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Experimental investigation on convective heat transfer and hydrodynamic characteristics of magnetite nanofluid under the influence of an alternating magnetic field
International Journal of Thermal Sciences 99 (2016) 113e124
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International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Experimental investigation on convective heat transfer and hydrodynamic characteristics of magnetite nanofluid under the influence of an alternating magnetic field Mohammad Goharkhah a, *, Mehdi Ashjaee b, Mahmoud Shahabadi c a b c
Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran Department of Mechanical Engineering, University of Tehran, Tehran, Iran Department of Electrical and Computer Engineering, University of Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 January 2015 Received in revised form 8 August 2015 Accepted 9 August 2015 Available online xxx
An experimental study has been carried out on the laminar forced convective heat transfer of Fe3O4/ water nanofluid (ferrofluid) under an external magnetic field. Here, the ferrofluid flows into a long uniformly heated parallel plate channel and is influenced by an external magnetic field generated by four electromagnets. The efficient arrangement of the electromagnets is obtained by numerical simulations and primary experiments. Effects of magnetic field intensity and frequency on the convective heat transfer and pressure drop have been investigated at different concentrations (1, 1.5, and 2 Vol%) and flow rates (200 Re 1200). It is observed that the convective heat transfer has a direct relation with the Reynolds number and ferrofluid concentration. Moreover, at a constant Reynolds number, the magnetic field intensity increases the heat transfer. Note that there exists an optimum frequency for every single Reynolds number which increases by Reynolds number. Our results also show a maximum heat transfer enhancement of 16.4% by the use of ferrofluid, in the absence of a magnetic field. This value is increased up to 24.9% and 37.3% by application of constant and alternating magnetic field, respectively. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Pressure drop Forced convection Magnetite Nanofluid Magnetic field Parallel plate channel
1. Introduction Augmentation of heat transfer is a key challenge for many industrial applications. Among several methods which have been proposed for heat transfer enhancement, using of nanofluids has achieved growing interest by many researchers recently. Several experimental and numerical studies have been carried out on the transport properties and heat transfer characteristics of different nanofluids [1e10]. A number of these studies have concentrated on the magnetic nanofluids (ferrofluids). Ferrofluid is a synthesized colloidal mixture of nonmagnetic carrier liquid, typically water or oil, containing single domain permanently magnetized nanoparticles, typically magnetite [11]. Similar to the other nanofluids, the thermal conductivity of the
* Corresponding author. Department of Mechanical Engineering, Sahand University of Technology, New Sahand Town, Tabriz, Iran. Tel.: þ98 41 33459424. E-mail addresses: [email protected] (M. Goharkhah), [email protected] (M. Ashjaee), [email protected] (M. Shahabadi). http://dx.doi.org/10.1016/j.ijthermalsci.2015.08.008 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
base fluid can be enhanced noticeably due to addition of the magnetic nanoparticles [12e16]. Moreover, the distinctive characteristic of the ferrofluid is the ability to respond to an external magnetic field. Recent studies show the significant increase of the ferrofluid thermal conductivity in the presence of an external magnetic field [17e20]. For example Philip et al. [17] and Gavili et al. [20] observed 300% and 200% thermal conductivity enhancement for Fe3O4 ferrofluid, respectively. The enhancement of the thermal conductivity is attributed to the formation of chainlike structures in the ferrofluid which grow with the intensity of the magnetic field [17]. Furthermore, the forced convection heat transfer of the ferrofluids has also been investigated in the absence and presence of an external magnetic field [21e27]. Sundar et al. [21] studied turbulent forced convection heat transfer and friction factor of Fe3O4 magnetic nanofluid in a tube in the absence of magnetic field and obtained correlations for estimation of the Nusselt number and friction factor. Their results show that the heat transfer coefficient is enhanced by 30.96% and friction factor by 10.01% at 0.6% volume fraction compared to the base fluid.
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Motozawa et al. [25] studied the effect of magnetic field on heat transfer of water-based magnetic fluid named W-40 in a rectangular duct. It is shown that heat transfer coefficient increases locally in the region where magnetic field exists and has a direct relation with magnetic field intensity. They reported a maximum of 20% heat transfer enhancement for their studied case. Lajvardi et al. [26] studied the convective heat transfer of ferrofluid flowing through a heated copper tube in the laminar flow regime in the presence of a magnetic field. They attributed the enhancement of the heat transfer to the improvement of thermophysical properties of ferrofluid under the influence of the magnetic field. Azizian et al. [27] studied the effect of a constant magnetic field on the laminar convective heat transfer and pressure drop of magnetite nanofluid in a vertical tube and reported large enhancement in the local heat transfer coefficient against only a 7.5% increase of pressure drop. They also showed that the convective heat transfer enhancement increases with the magnetic field intensity and gradient. Above mentioned works apply a constant magnetic field to increase the ferrofluid convective heat transfer. Application of an alternating magnetic field for heat transfer enhancement was first introduced by Murray [28] for a particle laden fluid. He employed time varying magnetic field to cause the iron filings in mineral oil to be attracted to and released from a heated pipe wall. He demonstrated a 267% increase in heat transfer coefficient against a 48% increase in flow differential pressure. With a similar mechanism to that used by Murray [28], the current research investigates the effect of an alternating magnetic field on the heat transfer and pressure drop of ferrofluid flow in a channel. Specifically, ferrofluid flows into a channel with uniformly heated top and bottom copper plates and is influenced by a magnetic field generated by four electromagnets. The efficient arrangement of the electromagnets is obtained by the numerical simulations and primary experiments. All the heat transfer experiments are configured based on the numerically designed arrangement. The convective heat transfer coefficients are then measured at both thermally developing and fully developed regions at different Reynolds numbers, nanoparticle concentrations, magnetic field intensities, and frequencies. The results have been compared with those of ferrofluid flow without external magnetic field and deionized water alone.
2. Experimental method 2.1. Experimental apparatus The experimental set-up is shown schematically in Fig. 1. The main components are: parallel plate channel test section, a closed loop for circulating the nanofluid, pressure drop measurement device, magnetic field generation and control system, and data acquisition system for temperature recording. The studied geometry is a parallel plate channel with a flow passage size of 40 mm (W) 4 mm (H) 2500 mm (L). The channel consists of a hydrodynamic entry section and a heat transfer section with lengths of 500 mm and 2000 mm, respectively. The length of entry section is selected such that the hydrodynamically fully developed flow is ensured at the heat transfer section for all the Reynolds numbers. Convective heat transfer coefficients are measured on the heat transfer section. Cross section of the heat transfer section is also shown in Fig. 1. It consists of two copper top and bottom plates which are fixed in a very low thermal conductivity polyethylene housing. A small mixing chamber is located at the exit of the heat transfer section for purpose of the proper measurement of fluid mean exit temperature. A constant surface heat flux is maintained on both copper plates by passing electric current through the two strip heaters which are pressed to the back of copper plates. The surface temperature of each copper plate is measured by 21 calibrated thermocouples. Two thermocouples are also inserted in the inlet and outlet of the test section to measure the inlet and exit temperatures of the fluid. The thermocouples are connected to two data loggers and all the temperatures can be monitored and recorded simultaneously during the tests. The pressure drop of the heat transfer section is measured by Endress Hauser differential pressure transducer with operation range of 0e250 kPa (0e2500 mbar) and 1% accuracy, as calibrated by the manufacturer. Ferrofluid is circulated in a loop from a reservoir tank by a DC pump. The volumetric flow rate passing through the loop is measured using a calibrated flow meter, and can be varied by changing the voltage of the DC power supply of the pump. A constant temperature bath is located upstream of the pump to control the inlet temperature.
Fig. 1. Schematic diagram of the experimental setup.
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The magnetic field generation system includes four electromagnets, a high voltage DC power supply, a signal generator and an oscilloscope, as shown in Fig. 2(a). Four electromagnets are used to generate the magnetic field. Dimensions of the electromagnets are shown in Fig. 2(b). Each electromagnet consists of an electrically insulated iron U core and two copper windings. The windings have N ¼ 3000 turns of 0.5 mm diameter copper wire with a total electric resistance of 35 U. The alternating magnetic field with specific frequency and phase shift is produced by a DC power supply connected to a signal generator. The signal generator converts the input DC current to rectangular pulses for driving the windings. With the help of its microcontroller, the digital circuit of the signal generator has the ability to adjust the frequency of the pulses and their relative phase shifts. An oscilloscope is used to monitor the wave form of the generated pulses. Furthermore, a HT201 Teslameter has been used to measure the magnetic field strength during the experiments. The electromagnets locations have a significant effect on the magnetic force distribution and consequently the convective heat transfer. The optimum configuration of the electromagnets has been obtained by a numerical simulation and supplementary experiments which is discussed in section 5. More details about the test section can be found in Refs. [24,29].
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2.2. Ferrofluid synthesis procedure The ferrofluid samples are synthesized using the conventional coprecipitation process. Briefly, stoichiometric amounts of FeCl2$4H2O and FeCl3$6H2O equivalent to the chemical composition of Fe3O4 are dissolved in deionized water and degassed via Argon gas purging. Then, NH4OH solution is gradually added to the iron solution under the mechanical stirring until pH reaches 12. The black precipitate is removed from the liquid phase via centrifugal and magnetic separation and washed several times by acetone and DI-water. The obtained solid product is redispersed in DI-water and, tetramethylammonium hydroxide (TMAH, (CH3)4NOH) is added to the solution under stirring in a manner that the desired volume fraction values of 1%, 1.5% and 2% are achieved. The stirring process is continued for an additional 1 h until the stable ferrofluid is obtained. The ferrofluid samples exhibited excellent stability due to the use of the TMAH surfactant. However, in order to avoid any agglomeration of the nanoparticles and ensure that all of the experiments have been carried out at equal conditions, the ferrofluid samples have been ultrasonicated before each experiment. SEM image of the synthesized sample is presented in Fig. 3. As seen in Fig. 3, nanoparticles with various shapes are aggregated and formed larger agglomerates. The mean particle size is 30 nm.
Fig. 2. (a) Magnetic field generation and control system, (b) dimensions of the electromagnets.
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dh ¼ h
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 00 2 2 2 dq dTs vTm þ þ dTm 00 q Ts Tm Ts Tm
(6)
The uncertainties of the measurements in the present study are summarized in Table 1. Uncertainty values have been calculated for all the measured cases. The average uncertainty in calculation of local convection heat transfer coefficient is ±3.2%. 5. Thermophysical properties of the ferrofluid The volume concentration of the samples are obtained by:
4 ¼ mp
mp rp
rp
þ
(7)
mf rf
The following equations have been used for calculation of nanofluid bulk density and specific heat [30]. Fig. 3. SEM image of the synthesized sample.
rnf ¼ 4rp þ ð1 4Þrf
(8)
3. Data processing The local convection heat transfer coefficient on each channel surface is calculated from: 00
q hðxÞ ¼ Ts ðxÞ Tm ðxÞ
(1)
00
where q is the imposed constant heat flux on both copper surfaces and Ts(x) and Tm(x) are the surface and bulk fluid temperatures, respectively. Ts(x) is measured at 21 points on the heat transfer section of each copper surface. Through the energy balance, Tm(x) is calculated from:
Tm ðxÞ ¼
qx þ Tmi _ p LmC
(2)
where L is the length of heated section of the channel, m_ is the mass flow rate, q is the total heat flow and Tmi is the inlet temperature of the fluid. The surface heat flux has been calculated from the net heat transfer to the fluid using the following equation: 00
q ¼
_ p ðTmi Tm0 Þ mC A
(3)
Finally, using the obtained local convection heat transfer coefficients, the average value on each surface is calculated from:
havg ¼
1 L
ZL hðxÞdx
(4)
0
4. Uncertainty analysis Uncertainty of the experimental data may origin from the measuring errors of quantities such as heat flux or temperature. The uncertainty of the local convection heat transfer coefficient is calculated as follows:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 vh 00 2 vh vh dh ¼ dq þ dT þ dT s m 00 vq vTs vTm Then,
(5)
cp;nf ¼
4rp cp;p þ ð1 4Þrf cp;f rnf
(9)
where rp is the particle density, rf is the base fluid density and cp,p and cp,f are the particle and the base fluid specific heats, respectively. The viscosity and thermal conductivity of the ferrofluid samples at different volume fractions of 4 ¼ 1, 1.5 and 2% have been measured by a viscometer (Antoon Paar Lovis 2000M) and a KD2 pro device (Decagon Devices Inc.) for the temperature range of 2060 C [24]. 6. Magnetic field simulation The appropriate locations of the electromagnets are needed to be determined prior to the heat transfer experiments. Three different configurations have been considered in the numerical simulations according to Fig. 4: in the opposite sides (case A), staggered assembly (case B), and one side of the channel (case C). These are the standard and typical configurations that can be considered in a systematic study. More importantly, through these cases, it is possible to investigate the effects of the magnetic field uniformity, intensity, and the resulting components of the magnetic force. It should also be mentioned that two different cases have been considered for layout A according to the direction of the electric current, I in the windings of the electromagnets. In the cases denoted by A-1 and A-2, I and consequently the magnetic field in top and bottom electromagnets have opposite and identical directions, respectively. However, I is set in the opposite directions in two windings of each electromagnet for all the cases. In all these cases the first electromagnet is located at x ¼ 1000 mm from the heat transfer section entrance and the distance between cores of the adjacent electromagnets is 60 mm.
Table 1 Uncertainty of the measured parameters. Quantity
Uncertainty
T ( C) Voltage (V) Current (I) L (m)
0.1 0.01 0.001 5 105
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Fig. 4. Different layouts of the electromagnets considered in the magnetic field simulations.
COMSOL has been used to simulate the magnetic field for different arrangements of the electromagnets along the channel. The magnetic flux density distribution is calculated from the following equations. .
V H ¼0 .
.
(10) .
B ¼ m0 mr H þ Br
(11)
where H is the magnetic field, B is the magnetic flux density, m0 is the magnetic permeability of free space and mr is the relative permeability. Computational domain is a sphere of radius 1 m which is much bigger than the electromagnets. The surface of the sphere is set as magnetically insulated. The external current density obtained from the electric current divided by the cross section area of the wire is imposed to the copper windings. The computational domain is discretized with fine tetrahedral meshes. Simulations have been carried for all of the configurations. Fig. 5 shows the magnetic flux density distribution, B, between the electromagnets at I ¼ 2A in the xz-plane. In case A-2, each electromagnet forms a magnetic field loop with the electromagnet in the opposite side. While, there are four
separate magnetic field loops for case A-1. Therefore, despite the same electromagnets arrangements in cases A-1 and A-2, the resulting magnetic field is shown to be completely different. In order to quantify the above discussion, the horizontal and vertical components (Bx, Bz) and the magnitude of the magnetic flux density (B) along the channel centerline are plotted for all the cases in Fig. 6. The identical directions of the electric current in the opposite electromagnets for case A-2 has led to very high magnetic field in the vertical direction, Bz against a negligible Bx. While, an inverse trend is obtained for case A-1. As shown in Fig. 5 the maximum magnetic field intensity exists near the tips of the electromagnets for cases B and C. Thus, the magnetic flux density B, has eight peaks of 700G along the channel centerline, as shown in Fig. 6. It can also be inferred from Fig. 6 that Bx has an alternating trend for these cases. This is due to the opposite direction of the electric current in the windings of each electromagnet. The magnetic force can be calculated from the magnetic flux density distribution as follows [31,32]: . FM
¼ Vp
ci . . BV B m0
(12)
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Fig. 5. Magnetic flux density distribution in longitudinal plane for (a) case A-1, (b) case A-2, (c) case B, (d) case c.
Fig. 6. Variations of the magnitude of the magnetic flux density B and its horizontal and vertical components along the channel centerline for the different studied cases.
M. Goharkhah et al. / International Journal of Thermal Sciences 99 (2016) 113e124
where Vp and ci are the magnetite nanoparticle volume and the magnetic susceptibility of the nanoparticles, respectively. Fig. 7 shows the calculated x and z components of the magnetic force across the channel centerline for all the cases. As shown in Fig. 7, for both cases of A-1 and A-2, fz is negligible compared to fx. However, the large magnetic flux density gradient near the electromagnets tips in case A-2 has led to an extremely high horizontal magnetic force in these regions. Thus, the xcomponent of the magnetic force can drive the magnetic nanoparticles towards the electromagnet tips and accelerate the ferrofluid in the axial direction as it flows. On the other hand, for cases B and C, z-component of the magnetic force is much larger than the x-component. This means that the magnetic particles can be attracted towards the channel surfaces at the electromagnets locations. However, the negative values of fz in case C implies that this layout attracts the magnetic nanoparticles to only one side of the channel. Above numerical analysis shows that the cases A-2 and B seem to be the most efficient electromagnets arrangements. The former results in a very high horizontal magnetic force while in the latter case both horizontal and vertical forces are present. 7. Recognition of the most efficient electromagnets arrangement Two cases of A-2 and B are selected by the numerical simulations as the most efficient electromagnet arrangement. Primary heat transfer tests are carried out in order to evaluate the effect of these two layouts on the local convective coefficients.
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Fig. 8 shows the surface temperature and the local convective heat transfer coefficients at Re ¼ 1200 and 4 ¼ 2% under the influence of a constant magnetic field B ¼ 500G generated by the electromagnet arrangements of A-2 and B. Due to the asymmetrical distribution of the magnetic field in case B, the convective coefficients on both surfaces of the channel are plotted. The difference between the variations of the convective heat transfer coefficient for layouts A-2 and B is due to the different magnetic force distribution resulted from these arrangements. As previously mentioned in Fig. 7 the horizontal component of the magnetic force is responsible for the observed heat transfer enhancement in case A-2. When the ferrofluid passes over the section of magnetic field it accelerates noticeably along the channel surface due to the magnetic force. On the other hand, both horizontal and vertical magnetic forces contribute to the heat transfer enhancement in case B. The x-component of the magnetic force drives the magnetic nanoparticles towards the electromagnet tips as the ferrofluid flows. Moreover, the magnetic particles can be attracted towards the channel surface at the electromagnets positions. Note that although the convective heat transfer is increased by both cases, Layout A-2 influences only a small part of the channel with lower increase of the local convective heat transfer coefficients. The average heat transfer enhancement values are obtained as 18.5% and 24.6% for cases A-2 and B, respectively. The numerical simulations and the above experiment reveal that the highest heat transfer enhancement can be achieved by arranging the electromagnets in the staggered configuration. Therefore, this arrangement has been selected to be used in all the
Fig. 7. Magnetic body force components on the channel centerline.
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Fig. 8. Surface temperature and the local convective heat transfer coefficients at Re ¼ 1200 and 4 ¼ 2% under the influence of a constant magnetic field generated B ¼ 500G by cases A-2 and B.
heat transfer experiments. The first electromagnet is located below the channel at the distance x ¼ 1000 mm from the heat transfer section entrance and the other three electromagnets are placed with equal distances of 60 mm from each other.
8. Results and discussion In order to verify the correct functioning of the experimental apparatus, the local convective heat transfer coefficients have been measured for deionized water flow in the channel at three different Reynolds numbers of 400, 800 and 1200. The convective coefficients have also been calculated from the well-known Shah equation for laminar flow under the constant heat flux boundary condition [33] expressed as:
8 9 1:49x1=3 ; x 0:0002 > > > > > > > > < = 1 3 ; 0:0002 < x 0:001 Nu ¼ 1:49x 0:4 > > > > > > > > : 8:235 þ 8:68 103 x 0:506 e164x ; x > 0:001 ; (13) where
x ¼
x=Dh Re Pr
(14)
Comparison of the experimental results with the predictions of Shah equation is shown in Fig. 9. Fig. 9 indicates that there is a good agreement between the current measurements and Shah equation for DI-Water flow in the channel. The main experiments are carried out using magnetite ferrofluid at different volume fractions (4 ¼ 1, 1.5 and 2%) and flow rates (200 Re 1200). Convective heat transfer coefficients are measured under the influence of an external constant and alternating magnetic field with different intensities (B ¼ 300G and 500G) and frequencies (f ¼ 0, 1, 2.5, 5, 10, 20 Hz). The alternating
Fig. 9. Measured values of local convective heat transfer coefficient for DI-water flow in the channel compared with the predictions of Shah [31].
magnetic field is generated by applying rectangular pulses with equal on and off duration to the electromagnets of layout B. Period of the alternating magnetic field function, T, is defined as the sum of the on and off durations. Obviously, the frequency, f, is equal to 1/T. Effects of the constant and alternating magnetic field on the local convective heat transfer coefficients are shown in Fig. 10 for Reynolds number of 400. It is shown in Fig. 10 that the curves plotted for ferrofluid almost coincide on each other until x ¼ 1 m then diverge at the second half of the channel where the magnetic field is applied. The nonuniform magnetic force distribution, resulted from layout B, has caused the fluctuations of the curves in this region. The convective heat transfer is increased under both constant and alternating magnetic field. However, the alternating magnetic field is more effective than the constant field case. A possible explanation can be the different behavior of the magnetic nanoparticles under the constant and alternating magnetic field. In the presence of a constant magnetic field, the magnetic force causes the migration of the nanoparticles to the channel copper plates. This leads to a higher local particle concentration and consequentially to a higher local thermal conductivity. Moreover, aggregation of the particles near each plate surface acts like an obstacle that disturbs and changes the thermal boundary layer thickness and flow pattern and results in further increase of the local convective heat transfer. On the other hand, the heat transfer enhancement under the alternating magnetic field is possibly associated with the attraction and releasing of nanoparticles. In each cycle, the nanoparticles are attracted to the heated surface of the channel as the electromagnets turn on. Thus, heat can be transferred to the nanoparticles. Next, the heated particles are released and heat is transferred to the bulk flow at the disconnection time of the electromagnets. The induced motion of the nanoparticles results in better mixing, the thermal boundary layer disturbance, and enhancement of the forced convection heat transfer. Another point worth mentioning is the dependency of the heat transfer on the frequency of the magnetic field. The effect of the frequency on heat transfer has been investigated at different Reynolds numbers.
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and releasing the particles is required to disrupt the thermal boundary layer effectively which means to increase the frequency of the magnetic field function. A heat transfer enhancement parameter can be defined as:
hth ¼
havg;nf havg;f
(15)
Variation of the average heat transfer coefficient with frequency of the magnetic field is plotted for different Reynolds numbers in Fig. 11. It can be inferred from Fig. 11 that an optimum frequency can be obtained at each flow rate to achieve the maximum heat transfer. The optimum frequency is shown to be increased with the Reynolds number. Obviously, as the Reynolds number increases, the ferrofluid passes over the electromagnets with a higher velocity and the time that ferrofluid particles are influenced by the magnetic field is decreased. Thus, faster attracting
where havg,nf and havg,f are the average heat transfer coefficients for the nanofluid and base fluid, respectively. Experimental measurements shows that the variation of hth is associated with different parameters such as nanoparticle volume fraction, fluid flow rate, magnetic field intensity and frequency. Fig. 12 shows the heat transfer enhancement as a function of frequency for different flow rates at B ¼ 500G and 4 ¼ 2%. As shown, the convective heat transfer increases with the Reynolds number under a constant magnetic field (f ¼ 0). This is also the case for the alternating magnetic field at high frequencies. However, at lower frequencies the heat transfer is shown to be decreased with the Reynolds number. This means that even at low Reynolds numbers, the convective heat transfer can be improved by application of an alternating magnetic field with an appropriate frequency. Fig. 13 shows the effect of the magnetic field intensity on the heat transfer enhancement at two different Reynolds numbers. As shown in Fig. 13, heat transfer can be enhanced by increasing the intensity of the external magnetic field. However, it should be noted that effect of the intensity is more pronounced under the alternating magnetic field. Variation of the heat transfer enhancement with frequency and volume fraction is plotted in Fig. 14. Increase of the heat transfer with the nanoparticle volume fraction, as shown in Fig. 14, can be justified considering the heat transfer mechanism described previously. It should be noted that the amount of the accumulated particles near the tube walls increases with increase of the volume fraction. This leads to higher local thermal conductivity near the electromagnets. Moreover, further magnetic nanoparticles participate in the disruption of the thermal boundary layer.
Fig. 11. Variation of the average heat transfer coefficient with frequency of the magnetic field at different Reynolds numbers.
Fig. 12. Heat transfer enhancement as a function of frequency for different flow rates at B ¼ 500 and 4 ¼ 2%.
Fig. 10. Effect of the magnetic field on the local convective heat transfer coefficient along the channel length for 4 ¼ 2% and at Re ¼ 400.
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Fig. 13. Effect of the magnetic field intensity on the heat transfer enhancement at two different Reynolds numbers.
Heat transfer enhancement under the alternating magnetic field is compared with the constant and no magnetic field cases in Fig. 15. As Fig. 15 demonstrates, in the absence of the magnetic field, using magnetite nanofluid with 4 ¼ 2% increases the convective heat transfer only up to a maximum of 16.4%, with respect to DIWater. While, it can be increased up to 24.8% and 37.3% by application of constant and alternating magnetic field, respectively. 8.1. Pressure drop measurements Pressure drop is an important parameter in the application of nanofluids in a heat exchanging equipment. Pressure drop of the
Fig. 14. Variation of the heat transfer enhancement with frequency and volume fraction.
Fig. 15. Comparison between heat transfer enhancement under the alternating, constant and no magnetic field for volume fractions of 4 ¼ 2%.
ferrofluid in the channel has been measured for all the studied cases. Fig. 16 shows the effect of magnetic field on the pressure drop of the ferrofluid at different volume fractions. Obviously the pressure drop increases with the ferrofluid volume fraction due to the increase of fluid viscosity. Moreover, in the presence of an external magnetic field, the magnetic particles suspended in the base fluid tend to remain chainedalignment in the direction of the magnetic field [34]. This increases the ferrofluid viscosity and consequently the pressure drop. An important point that can be concluded from Figs. 15 and 16 is that there is a trade-off between pressure drop and heat transfer enhancement. In order to compare these two effects and evaluate the overall performance of the ferrofluid as a heat transfer fluid, the total efficiency index is defined as follows:
Fig. 16. Effect of the magnetic field on the pressure drop across the channel.
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Fig. 17. Variation of efficiency index, h with Reynolds number (a) at different magnetic field intensities for 4 ¼ 1.5%, (b) at different concentrations for B ¼ 300G.
hnf h
h ¼ DPf
nf
(16)
DPf
where the subscripts f and nf refer to the base fluid and nanofluid, respectively. Values of h lower than unity means that the pressure drop increase dominates heat transfer enhancement and vice versa. Effect of magnetic field and concentration on the efficiency index are shown in Fig. 17(a) and (b), respectively. Fig. 17(a) implies that the heat transfer and pressure drop increase are in the same order for 4 ¼ 1.5% in the absence of the magnetic field. It is also shown that h can be improved by application of a magnetic field with the intensity of B ¼ 300G. By contrast, the pressure drop increase becomes larger than the heat transfer enhancement when the magnetic field intensity is increased to B ¼ 500G. Moreover, Fig. 17(b) shows that h decreases with the ferrofluid volume fraction. Therefore, use of ferrofluid at higher concentrations may not be beneficial considering the excess power needed for the pump.
Fig. 18. Effect of the alternating magnetic field on the efficiency index.
Similar to the convective heat transfer, the pressure drop of the ferrofluid depends on the frequency of the external magnetic field. Fig. 18 plots the efficiency index, h as function of the frequency. It can be observed in Fig. 18 that the increase of pressure drop is not as great as heat transfer enhancement in the presence of the alternating magnetic field. Thus, h increases compared to the case of constant magnetic field (f ¼ 0). 9. Conclusion This paper presents an experimental study on the convective heat transfer and pressure drop of Fe3O4/water nanofluid (ferrofluid) in a parallel plate channel under the influence of constant and alternating magnetic field. Effects of Reynolds number, volume fraction, magnetic field intensity, and frequency are investigated. The following notes can be concluded. Electromagnets arrangement and locations are two important parameters that affect the convective heat transfer. The optimum arrangement of the electromagnets is obtained by a numerical simulation and supporting experiments. The heat transfer enhancement is shown to have a direct relation with nanofluid concentration and Reynolds number. At a constant Reynolds number, heat transfer increases with the magnetic field intensity. It is also shown that there exists an optimum frequency for every single Reynolds number which increases by Reynolds number. Effect of magnetic field is more pronounced at the thermally developing region. The maximum convective heat transfer enhancement is obtained as 16.4% in the absence of magnetic field at Re ¼ 1200 and 4 ¼ 2%. It is increased up to 24.9% and 37.3% by application of constant and alternating magnetic field, respectively. Heat transfer enhancement under the influence of a constant magnetic field is attributed to the migration of the nanoparticles to the channel surface which leads to an increase in local particles concentration and consecutively the local thermal conductivity. In the presence of an alternating magnetic field, periodic attraction of the cold fluid to the heated surface and release of it to the bulk flow disturbs the thermal boundary layer, improves the flow mixing and increases the heat transfer. Increase of pressure drop is an inevitable consequence of applying the external magnetic field to the ferrofluid flow. Heat
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transfer enhancement is shown to be greater than the increase of pressure drop under the alternating magnetic field. Nomenclature B Cp Dh FM h H I L Nu P Pr Q 00 q Re T T V W u,v x,y x*
magnetic flux density (T) specific heat (J/kgK) hydrodynamic diameter (m) magnetic force (N) convective heat transfer coefficient (W/m2K) channel height (mm) electric current (A) channel length (mm) Nusselt number pressure (Pa) Prantdl number (Pr ¼ n/a) total heat flow (W) heat flux (W/m2) Reynolds number (Re ¼ ruDh/m) temperature (K) time (s) electric voltage (Volt) channel width (mm) fluid velocities (horizontal, vertical, m/s) Cartesian coordinates (horizontal, vertical,m) a parameter in Eq. 14
Greek symbols m dynamic viscosity (kg/m s) m0 magnetic permeability r density (kg/m3) h efficiency index ci magnetic susceptibility 4 volume fraction Subscripts Avg average value F base fluid I inlet condition M bulk value nf nanofluid O outlet condition Th thermal P particle S surface References [1] S.U.S. Choi, Enhancing thermal conductivity of fluids with nanoparticles, in: D.A. Siginer, H.P. Wang (Eds.), Developments and Applications of NonNewtonian Flows, ASME, New York, 1995, pp. 99e105. FED-vol. 231/MDvol. 66. [2] X.Qi Wang, A.S. Mujumdar, Heat transfer characteristics of nanofluids: a review, Int. J. Therm. Sci. 46 (2007) 1e19. [3] L. Godson, B. Raja, D. Mohan Lal, S. Wongwises, Enhancement of heat transfer using nanofluidsdAn overview, Renew. Sustain. Energy Rev. 14 (2010) 629e641. [4] M. Shaker, E. Birgersson, A.S. Mujumdar, Extended Maxwell model for the thermal conductivity of nanofluids that accounts for nonlocal heat transfer, Int. J. Therm. Sci. 84 (2014) 260e266. [5] G. Roy, I. Gherasim, F. Nadeau, G. Poitras, C.T. Nguyen, Heat transfer performance and hydrodynamic behavior of turbulent nanofluid radial flows, Int. J. Therm. Sci. 58 (2012) 120e129. [6] B.C. Pak, Y.I. Cho, Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Exp. Heat. Transf. 11 (1998) 151e170.
[7] W.H. Azmi, K.V. Sharma, P.K. Sarma, R. Mamat, S. Anuar, Comparison of convective heat transfer coefficient and friction factor of TiO2 nanofluid flow in a tube with twisted tape inserts, Int. J. Therm. Sci. 81 (2014) 84e93. [8] A.K. Santra, S. Sen, N. Chakraborty, Study of heat transfer due to laminar flow of copperewater nanofluid through two isothermally heated parallel plates, Int. J. Therm. Sci. 48 (2009) 391e400. [9] S.K. Das, N. Putra, P. Theisen, W. Roetzel, Temperature dependence of thermal conductivity enhancement for nanofluid, J. Heat. Transf. 125 (2003) 567e574. [10] P. Keblinski, S.R. Phillpot, S.U.S. Choi, J.A. Eastman, Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), Int. J. Heat Mass Transf. 45 (4) (2002) 855e863. [11] C. Rinaldi, A. Chaves, Sh Elborai, X. He, M. Zahn, Magnetic fluid rheology and flows, Curr. Opin. Colloid Interface Sci. 10 (2005) 141e157. [12] L.S. Sundar, M.K. Singh, A.C.M. Sousa, Thermal conductivity of ethylene glycol and water mixture based Fe3O4 nanofluid, Int. Commun. Heat Mass Transf. 49 (2013) 17e24. [13] H. Zhu, C. Zhang, Sh Liu, Y. Tang, Y. Yin, Effects of nanoparticle clustering and alignment on thermal conductivities of Fe3O4 aqueous nanofluids, Appl. Phys. Lett. 89 (2006) 023123. [14] T.H. Tsai1, L.S. Kuo1, P.H. Chen, C.T. Yang, Thermal conductivity of nanofuid with magnetic nanoparticles, Piers Online 5 (2009) 154e162. [15] M. Abareshi, E.K. Goharshadi, S.M. Zebarjad, H.Kh Fadafan, A. Youssefi, Fabrication, characterization and measurement of thermal conductivity of Fe3O4 nanofluids, J. Magn. Magn. Mater. 322 (2010) 3895e3901. ~ eiro, Enhancement of thermal conductivity and [16] L. Lugo, J.L. Legido, M.M. Pin volumetric behavior of FexOy nanofluids M. J. Pastoriza-Gallego, J. Appl. Phys. 110 (2011) 014309. [17] J. Philip, P.D. Shima, B. Raj, Enhancement of thermal conductivity in magnetite based nanofluid due to chainlike structures, Appl. Phys. 91 (2007) 203108. [18] B. Wright, D. Thomas, H. Hong, L. Groven, J. Puszynski, E. Duke, X. Ye, S. Jin, Magnetic field enhanced thermal conductivity in heat transfer nanofluids, containing Ni coated single wall carbon nanotubes, Appl. Phys. Lett. 91 (2007) 173116. [19] K. Parekh, H.S. Lee, Magnetic field induced enhancement in thermal conductivity of magnetite nanofluid, Appl. Phys. 107 (2010) 09A310. [20] A. Gavili, F. Zabihi, T.D. Isfahani, J. Sabbaghzadeh, The thermal conductivity of water base ferrofluids under magnetic field, Exp. Therm. Fluid Sci. 41 (2012) 94e98. [21] L.S. Sundar, M.T. Naik, K.V. Sharma, M.K. Singh, T.Ch Reddy, Experimental investigation of forced convection heat transfer and friction factor in a tube with Fe3O4 magnetic nanofluid, Exp. Therm. Fluid Sci. 37 (2012) 65e71. [22] Y. Xuan, Q. Li, M.Y. Abu-Nada, Z. Masoud, H.F. Oztop, A. Campo, Investigations of convective heat transfer in ferrofluid microflows using lattice-Boltzmann approach, Int. J. Therm. Sci. 46 (2007) 105e111. € [23] F. Selimefendigil, H.F. Oztop, Forced convection of ferrofluids in a vented cavity with a rotating cylinder, Int. J. Therm. Sci. 86 (2014) 258e275. [24] M. Goharkhah, M. Ashjaee, J. Jamali, Experimental investigation on heat transfer and hydrodynamic behavior of magnetite nanofluid flow in a channel with recognition of the best models for transport properties, Exp. Therm. Fluid Sci. 68 (2015) 582e592. [25] M. Motozawaa, J. Chang, T. Sawada, Y. Kawaguchi, Effect of magnetic field on heat transfer in rectangular duct flow of a magnetic fluid, Phys. Procedia 9 (2010) 190e193. [26] M. Lajvardi, J. Moghimi-Rad, I. Hadi, A. Gavili, T.D. Isfahani, F. Zabihi, J. Sabbaghzadeh, Experimental investigation for enhanced ferrofluid heat transfer under magnetic field effect, J. Magn. Magn. Mater. 322 (2010) 3508e3513. [27] R. Azizian, E. Doroodchi, T. McKrell, J. Buongiorno, L.W. Hu, B. Moghtaderi, Effect of magnetic field on laminar convective heat transfer of magnetite nanofluids, Int. J. Heat Mass Transf. 68 (2014) 94e109. [28] M.M. Murray, Demonstration of heat transfer enhancement using ferromagnetic particle laden fluid and switched magnetic fields, J. Heat Transf. 130 (2008) 114508-1e114508-4. [29] M. Goharkhah, A. Salarian, M. Ashjaee, M. Shahabadi, Convective heat transfer characteristics of magnetite nanofluid under the influence of constant and alternating magnetic field, Powder Technol. 274 (2015) 258e267. [30] U. Rea, T. McKrell, L.W. Hu, J. Buongiorno, Laminar convective heat transfer and viscous pressure loss of aluminaewater and zirconiaewater nanofluids, Int. J. Heat Mass Transf. 52 (2009) 2042e2048. [31] Q.A. Pankhurst, J. Connolly, S.K. Jones, J. Dobson, Applications of magnetic nanoparticles in biomedicine, J. Phys. D. Appl. Phys. 36 (2003) 167e181. [32] A. Nacev, C. Beni, O. Bruno, B. Shapiro, The behaviors of ferromagnetic nanoparticles in and around blood vessels under applied magnetic fields, J. Magn. Magn. Mater. 323 (2011) 651e668. [33] A. Bejan, A.D. Kraus, Heat Transfer Handbook, John Wiley & Sons, 2003, p. 411. [34] Q. Li, Y. Xuan, J. Wang, Experimental investigations on transport properties of magnetic fluids, Exp. Therm. Fluid Sci. 30 (2005) 109e116.
Contents lists available at ScienceDirect
International Journal of Thermal Sciences journal homepage: www.elsevier.com/locate/ijts
Experimental investigation on convective heat transfer and hydrodynamic characteristics of magnetite nanofluid under the influence of an alternating magnetic field Mohammad Goharkhah a, *, Mehdi Ashjaee b, Mahmoud Shahabadi c a b c
Department of Mechanical Engineering, Sahand University of Technology, Tabriz, Iran Department of Mechanical Engineering, University of Tehran, Tehran, Iran Department of Electrical and Computer Engineering, University of Tehran, Iran
a r t i c l e i n f o
a b s t r a c t
Article history: Received 22 January 2015 Received in revised form 8 August 2015 Accepted 9 August 2015 Available online xxx
An experimental study has been carried out on the laminar forced convective heat transfer of Fe3O4/ water nanofluid (ferrofluid) under an external magnetic field. Here, the ferrofluid flows into a long uniformly heated parallel plate channel and is influenced by an external magnetic field generated by four electromagnets. The efficient arrangement of the electromagnets is obtained by numerical simulations and primary experiments. Effects of magnetic field intensity and frequency on the convective heat transfer and pressure drop have been investigated at different concentrations (1, 1.5, and 2 Vol%) and flow rates (200 Re 1200). It is observed that the convective heat transfer has a direct relation with the Reynolds number and ferrofluid concentration. Moreover, at a constant Reynolds number, the magnetic field intensity increases the heat transfer. Note that there exists an optimum frequency for every single Reynolds number which increases by Reynolds number. Our results also show a maximum heat transfer enhancement of 16.4% by the use of ferrofluid, in the absence of a magnetic field. This value is increased up to 24.9% and 37.3% by application of constant and alternating magnetic field, respectively. © 2015 Elsevier Masson SAS. All rights reserved.
Keywords: Pressure drop Forced convection Magnetite Nanofluid Magnetic field Parallel plate channel
1. Introduction Augmentation of heat transfer is a key challenge for many industrial applications. Among several methods which have been proposed for heat transfer enhancement, using of nanofluids has achieved growing interest by many researchers recently. Several experimental and numerical studies have been carried out on the transport properties and heat transfer characteristics of different nanofluids [1e10]. A number of these studies have concentrated on the magnetic nanofluids (ferrofluids). Ferrofluid is a synthesized colloidal mixture of nonmagnetic carrier liquid, typically water or oil, containing single domain permanently magnetized nanoparticles, typically magnetite [11]. Similar to the other nanofluids, the thermal conductivity of the
* Corresponding author. Department of Mechanical Engineering, Sahand University of Technology, New Sahand Town, Tabriz, Iran. Tel.: þ98 41 33459424. E-mail addresses: [email protected] (M. Goharkhah), [email protected] (M. Ashjaee), [email protected] (M. Shahabadi). http://dx.doi.org/10.1016/j.ijthermalsci.2015.08.008 1290-0729/© 2015 Elsevier Masson SAS. All rights reserved.
base fluid can be enhanced noticeably due to addition of the magnetic nanoparticles [12e16]. Moreover, the distinctive characteristic of the ferrofluid is the ability to respond to an external magnetic field. Recent studies show the significant increase of the ferrofluid thermal conductivity in the presence of an external magnetic field [17e20]. For example Philip et al. [17] and Gavili et al. [20] observed 300% and 200% thermal conductivity enhancement for Fe3O4 ferrofluid, respectively. The enhancement of the thermal conductivity is attributed to the formation of chainlike structures in the ferrofluid which grow with the intensity of the magnetic field [17]. Furthermore, the forced convection heat transfer of the ferrofluids has also been investigated in the absence and presence of an external magnetic field [21e27]. Sundar et al. [21] studied turbulent forced convection heat transfer and friction factor of Fe3O4 magnetic nanofluid in a tube in the absence of magnetic field and obtained correlations for estimation of the Nusselt number and friction factor. Their results show that the heat transfer coefficient is enhanced by 30.96% and friction factor by 10.01% at 0.6% volume fraction compared to the base fluid.
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Motozawa et al. [25] studied the effect of magnetic field on heat transfer of water-based magnetic fluid named W-40 in a rectangular duct. It is shown that heat transfer coefficient increases locally in the region where magnetic field exists and has a direct relation with magnetic field intensity. They reported a maximum of 20% heat transfer enhancement for their studied case. Lajvardi et al. [26] studied the convective heat transfer of ferrofluid flowing through a heated copper tube in the laminar flow regime in the presence of a magnetic field. They attributed the enhancement of the heat transfer to the improvement of thermophysical properties of ferrofluid under the influence of the magnetic field. Azizian et al. [27] studied the effect of a constant magnetic field on the laminar convective heat transfer and pressure drop of magnetite nanofluid in a vertical tube and reported large enhancement in the local heat transfer coefficient against only a 7.5% increase of pressure drop. They also showed that the convective heat transfer enhancement increases with the magnetic field intensity and gradient. Above mentioned works apply a constant magnetic field to increase the ferrofluid convective heat transfer. Application of an alternating magnetic field for heat transfer enhancement was first introduced by Murray [28] for a particle laden fluid. He employed time varying magnetic field to cause the iron filings in mineral oil to be attracted to and released from a heated pipe wall. He demonstrated a 267% increase in heat transfer coefficient against a 48% increase in flow differential pressure. With a similar mechanism to that used by Murray [28], the current research investigates the effect of an alternating magnetic field on the heat transfer and pressure drop of ferrofluid flow in a channel. Specifically, ferrofluid flows into a channel with uniformly heated top and bottom copper plates and is influenced by a magnetic field generated by four electromagnets. The efficient arrangement of the electromagnets is obtained by the numerical simulations and primary experiments. All the heat transfer experiments are configured based on the numerically designed arrangement. The convective heat transfer coefficients are then measured at both thermally developing and fully developed regions at different Reynolds numbers, nanoparticle concentrations, magnetic field intensities, and frequencies. The results have been compared with those of ferrofluid flow without external magnetic field and deionized water alone.
2. Experimental method 2.1. Experimental apparatus The experimental set-up is shown schematically in Fig. 1. The main components are: parallel plate channel test section, a closed loop for circulating the nanofluid, pressure drop measurement device, magnetic field generation and control system, and data acquisition system for temperature recording. The studied geometry is a parallel plate channel with a flow passage size of 40 mm (W) 4 mm (H) 2500 mm (L). The channel consists of a hydrodynamic entry section and a heat transfer section with lengths of 500 mm and 2000 mm, respectively. The length of entry section is selected such that the hydrodynamically fully developed flow is ensured at the heat transfer section for all the Reynolds numbers. Convective heat transfer coefficients are measured on the heat transfer section. Cross section of the heat transfer section is also shown in Fig. 1. It consists of two copper top and bottom plates which are fixed in a very low thermal conductivity polyethylene housing. A small mixing chamber is located at the exit of the heat transfer section for purpose of the proper measurement of fluid mean exit temperature. A constant surface heat flux is maintained on both copper plates by passing electric current through the two strip heaters which are pressed to the back of copper plates. The surface temperature of each copper plate is measured by 21 calibrated thermocouples. Two thermocouples are also inserted in the inlet and outlet of the test section to measure the inlet and exit temperatures of the fluid. The thermocouples are connected to two data loggers and all the temperatures can be monitored and recorded simultaneously during the tests. The pressure drop of the heat transfer section is measured by Endress Hauser differential pressure transducer with operation range of 0e250 kPa (0e2500 mbar) and 1% accuracy, as calibrated by the manufacturer. Ferrofluid is circulated in a loop from a reservoir tank by a DC pump. The volumetric flow rate passing through the loop is measured using a calibrated flow meter, and can be varied by changing the voltage of the DC power supply of the pump. A constant temperature bath is located upstream of the pump to control the inlet temperature.
Fig. 1. Schematic diagram of the experimental setup.
M. Goharkhah et al. / International Journal of Thermal Sciences 99 (2016) 113e124
The magnetic field generation system includes four electromagnets, a high voltage DC power supply, a signal generator and an oscilloscope, as shown in Fig. 2(a). Four electromagnets are used to generate the magnetic field. Dimensions of the electromagnets are shown in Fig. 2(b). Each electromagnet consists of an electrically insulated iron U core and two copper windings. The windings have N ¼ 3000 turns of 0.5 mm diameter copper wire with a total electric resistance of 35 U. The alternating magnetic field with specific frequency and phase shift is produced by a DC power supply connected to a signal generator. The signal generator converts the input DC current to rectangular pulses for driving the windings. With the help of its microcontroller, the digital circuit of the signal generator has the ability to adjust the frequency of the pulses and their relative phase shifts. An oscilloscope is used to monitor the wave form of the generated pulses. Furthermore, a HT201 Teslameter has been used to measure the magnetic field strength during the experiments. The electromagnets locations have a significant effect on the magnetic force distribution and consequently the convective heat transfer. The optimum configuration of the electromagnets has been obtained by a numerical simulation and supplementary experiments which is discussed in section 5. More details about the test section can be found in Refs. [24,29].
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2.2. Ferrofluid synthesis procedure The ferrofluid samples are synthesized using the conventional coprecipitation process. Briefly, stoichiometric amounts of FeCl2$4H2O and FeCl3$6H2O equivalent to the chemical composition of Fe3O4 are dissolved in deionized water and degassed via Argon gas purging. Then, NH4OH solution is gradually added to the iron solution under the mechanical stirring until pH reaches 12. The black precipitate is removed from the liquid phase via centrifugal and magnetic separation and washed several times by acetone and DI-water. The obtained solid product is redispersed in DI-water and, tetramethylammonium hydroxide (TMAH, (CH3)4NOH) is added to the solution under stirring in a manner that the desired volume fraction values of 1%, 1.5% and 2% are achieved. The stirring process is continued for an additional 1 h until the stable ferrofluid is obtained. The ferrofluid samples exhibited excellent stability due to the use of the TMAH surfactant. However, in order to avoid any agglomeration of the nanoparticles and ensure that all of the experiments have been carried out at equal conditions, the ferrofluid samples have been ultrasonicated before each experiment. SEM image of the synthesized sample is presented in Fig. 3. As seen in Fig. 3, nanoparticles with various shapes are aggregated and formed larger agglomerates. The mean particle size is 30 nm.
Fig. 2. (a) Magnetic field generation and control system, (b) dimensions of the electromagnets.
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dh ¼ h
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 00 2 2 2 dq dTs vTm þ þ dTm 00 q Ts Tm Ts Tm
(6)
The uncertainties of the measurements in the present study are summarized in Table 1. Uncertainty values have been calculated for all the measured cases. The average uncertainty in calculation of local convection heat transfer coefficient is ±3.2%. 5. Thermophysical properties of the ferrofluid The volume concentration of the samples are obtained by:
4 ¼ mp
mp rp
rp
þ
(7)
mf rf
The following equations have been used for calculation of nanofluid bulk density and specific heat [30]. Fig. 3. SEM image of the synthesized sample.
rnf ¼ 4rp þ ð1 4Þrf
(8)
3. Data processing The local convection heat transfer coefficient on each channel surface is calculated from: 00
q hðxÞ ¼ Ts ðxÞ Tm ðxÞ
(1)
00
where q is the imposed constant heat flux on both copper surfaces and Ts(x) and Tm(x) are the surface and bulk fluid temperatures, respectively. Ts(x) is measured at 21 points on the heat transfer section of each copper surface. Through the energy balance, Tm(x) is calculated from:
Tm ðxÞ ¼
qx þ Tmi _ p LmC
(2)
where L is the length of heated section of the channel, m_ is the mass flow rate, q is the total heat flow and Tmi is the inlet temperature of the fluid. The surface heat flux has been calculated from the net heat transfer to the fluid using the following equation: 00
q ¼
_ p ðTmi Tm0 Þ mC A
(3)
Finally, using the obtained local convection heat transfer coefficients, the average value on each surface is calculated from:
havg ¼
1 L
ZL hðxÞdx
(4)
0
4. Uncertainty analysis Uncertainty of the experimental data may origin from the measuring errors of quantities such as heat flux or temperature. The uncertainty of the local convection heat transfer coefficient is calculated as follows:
sffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi 2 2 vh 00 2 vh vh dh ¼ dq þ dT þ dT s m 00 vq vTs vTm Then,
(5)
cp;nf ¼
4rp cp;p þ ð1 4Þrf cp;f rnf
(9)
where rp is the particle density, rf is the base fluid density and cp,p and cp,f are the particle and the base fluid specific heats, respectively. The viscosity and thermal conductivity of the ferrofluid samples at different volume fractions of 4 ¼ 1, 1.5 and 2% have been measured by a viscometer (Antoon Paar Lovis 2000M) and a KD2 pro device (Decagon Devices Inc.) for the temperature range of 2060 C [24]. 6. Magnetic field simulation The appropriate locations of the electromagnets are needed to be determined prior to the heat transfer experiments. Three different configurations have been considered in the numerical simulations according to Fig. 4: in the opposite sides (case A), staggered assembly (case B), and one side of the channel (case C). These are the standard and typical configurations that can be considered in a systematic study. More importantly, through these cases, it is possible to investigate the effects of the magnetic field uniformity, intensity, and the resulting components of the magnetic force. It should also be mentioned that two different cases have been considered for layout A according to the direction of the electric current, I in the windings of the electromagnets. In the cases denoted by A-1 and A-2, I and consequently the magnetic field in top and bottom electromagnets have opposite and identical directions, respectively. However, I is set in the opposite directions in two windings of each electromagnet for all the cases. In all these cases the first electromagnet is located at x ¼ 1000 mm from the heat transfer section entrance and the distance between cores of the adjacent electromagnets is 60 mm.
Table 1 Uncertainty of the measured parameters. Quantity
Uncertainty
T ( C) Voltage (V) Current (I) L (m)
0.1 0.01 0.001 5 105
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Fig. 4. Different layouts of the electromagnets considered in the magnetic field simulations.
COMSOL has been used to simulate the magnetic field for different arrangements of the electromagnets along the channel. The magnetic flux density distribution is calculated from the following equations. .
V H ¼0 .
.
(10) .
B ¼ m0 mr H þ Br
(11)
where H is the magnetic field, B is the magnetic flux density, m0 is the magnetic permeability of free space and mr is the relative permeability. Computational domain is a sphere of radius 1 m which is much bigger than the electromagnets. The surface of the sphere is set as magnetically insulated. The external current density obtained from the electric current divided by the cross section area of the wire is imposed to the copper windings. The computational domain is discretized with fine tetrahedral meshes. Simulations have been carried for all of the configurations. Fig. 5 shows the magnetic flux density distribution, B, between the electromagnets at I ¼ 2A in the xz-plane. In case A-2, each electromagnet forms a magnetic field loop with the electromagnet in the opposite side. While, there are four
separate magnetic field loops for case A-1. Therefore, despite the same electromagnets arrangements in cases A-1 and A-2, the resulting magnetic field is shown to be completely different. In order to quantify the above discussion, the horizontal and vertical components (Bx, Bz) and the magnitude of the magnetic flux density (B) along the channel centerline are plotted for all the cases in Fig. 6. The identical directions of the electric current in the opposite electromagnets for case A-2 has led to very high magnetic field in the vertical direction, Bz against a negligible Bx. While, an inverse trend is obtained for case A-1. As shown in Fig. 5 the maximum magnetic field intensity exists near the tips of the electromagnets for cases B and C. Thus, the magnetic flux density B, has eight peaks of 700G along the channel centerline, as shown in Fig. 6. It can also be inferred from Fig. 6 that Bx has an alternating trend for these cases. This is due to the opposite direction of the electric current in the windings of each electromagnet. The magnetic force can be calculated from the magnetic flux density distribution as follows [31,32]: . FM
¼ Vp
ci . . BV B m0
(12)
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Fig. 5. Magnetic flux density distribution in longitudinal plane for (a) case A-1, (b) case A-2, (c) case B, (d) case c.
Fig. 6. Variations of the magnitude of the magnetic flux density B and its horizontal and vertical components along the channel centerline for the different studied cases.
M. Goharkhah et al. / International Journal of Thermal Sciences 99 (2016) 113e124
where Vp and ci are the magnetite nanoparticle volume and the magnetic susceptibility of the nanoparticles, respectively. Fig. 7 shows the calculated x and z components of the magnetic force across the channel centerline for all the cases. As shown in Fig. 7, for both cases of A-1 and A-2, fz is negligible compared to fx. However, the large magnetic flux density gradient near the electromagnets tips in case A-2 has led to an extremely high horizontal magnetic force in these regions. Thus, the xcomponent of the magnetic force can drive the magnetic nanoparticles towards the electromagnet tips and accelerate the ferrofluid in the axial direction as it flows. On the other hand, for cases B and C, z-component of the magnetic force is much larger than the x-component. This means that the magnetic particles can be attracted towards the channel surfaces at the electromagnets locations. However, the negative values of fz in case C implies that this layout attracts the magnetic nanoparticles to only one side of the channel. Above numerical analysis shows that the cases A-2 and B seem to be the most efficient electromagnets arrangements. The former results in a very high horizontal magnetic force while in the latter case both horizontal and vertical forces are present. 7. Recognition of the most efficient electromagnets arrangement Two cases of A-2 and B are selected by the numerical simulations as the most efficient electromagnet arrangement. Primary heat transfer tests are carried out in order to evaluate the effect of these two layouts on the local convective coefficients.
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Fig. 8 shows the surface temperature and the local convective heat transfer coefficients at Re ¼ 1200 and 4 ¼ 2% under the influence of a constant magnetic field B ¼ 500G generated by the electromagnet arrangements of A-2 and B. Due to the asymmetrical distribution of the magnetic field in case B, the convective coefficients on both surfaces of the channel are plotted. The difference between the variations of the convective heat transfer coefficient for layouts A-2 and B is due to the different magnetic force distribution resulted from these arrangements. As previously mentioned in Fig. 7 the horizontal component of the magnetic force is responsible for the observed heat transfer enhancement in case A-2. When the ferrofluid passes over the section of magnetic field it accelerates noticeably along the channel surface due to the magnetic force. On the other hand, both horizontal and vertical magnetic forces contribute to the heat transfer enhancement in case B. The x-component of the magnetic force drives the magnetic nanoparticles towards the electromagnet tips as the ferrofluid flows. Moreover, the magnetic particles can be attracted towards the channel surface at the electromagnets positions. Note that although the convective heat transfer is increased by both cases, Layout A-2 influences only a small part of the channel with lower increase of the local convective heat transfer coefficients. The average heat transfer enhancement values are obtained as 18.5% and 24.6% for cases A-2 and B, respectively. The numerical simulations and the above experiment reveal that the highest heat transfer enhancement can be achieved by arranging the electromagnets in the staggered configuration. Therefore, this arrangement has been selected to be used in all the
Fig. 7. Magnetic body force components on the channel centerline.
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Fig. 8. Surface temperature and the local convective heat transfer coefficients at Re ¼ 1200 and 4 ¼ 2% under the influence of a constant magnetic field generated B ¼ 500G by cases A-2 and B.
heat transfer experiments. The first electromagnet is located below the channel at the distance x ¼ 1000 mm from the heat transfer section entrance and the other three electromagnets are placed with equal distances of 60 mm from each other.
8. Results and discussion In order to verify the correct functioning of the experimental apparatus, the local convective heat transfer coefficients have been measured for deionized water flow in the channel at three different Reynolds numbers of 400, 800 and 1200. The convective coefficients have also been calculated from the well-known Shah equation for laminar flow under the constant heat flux boundary condition [33] expressed as:
8 9 1:49x1=3 ; x 0:0002 > > > > > > > > < = 1 3 ; 0:0002 < x 0:001 Nu ¼ 1:49x 0:4 > > > > > > > > : 8:235 þ 8:68 103 x 0:506 e164x ; x > 0:001 ; (13) where
x ¼
x=Dh Re Pr
(14)
Comparison of the experimental results with the predictions of Shah equation is shown in Fig. 9. Fig. 9 indicates that there is a good agreement between the current measurements and Shah equation for DI-Water flow in the channel. The main experiments are carried out using magnetite ferrofluid at different volume fractions (4 ¼ 1, 1.5 and 2%) and flow rates (200 Re 1200). Convective heat transfer coefficients are measured under the influence of an external constant and alternating magnetic field with different intensities (B ¼ 300G and 500G) and frequencies (f ¼ 0, 1, 2.5, 5, 10, 20 Hz). The alternating
Fig. 9. Measured values of local convective heat transfer coefficient for DI-water flow in the channel compared with the predictions of Shah [31].
magnetic field is generated by applying rectangular pulses with equal on and off duration to the electromagnets of layout B. Period of the alternating magnetic field function, T, is defined as the sum of the on and off durations. Obviously, the frequency, f, is equal to 1/T. Effects of the constant and alternating magnetic field on the local convective heat transfer coefficients are shown in Fig. 10 for Reynolds number of 400. It is shown in Fig. 10 that the curves plotted for ferrofluid almost coincide on each other until x ¼ 1 m then diverge at the second half of the channel where the magnetic field is applied. The nonuniform magnetic force distribution, resulted from layout B, has caused the fluctuations of the curves in this region. The convective heat transfer is increased under both constant and alternating magnetic field. However, the alternating magnetic field is more effective than the constant field case. A possible explanation can be the different behavior of the magnetic nanoparticles under the constant and alternating magnetic field. In the presence of a constant magnetic field, the magnetic force causes the migration of the nanoparticles to the channel copper plates. This leads to a higher local particle concentration and consequentially to a higher local thermal conductivity. Moreover, aggregation of the particles near each plate surface acts like an obstacle that disturbs and changes the thermal boundary layer thickness and flow pattern and results in further increase of the local convective heat transfer. On the other hand, the heat transfer enhancement under the alternating magnetic field is possibly associated with the attraction and releasing of nanoparticles. In each cycle, the nanoparticles are attracted to the heated surface of the channel as the electromagnets turn on. Thus, heat can be transferred to the nanoparticles. Next, the heated particles are released and heat is transferred to the bulk flow at the disconnection time of the electromagnets. The induced motion of the nanoparticles results in better mixing, the thermal boundary layer disturbance, and enhancement of the forced convection heat transfer. Another point worth mentioning is the dependency of the heat transfer on the frequency of the magnetic field. The effect of the frequency on heat transfer has been investigated at different Reynolds numbers.
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and releasing the particles is required to disrupt the thermal boundary layer effectively which means to increase the frequency of the magnetic field function. A heat transfer enhancement parameter can be defined as:
hth ¼
havg;nf havg;f
(15)
Variation of the average heat transfer coefficient with frequency of the magnetic field is plotted for different Reynolds numbers in Fig. 11. It can be inferred from Fig. 11 that an optimum frequency can be obtained at each flow rate to achieve the maximum heat transfer. The optimum frequency is shown to be increased with the Reynolds number. Obviously, as the Reynolds number increases, the ferrofluid passes over the electromagnets with a higher velocity and the time that ferrofluid particles are influenced by the magnetic field is decreased. Thus, faster attracting
where havg,nf and havg,f are the average heat transfer coefficients for the nanofluid and base fluid, respectively. Experimental measurements shows that the variation of hth is associated with different parameters such as nanoparticle volume fraction, fluid flow rate, magnetic field intensity and frequency. Fig. 12 shows the heat transfer enhancement as a function of frequency for different flow rates at B ¼ 500G and 4 ¼ 2%. As shown, the convective heat transfer increases with the Reynolds number under a constant magnetic field (f ¼ 0). This is also the case for the alternating magnetic field at high frequencies. However, at lower frequencies the heat transfer is shown to be decreased with the Reynolds number. This means that even at low Reynolds numbers, the convective heat transfer can be improved by application of an alternating magnetic field with an appropriate frequency. Fig. 13 shows the effect of the magnetic field intensity on the heat transfer enhancement at two different Reynolds numbers. As shown in Fig. 13, heat transfer can be enhanced by increasing the intensity of the external magnetic field. However, it should be noted that effect of the intensity is more pronounced under the alternating magnetic field. Variation of the heat transfer enhancement with frequency and volume fraction is plotted in Fig. 14. Increase of the heat transfer with the nanoparticle volume fraction, as shown in Fig. 14, can be justified considering the heat transfer mechanism described previously. It should be noted that the amount of the accumulated particles near the tube walls increases with increase of the volume fraction. This leads to higher local thermal conductivity near the electromagnets. Moreover, further magnetic nanoparticles participate in the disruption of the thermal boundary layer.
Fig. 11. Variation of the average heat transfer coefficient with frequency of the magnetic field at different Reynolds numbers.
Fig. 12. Heat transfer enhancement as a function of frequency for different flow rates at B ¼ 500 and 4 ¼ 2%.
Fig. 10. Effect of the magnetic field on the local convective heat transfer coefficient along the channel length for 4 ¼ 2% and at Re ¼ 400.
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Fig. 13. Effect of the magnetic field intensity on the heat transfer enhancement at two different Reynolds numbers.
Heat transfer enhancement under the alternating magnetic field is compared with the constant and no magnetic field cases in Fig. 15. As Fig. 15 demonstrates, in the absence of the magnetic field, using magnetite nanofluid with 4 ¼ 2% increases the convective heat transfer only up to a maximum of 16.4%, with respect to DIWater. While, it can be increased up to 24.8% and 37.3% by application of constant and alternating magnetic field, respectively. 8.1. Pressure drop measurements Pressure drop is an important parameter in the application of nanofluids in a heat exchanging equipment. Pressure drop of the
Fig. 14. Variation of the heat transfer enhancement with frequency and volume fraction.
Fig. 15. Comparison between heat transfer enhancement under the alternating, constant and no magnetic field for volume fractions of 4 ¼ 2%.
ferrofluid in the channel has been measured for all the studied cases. Fig. 16 shows the effect of magnetic field on the pressure drop of the ferrofluid at different volume fractions. Obviously the pressure drop increases with the ferrofluid volume fraction due to the increase of fluid viscosity. Moreover, in the presence of an external magnetic field, the magnetic particles suspended in the base fluid tend to remain chainedalignment in the direction of the magnetic field [34]. This increases the ferrofluid viscosity and consequently the pressure drop. An important point that can be concluded from Figs. 15 and 16 is that there is a trade-off between pressure drop and heat transfer enhancement. In order to compare these two effects and evaluate the overall performance of the ferrofluid as a heat transfer fluid, the total efficiency index is defined as follows:
Fig. 16. Effect of the magnetic field on the pressure drop across the channel.
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Fig. 17. Variation of efficiency index, h with Reynolds number (a) at different magnetic field intensities for 4 ¼ 1.5%, (b) at different concentrations for B ¼ 300G.
hnf h
h ¼ DPf
nf
(16)
DPf
where the subscripts f and nf refer to the base fluid and nanofluid, respectively. Values of h lower than unity means that the pressure drop increase dominates heat transfer enhancement and vice versa. Effect of magnetic field and concentration on the efficiency index are shown in Fig. 17(a) and (b), respectively. Fig. 17(a) implies that the heat transfer and pressure drop increase are in the same order for 4 ¼ 1.5% in the absence of the magnetic field. It is also shown that h can be improved by application of a magnetic field with the intensity of B ¼ 300G. By contrast, the pressure drop increase becomes larger than the heat transfer enhancement when the magnetic field intensity is increased to B ¼ 500G. Moreover, Fig. 17(b) shows that h decreases with the ferrofluid volume fraction. Therefore, use of ferrofluid at higher concentrations may not be beneficial considering the excess power needed for the pump.
Fig. 18. Effect of the alternating magnetic field on the efficiency index.
Similar to the convective heat transfer, the pressure drop of the ferrofluid depends on the frequency of the external magnetic field. Fig. 18 plots the efficiency index, h as function of the frequency. It can be observed in Fig. 18 that the increase of pressure drop is not as great as heat transfer enhancement in the presence of the alternating magnetic field. Thus, h increases compared to the case of constant magnetic field (f ¼ 0). 9. Conclusion This paper presents an experimental study on the convective heat transfer and pressure drop of Fe3O4/water nanofluid (ferrofluid) in a parallel plate channel under the influence of constant and alternating magnetic field. Effects of Reynolds number, volume fraction, magnetic field intensity, and frequency are investigated. The following notes can be concluded. Electromagnets arrangement and locations are two important parameters that affect the convective heat transfer. The optimum arrangement of the electromagnets is obtained by a numerical simulation and supporting experiments. The heat transfer enhancement is shown to have a direct relation with nanofluid concentration and Reynolds number. At a constant Reynolds number, heat transfer increases with the magnetic field intensity. It is also shown that there exists an optimum frequency for every single Reynolds number which increases by Reynolds number. Effect of magnetic field is more pronounced at the thermally developing region. The maximum convective heat transfer enhancement is obtained as 16.4% in the absence of magnetic field at Re ¼ 1200 and 4 ¼ 2%. It is increased up to 24.9% and 37.3% by application of constant and alternating magnetic field, respectively. Heat transfer enhancement under the influence of a constant magnetic field is attributed to the migration of the nanoparticles to the channel surface which leads to an increase in local particles concentration and consecutively the local thermal conductivity. In the presence of an alternating magnetic field, periodic attraction of the cold fluid to the heated surface and release of it to the bulk flow disturbs the thermal boundary layer, improves the flow mixing and increases the heat transfer. Increase of pressure drop is an inevitable consequence of applying the external magnetic field to the ferrofluid flow. Heat
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transfer enhancement is shown to be greater than the increase of pressure drop under the alternating magnetic field. Nomenclature B Cp Dh FM h H I L Nu P Pr Q 00 q Re T T V W u,v x,y x*
magnetic flux density (T) specific heat (J/kgK) hydrodynamic diameter (m) magnetic force (N) convective heat transfer coefficient (W/m2K) channel height (mm) electric current (A) channel length (mm) Nusselt number pressure (Pa) Prantdl number (Pr ¼ n/a) total heat flow (W) heat flux (W/m2) Reynolds number (Re ¼ ruDh/m) temperature (K) time (s) electric voltage (Volt) channel width (mm) fluid velocities (horizontal, vertical, m/s) Cartesian coordinates (horizontal, vertical,m) a parameter in Eq. 14
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