifies that the pressure drop of the channel increases with Reynolds number, volume fraction, magnetic field intensity. Increase in the volume fraction of nanoparticles and formation of chain-like structures due to applied constant magnetic field increase the dynamic viscosity of ferrofluid leading to the growth of the pressure drop along the channel which demands more power consumption specifically at high Reynolds numbers. It is worth to mention, converting the constant magnetic field to alternating reduces the pressure drop because of the pulsating magnetic force.

p (Pa)

350 300

Y

250

X

DI Water =1.0%-B=0 G-f=0 Hz =1.5%-B=0 G-f=0 Hz =1.5%-B=250 G-f=0 Hz =1.5%-B=450 G-f=0 Hz =1.5%-B=450 G-f=5 Hz =1.5%-B=450 G-f=10 Hz

200

Y X Y X

150

Y X X Y

100 X Y

50 0

X Y

400

600

800 Re

1000

1200

Figure 17. Variation of pressure drop along the channel with Reynolds number for different volume fractions, magnetic field intensities and frequencies.

By defining the overall performance ratio η2, respective effects of thermal and hydrodynamic performances of the channel can be studied. Figs 18 (a) and (b) plot the effects of and magnetic field intensity and volume fraction of ferrofluid on the overall performance ratio of the channel top plate. Although increasing constant magnetic field intensity improves the heat transfer of the channel, η2 is decreased due to the higher increment of pressure drop (Fig 18a). The similar trend is observed with increasing volume fraction that results in overall performance ratio reduction (Fig 18b). The alternating magnetic field enhances the heat transfer rate and reduces the pressure

25

drop. Therefore, as shown in Fig. 19(a), these two positive effects remarkably increase the overall performance ratio of the channel. Moreover, Fig 19 (b) clarifies that η2 decreases with increasing volume fraction at a constant frequency (f=5 Hz) because of the pressure drop growth.

0.2

0.2

(a)

B=0 G B=250 G B=450 G

0.18

0.18

2

0.16

2

0.16

(b)

=0.5% =1.0% =1.5%

0.14

0.14

0.12

0.12

0.1

400

600

800 Re

1000

0.1

1200

400

600

800 Re

1000

1200

Figure 18. Variation of overall performance ratio of the channel top plate with Reynolds number for constant magnetic field, (a) effect of magnetic field intensity and (b) effect of volume fraction

(a)

0.24 f=0 Hz f=5 Hz f=10 Hz

0.22

=0.5% =1.0% =1.5%

0.22

0.18

0.18

2

0.2

2

0.2

0.16

0.16

0.14

0.14

0.12

0.12

0.1

(b)

0.24

400

600

800 Re

1000

0.1

1200

400

600

800 Re

1000

1200

Figure 19. Variation of overall performance ratio of the channel top plate with Reynolds number for alternating magnetic field, (a) effect of magnetic field frequency and (b) effect of volume fraction

26

7. Conclusion MHD mixed convection heat transfer and pressure drop of ferrofluid inside a porous rectangular channel, have been experimentally examined in this paper. The top and bottom plates of the channel were uniformly heated while the side walls were adiabatic. The flow was affected by external constant and alternating magnetic fields generated using two electromagnets. The Richardson number indicates the importance of the buoyant force and presence of mixed convection flow regime. Effects of copper foam as porous media, volume fraction of ferrofluid, Reynolds number and intensity and frequency of magnetic field on the heat transfer rate and pressure drop of the channel were studied. The main findings of the paper can be concluded as follows. 

A remarkable temperature difference between top and bottom plates of the plain channel (without copper foam) was observed due to the buoyant effects. The secondary flows induced by mixed convection cause heat transfer enhancement of the bottom plate and asymmetrical temperature distribution.



Embedding copper foam significantly improved the heat transfer rate and decreased the temperature difference between top and bottom plates due to the heat conduction of the copper foam, mixing of the fluid and the increase in specific area of heat transfer. Maximum increase in the local convective coefficients of the top and bottom plates for DI water at Re=1186 are about 107% and 269%, respectively.



Employing ferrofluid increased the heat transfer rate, because of the thermal conductivity improvement and disturbance of thermal boundary layer. It was observed that the heat transfer enhancement increases with volume fraction and Reynolds number.



Applying constant magnetic field enhanced the cooling effect of ferrofluid especially in the vicinity of electromagnets. Heat transfer enhancement improved with the magnetic field intensity because of the aggregation of nanoparticles, destruction of boundary layer growth and formation of chain-like strings which increased the thermal conductivity of ferrofluid.



Alternating magnetic field improved the particles migration and boundary layer disturbance, which results in more intensified mixing and further augmentation of heat

27

transfer. Maximum heat transfer enhancement observed for the alternating magnetic field were 361% and 160% for top and bottom plates, respectively 

Pressure drop of the channel increased with Reynolds number, volume fraction, magnetic field intensity. It was observed that employing alternating magnetic field reduces pressure drop with respect to constant one.



Although increasing volume fraction and constant magnetic field intensity improved the heat transfer of the channel, the overall performance ratio was decreased due to the higher increment of pressure drop. On the other hand, the alternating magnetic field significantly enhanced the overall performance ratio due to the heat transfer rate improvement and pressure drop reduction.

Appendix A. Uncertainty analysis The uncertainty of derived parameters (Reynolds number, heat flux, area, thermal performance ratio...) are obtained using Eq. (14). In this appendix uncertainty formulas for all derived parameters mentioned in Table. 2 are presented.

A

 W    L       A W   L 

 ACS ACS

2

2

 W    H       W   H  2



T m   T mi



(1-A) 2

(2-A)

2   q 2  x   q   x  LmC   LmC p p   

 q 

2 2 2 2           qx  L    qx  m    qx  C      p 2 2   L2 mC   Lm C p   LmC p    p     

 V    I    A         q  V   I   A  2

2

2

2

(4-A) 2

  m    D H    ACS              Re  m   D H   ACS    

 Re

q

2

 V    I       q V   I  2

(3-A)

2

(5-A)

2

(6-A)

28

2

h  h  1    ff    w  1  hff   hw  2

2

(7-A) 2

2

  h    h   Pff   Pw  2    ff    w       2  hff   hw   Pff   Pw 

29

2

(8-A)

Reference [1] [2] [3] [4]

[5] [6]

[7]

[8] [9] [10]

[11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23]

[24]

[25]

R. L. Webb and N.-H. Kim, “Principl of enhanced heat transfer,” Taylor Fr. New York, NY, USA, 1994. A. E. Bergles, “Techniques to augment heat transfer,” Handbook of heat transfer.(A 74-17085 05-33) New York, McGraw-Hill Book Co., 1973,. pp. 10–11, 1973. S. K. Das, S. U. S. Choi, W. Yu, and T. Pradeep, Nanofluids: Science and Technology. 2007. J. A. Eastman, S. U. S. Choi, S. Li, W. Yu, and L. J. Thompson, “Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles,” Appl. Phys. Lett., vol. 78, no. 6, pp. 718–720, 2001. P. Keblinski, R. Phillpot, S. Choi, and A. Eastman, “Mechanisms of heat ¯ow in suspensions of nano-sized particles (nano¯uids),” vol. 45, pp. 855–863, 2002. C. H. Li and G. P. Peterson, “Experimental investigation of temperature and volume fraction variations on the effective thermal conductivity of nanoparticle suspensions (nanofluids),” J. Appl. Phys., vol. 99, no. 8, 2006. P. Bhattacharya, S. K. Saha, A. Yadav, P. E. Phelan, and R. S. Prasher, “Brownian dynamics simulation to determine the effective thermal conductivity of nanofluids,” J. Appl. Phys., vol. 95, no. 11 I, pp. 6492–6494, 2004. H. Zhu, C. Zhang, S. Liu, Y. Tang, and Y. Yin, “Effects of nanoparticle clustering and alignment on thermal conductivities of Fe3O4 aqueous nanofluids,” Appl. Phys. Lett., vol. 89, no. 2, 2006. L. S. Sundar, M. K. Singh, and A. C. M. Sousa, “Thermal conductivity of ethylene glycol and water mixture based Fe3O4 nanofluid,” Int. Commun. Heat Mass Transf., vol. 49, pp. 17–24, 2013. A. Karimi, M. Goharkhah, M. Ashjaee, and M. B. Shafii, “Thermal Conductivity of Fe 2 O 3 and Fe 3 O 4 Magnetic Nanofluids Under the Influence of Magnetic Field,” Int. J. Thermophys., vol. 36, no. 10, pp. 2720–2739, 2015. I. Djurek and D. Djurek, “Thermal Conductivity Measurements of the CoFe 2 O 4 and g-Fe 2 O 3 based Nanoparticle Ferrofluids *,” Croat. Chem. Acta, vol. 80, pp. 529–532, 2007. M. J. Pastoriza-Gallego, L. Lugo, J. L. Legido, and M. M. Piñeiro, “Enhancement of thermal conductivity and volumetric behavior of Fe xOy nanofluids,” J. Appl. Phys., vol. 110, no. 1, 2011. M. Sheikholeslami and H. B. Rokni, “Nanofluid two phase model analysis in existence of induced magnetic field,” Int. J. Heat Mass Transf., vol. 107, pp. 288–299, 2017. M. Sheikholeslami and H. B. Rokni, “Numerical modeling of nanofluid natural convection in a semi annulus in existence of Lorentz force,” Comput. Methods Appl. Mech. Eng., vol. 317, pp. 419–430, 2017. M. Sheikholeslami and A. J. Chamkha, “Influence of Lorentz forces on nanofluid forced convection considering Marangoni convection,” J. Mol. Liq., vol. 225, pp. 750–757, 2017. R. E. Rosensweig, Ferrohydrodynamics. Dover Publications, 1997. J. Philip, P. D. Shima, and B. Raj, “Enhancement of thermal conductivity in magnetite based nanofluid due to chainlike structures,” Appl. Phys. Lett., vol. 91, no. 20, pp. 2005–2008, 2007. Q. Li, Y. Xuan, and J. Wang, “Experimental investigations on transport properties of magnetic fluids,” Exp. Therm. Fluid Sci., vol. 30, no. 2, pp. 109–116, 2005. A. Gavili, F. Zabihi, T. D. Isfahani, and J. Sabbaghzadeh, “The thermal conductivity of water base ferrofluids under magnetic field,” Exp. Therm. Fluid Sci., vol. 41, pp. 94–98, 2012. Y. Xuan, Q. Li, and M. Ye, “Investigations of convective heat transfer in ferrofluid microflows using latticeBoltzmann approach,” Int. J. Therm. Sci., vol. 46, no. 2, pp. 105–111, 2007. F. Selimefendigil and H. F. Öztop, “Forced convection of ferrofluids in a vented cavity with a rotating cylinder,” Int. J. Therm. Sci., vol. 86, pp. 258–275, 2014. M. Motozawa, J. Chang, T. Sawada, and Y. Kawaguchi, “Effect of magnetic field on heat transfer in rectangular duct flow of a magnetic fluid,” Phys. Procedia, vol. 9, no. 2, pp. 190–193, 2010. R. Azizian, E. Doroodchi, T. McKrell, J. Buongiorno, L. W. Hu, and B. Moghtaderi, “Effect of magnetic field on laminar convective heat transfer of magnetite nanofluids,” Int. J. Heat Mass Transf., vol. 68, pp. 94–109, 2014. M. Lajvardi et al., “Journal of Magnetism and Magnetic Materials Experimental investigation for enhanced ferrofluid heat transfer under magnetic field effect,” J. Magn. Magn. Mater., vol. 322, no. 21, pp. 3508– 3513, 2010. M. M. Murray, “Demonstration of Heat Transfer Enhancement Using Ferromagnetic Particle Laden Fluid and Switched Magnetic Fields,” Journal of Heat Transfer, vol. 130, no. 11. p. 114508, 2008.

30

[26]

[27]

[28] [29] [30] [31] [32] [33]

[34]

[35] [36] [37]

[38] [39]

[40] [41] [42] [43]

[44] [45] [46] [47] [48] [49]

[50]

M. Goharkhah, M. Ashjaee, and M. Shahabadi, “Experimental investigation on convective heat transfer and hydrodynamic characteristics of magnetite nanofluid under the influence of an alternating magnetic field,” Int. J. Therm. Sci., vol. 99, pp. 113–124, 2016. A. Ghofrani, M. H. Dibaei, A. Hakim Sima, and M. B. Shafii, “Experimental investigation on laminar forced convection heat transfer of ferrofluids under an alternating magnetic field,” Exp. Therm. Fluid Sci., vol. 49, pp. 193–200, 2013. D. a. Nield and A. Bejan, Convection in Porous Media. 2013. N. Dukhan, “Analysis of Brinkman-Extended Darcy Flow in Porous Media and Experimental Verification Using Metal Foam,” J. Fluids Eng., vol. 134, no. July 2012, p. 71201, 2012. K. Boomsma, D. Poulikakos, and F. Zwick, “Metal foams as compact high performance heat exchangers,” Mech. Mater., vol. 35, no. 12, pp. 1161–1176, 2003. C. Hutter, D. B??chi, V. Zuber, and P. Rudolf von Rohr, “Heat transfer in metal foams and designed porous media,” Chem. Eng. Sci., vol. 66, no. 17, pp. 3806–3814, 2011. M. Sheikholeslami, “Numerical simulation of magnetic nanofluid natural convection in porous media,” Phys. Lett. A, vol. 381, no. 5, pp. 494–503, 2017. R. A. Mahdi, H. A. Mohammed, K. M. Munisamy, and N. H. Saeid, “Influence of various geometrical shapes on mixed convection through an open-cell aluminium foam filled with nanofluid,” J. Comput. Theor. Nanosci., vol. 11, no. 5, pp. 1275–1289, 2014. K. Javaherdeh and H. R. Ashorynejad, “Magnetic field effects on force convection flow of a nanofluid in a channel partially filled with porous media using Lattice Boltzmann Method,” Adv. Powder Technol., vol. 25, no. 2, pp. 666–675, 2014. M. Hajipour and A. Molaei Dehkordi, “Analysis of nanofluid heat transfer in parallel-plate vertical channels partially filled with porous medium,” Int. J. Therm. Sci., vol. 55, pp. 103–113, 2012. D. S. Cimpean and I. Pop, “Fully developed mixed convection flow of a nanofluid through an inclined channel filled with a porous medium,” Int. J. Heat Mass Transf., vol. 55, no. 4, pp. 907–914, 2012. M. Hajipour and A. Molaei Dehkordi, “Mixed-convection flow of Al2O3-H2O nanofluid in a channel partially filled with porous metal foam: Experimental and numerical study,” Exp. Therm. Fluid Sci., vol. 53, pp. 49–56, 2014. M. Nazari, M. Ashouri, M. H. Kayhani, and A. Tamayol, “Experimental study of convective heat transfer of a nanofluid through a pipe filled with metal foam,” Int. J. Therm. Sci., vol. 88, pp. 33–39, 2014. Y. Sheikhnejad, R. Hosseini, and M. Saffar Avval, “Experimental study on heat transfer enhancement of laminar ferrofluid flow in horizontal tube partially filled porous media under fixed parallel magnet bars,” J. Magn. Magn. Mater., vol. 424, pp. 16–25, 2017. L. J. Gibson and M. F. Ashby, Cellular Solids: Structure and Properties. Cambridge University Press, 1999. S. Mancin, C. Zilio, A. Diani, and L. Rossetto, “Air forced convection through metal foams: Experimental results and modeling,” Int. J. Heat Mass Transf., vol. 62, no. 1, pp. 112–123, 2013. T. L. Bergman, A. S. Lavine, F. P. Incropera, and D. P. DeWitt, Fundamentals of Heat and Mass Transfer. 2011. H. Bagheri, O. Zandi, and A. Aghakhani, “Reprint of: Extraction of fluoxetine from aquatic and urine samples using sodium dodecyl sulfate-coated iron oxide magnetic nanoparticles followed by spectrofluorimetric determination,” Anal. Chim. Acta, vol. 716, no. 1–2, pp. 61–65, 2012. R. K. Shah and A. L. London, Laminar Flow Forced Convection in Ducts: A Source Book for Compact Heat Exchanger Analytical Data. 1978. D. G. Osborne and F. P. Incropera, “Laminar, mixed convection heat transfer for flow between horizontal parallel plates with asymmetric heating,” Ini. 1. Heat Maw Transf., vol. 28, no. 1, pp. 207–217, 1985. T. Fujii and H. Imura, “Natural-convection heat transfer from a plate with arbitrary inclination,” Int. J. Heat Mass Transf., vol. 15, no. 4, pp. 755–767, 1972. S. W. Churchill, “A comprehensive correlating equation for laminar, assisting, force and free convection,” AIChE J., vol. 23, no. 1, pp. 10–16, 1977. A. Acrivos, “On the combined effect of forced and free convection heat transfer in boundary layer flow,” Chem. Eng. Sci., vol. 21, no. 4, pp. 343–352, 1966. D. G. Osborne and F. P. Incropera, “Experimental study of mixed convection heat transfer for transitional and turbulent flow between horizontal, parallel plates,” hf. J. Hear Mass Trmfer, vol. 28, no. 7, pp. 1337– 1344, 1985. R. J. Moffat, “Describing the uncertainties in experimental results,” Exp. Therm. Fluid Sci., vol. 1, no. 1, pp.

31

[51] [52] [53] [54]

3–17, 1988. R. J. Moffat, “Contributions to the Theroy of Single-Sample Uncertainity Analysis,” J. Fluids Eng., vol. 104, no. June, pp. 250–258, 1982. R. S. Figliola and D. E. Beasley, “Theory and Design for Mechanical Measurements,” p. 585, 2011. Y. Ding, H. Alias, D. Wen, and R. A. Williams, “Heat transfer of aqueous suspensions of carbon nanotubes (CNT nanofluids),” Int. J. Heat Mass Transf., vol. 49, no. 1–2, pp. 240–250, 2006. D. Wen and Y. Ding, “Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions,” Int. J. Heat Mass Transf., vol. 47, no. 24, pp. 5181–5188, 2004.

32

Highlights 

An asymmetrical temperature distribution is observed due to the buoyant effects.



Copper foam significantly increases heat transfer and pressure drop of the channel.



Applying constant and alternating magnetic field enhances heat transfer rate.



Alternating field reduces ∆p with respect to constant one leading to developed η2.

33