Effect of Magnetic Field Direction on Forced Convective Heat Transfer of Magnetic Fluid

Transcription

1 APSAEM14 Jorunal of the Japan Society of Applied Electromagnetics and Mechanics Vol.23, No.3 (2015) Regular Paper Effect of Magnetic Field Direction on Forced Convective Heat Transfer of Magnetic Fluid Masaaki MOTOZAWA *1, Kyohei KINO *1, Tatsuo SAWADA *2, Yasuo KAWAGUCHI *3 and Mitsuhiro FUKUTA *1 Effect of magnetic field direction on forced convective heat transfer of magnetic fluid flow in a rectangular duct was investigated experimentally. Magnetic fields were applied to magnetic fluid flow in three directions, which were an axial direction, a parallel direction and a vertical direction against the heat transfer direction. Reynolds numbers based on hydraulic diameter and bulk mean velocity were set at about 980 for laminar flow and about 6700 for turbulent flow. In the case of laminar flow, heat transfer was enhanced in the vertical direction and slightly enhanced in the axial direction, but hardly changed in the parallel direction. In contrast, in the case of turbulent flow, heat transfer was suppressed in all directions. The suppression level in vertical and parallel direction is similar, but the suppression in axial direction is much weaker than those in other directions. Moreover, in order to discuss the heat transfer characteristics, the velocity distribution was also measured by an ultrasonic technique. Keywords: Magnetic fluid, Convective heat transfer, Magnetic field direction, Rectangular duct, UVP. (Received: 12 August 2014) 1. Introduction An innovative cooling technology for CPU, fuel cell, power generator, space station etc. is strongly required in recent years. A nanofluid is one of media which has great potential for heat transfer applications, and several studies on heat transfer characteristics of nanofluid have been carried out [1]. A magnetic fluid [2] is a kind of the nanofluid and a stable colloidal dispersion of surfactant-coated nano-order-size magnetic particles in base liquid such as water. Because the magnetic fluid has unique characteristics under magnetic field, many studies on physical properties or flow phenomena of magnetic fluid have been conducted [3,4], and also many applications are proposed [5,6] since magnetic fluid had been developed. In the thermal engineering field, heat transfer characteristics of magnetic fluid also have attracted attention same as the nanofluid. Therefore, several studies of heat transfer characteristics of magnetic fluid have been done by both magnetic fluid researchers [7] and nanofluid researchers [8]. For instance, Sawada et al. [9] experimentally investigated natural convection of a magnetic fluid in concentric annuli. They reported that reverse natural convection occurs by applying magnetic field in the opposite direction of the gravity. Iwamoto et al. [10] proposed the self-driven flow of binary temperaturesensitive magnetic fluid for the application of heat transport device, and investigated influence of the magnetic field on the flow driving force. They con- Correspondence: M. MOTOZAWA, Department of Mechanical Engineering, Shizuoka University, Johoku, Naka-ku, Hamamatsu, Japan motozawa.masaaki@ipc.shizuoka.ac.jp *1 Shizuoka University *2 Keio University *3 Tokyo University of Science firmed the enhancement of the driving force by using the binary temperature-sensitive magnetic fluid. Regarding forced convective heat transfer, some researches [11,12] including our previous study [13] reported the heat transfer enhancement by applying external magnetic field in laminar flow regime. However, there is not enough knowledge about the reason for this enhancement. In our previous study [14], we investigated forced convective heat transfer of magnetic fluid in both laminar and turbulent flow regime by applying uniform magnetic field in perpendicular direction of the heat transfer direction. However, some researchers reported that the thermal conductivity of magnetic fluid has characteristic anisotropy in the relation to magnetic field direction [15,16] because inner magnetic particles form chain-like structure in the direction of magnetic field. Therefore, it is important to discuss the effect of magnetic field direction on forced convective heat transfer of magnetic fluid. In this study, we investigated the forced convective heat transfer with applying uniform magnetic fields in an axial, a vertical, and a parallel direction against the heat transfer direction. In addition, in order to discuss the heat transfer phenomena in more details, we measured the velocity distribution by UVP (Ultrasonic Velocity Profiler) and flow resistance. 2. Experimental 2.1 Experimental apparatus Figure 1 shows a schematic diagram of the experimental apparatus. The flow system consists of a storage tank, a pump, and a rectangular duct as a test section. Flow rate can be adjusted by rotational speed of the pump and a bypass. Heater and cooling system are equipped in the storage tank and temperature of the test fluid can be controlled. The inlet (T in ) and outlet (T out ) temperature of the test fluid are measured by two 612

2 Fig. 1. Experimental apparatus. (a) Axial direction, (A) (b) Parallel direction, (P) (c) Vertical direction, (V) Fig. 2. Magnetic field directions; (a) Axial direction, (b) Parallel direction and (c) Vertical direction. thermocouples set at inlet and outlet of the duct. The rectangular duct has dimensions of 950 mm in length and 18 mm 18 mm in cross section, and is made of acrylic resin. The heater plate is made of a copper plate with an embedded heater, and is attached on the oneside of the duct. Ten thermocouples are installed in this heater plate Therefore, local wall temperatures at each position (T x ) can be measured. The positions of these thermocouples are also shown in Fig.1, and the position of T 5 is the center of the test section. Experiment was performed under uniform heat flux. A differential pressure gage is also set on the duct with the interval of 700 mm for measurement of the pressure difference across the magnetic field area. In this study, the Cartesian coordinates are defined as follows; x: Streamwise direction, y: Direction of normal to the heater plate, and z: Spanwise direction. Water-based magnetic fluid named MSG-W10 produced by Ferrotec Co. was used in this experiment. The density and viscosity of this magnetic fluid without magnetic field are kg/m 3 and 2.8 mpa s at 25 C measured by ourselves, respectively. Experiment was carried out in both laminar (about 980 of Re) and turbulent flow (about 6700 of Re). In these cases, the Reynolds number is defined by the bulk mean velocity and hydraulic diameter (D h = 18 mm). 2.2 Magnetic field Magnetic fields are applied to the magnetic fluid flow in three directions such as (a) an axial direction, (b) a parallel direction and (c) a vertical direction against the heat transfer direction as shown in Fig. 2. These directions are labelled as (A), (P) and (V), respectively. For applying the magnetic field in (A), we used a solenoid which is 200 mm in length, and the test section is set through in this solenoid having the same axis as shown in Fig. 2(a). This solenoid can apply up to 50 mt of magnetic field on the axis of the solenoid to the magnetic fluid flow. In contrast, uniform magnetic field is applied in (P) and (V) by an electromagnet, and magnetic field intensity can be varied from 0 mt to 500 mt in this study. The diameter of an iron core of this electromagnet is 150 mm. The centers of the solenoid and the electromagnet are set at the center of the test section where is the position of T 5. Therefore, the position of magnetic field areas are (x/d h ) for (V) and (P), and for (A). 2.3 Velocity profile measurement Since magnetic fluid is opaque, it is impossible to measure the velocity distribution by conventional optical methods such as LDV or PIV. Against this difficulty, UVP was applied to the measurement of velocity distribution in this study. UVP, which was developed by Takeda [17], is the measuring method for velocity distribution by ultrasound. Velocity distribution can be composed along the ultrasonic beam emitted from the UVP transducer. Seeding particles used in this study are polymethylmethacrylate particles (MBX-100, produced by Sekisui Plastics Co., Ltd.). These particles have 115 m in mean diameter. The UVP transducer was set on the rectangular duct where the magnetic field exists. In this study, it is important to measure the velocity distribution in an x-y plane, that is, the profile normal to the heater plate. In the case of applying magnetic field in (A), UVP transducer is set just down- 613

3 Fig. 3. Streamwise variation of heat transfer under magnetic field in laminar flow. stream outlet of the solenoid and measured the velocity distribution in an x-y plane. In the case of applying magnetic field by electromagnet (i.e. (V) and (P)), the velocity distribution in x-y plane can be measured in (V) but cannot be measured in (P) because of existence of electromagnet. 2.4 Data reduction The local heat transfer coefficient at each position (h x ) and local Nusselt number (Nu x ) are calculated by the following equations. q hx T T x b, x (1) hx Dh Nux (2) k where, k and q are thermal conductivity and heat flux, respectively. T x is local wall temperature at each positions which was measured by the thermocouples installed in the heater plate as mentioned above. T b, x is bulk temperature of the test fluid flow in the test section. This is estimated by using Eq. (3). Qx Tb, x Tin (3) m c Q x is the amount of heat from inlet of the test section to the position x. c is specific heat of the test fluid. m f is mass flow rate. 3. Results and discussion 3.1 Heat transfer Laminar flow regime Figure 3 shows the streamwise variation of heat transfer under magnetic field in laminar flow regime. The horizontal axis is the position x normalized by hydraulic diameter D h. The vertical axis is the ratio of local Nusselt number under no magnetic field (Nu no mag ) to f Fig. 4. Same as Fig. 3 for (P) and (V) under stronger magnetic field. that under magnetic field (Nu mag ). The magnetic field intensity is 50 mt because of the limitation of applying magnetic field in (A). This figure indicates that the heat transfer significantly increases in (V) and slightly increases in (A), but hardly changes in (P) in the region where the magnetic field is applied. Comparing (P) with (V), Fig. 4 shows the same as Fig. 3 for (P) and (V), but stronger magnetic fields which are 300 and 500 mt are applied. Fig. 4 clearly indicates that enhancement of the heat transfer in (V) becomes large with increasing the magnetic field, but the heat transfer in (P) hardly changes with increasing the magnetic field. In our previous study [14], we made similar experiment for heat transfer in (V) but using other kind of water-based magnetic field, and similar trend of heat transfer enhancement was obtained in (V). In addition, the heat transfer near the inlet and outlet of the magnetic field (i.e. T 4 and T 6 ) is larger than that at the center of the magnetic field. Since magnetic field gradient exist at inlet and outlet of the magnet, it seems that weak convection occurs in these positions. Therefore, heat transfer becomes larger than that at the center position. We discuss the reason for characteristic dependence of heat transfer on magnetic field direction below. Generally, as reasons for the heat transfer enhancement in this case, the change in thermal conductivity and the change in velocity gradient near the heater plate by applying magnetic field can be considered. Considering the change in the thermal conductivity, some researchers reported [15,16] that the thermal conductivity of magnetic fluid increases in the direction of magnetic field because of the formation of chain-like clusters. This increment of thermal conductivity in the magnetic field direction should result in heat transfer enhancement in (P). However, comparing heat transfer in (V) with (P), the opposite result, i.e. the heat transfer is enhanced in (V), was obtained. In addition, the heat transfer in (P) hardly changes even if strong magnetic field is applied as shown in Fig. 4. This fact indicates that the increment of thermal conductivity hardly influence on the heat transfer of magnetic fluid flow. 614

4 Fig. 5. Velocity distribution under magnetic field in (A). Fig. 7. Streamwise variation of the heat transfer under magnetic field in turbulent flow. Fig. 6. Change in the velocity gradient by applying magnetic field in (A) and (V). Actually, in this experiment, since the region of magnetic field is very short and flow exists, it seems that the chain-like cluster cannot be formed in the magnetic field area and the thermal conductivity hardly changes. Regarding velocity distribution, Figs. 5 and 6 show the actual velocity distribution in (A) measured by UVP and changes in the flow velocity by applying magnetic field in (V) and (A), respectively. In Fig. 5, the vertical axis is the flow velocity (u) normalized by the bulk mean velocity (u b ). The horizontal axis is the distance from the wall (y) normalized by the half of the duct side. On the contrary, in Fig. 6, the vertical axis is the change ratio of the flow velocity by applying magnetic field (u mag /u no mag ). These figures indicate that the velocity gradient near the heater plate slightly decreases in (A), but increases in (V) with increasing the magnetic field intensity. Previously, we measured the velocity distribution in (V) but using different kind of water-based magnetic field [14] and similar result (i.e. increment of velocity gradient in (V)) was obtained. The detail can be found in [14]. Therefore, in the case of (V) in this study, the increment of velocity gradient results in the significant heat transfer enhancement as we have already Fig. 8. Same as Fig. 7 for (P) and (V) under stronger magnetic field discussed previously. In contrast, although it is impossible to measure the velocity gradient near the heater plate in the case of (P), we guess that the velocity gradient decreases near the heater plate with considering our previous measurement [18] of velocity distribution under non-uniform magnetic field. Consequently, the heat transfer hardly changes in (P). On the other hand, in the case of (A), Fig. 5 indicates that the velocity gradient near the heater plate slightly decreases. Considering the results of the change in the thermal conductivity and velocity gradient, the heat transfer should not be enhanced so much because there is no reason for the heat transfer enhancement. However, in fact, the heat transfer is enhanced in (A) and the enhancement level is larger than that in (P) as shown in Fig. 3. It is thought that because magnetic field is not uniform in the solenoid, especially, at inlet and outlet of the solenoid, the weak convection induced by the magnetic field gradient, and this convection results in the heat transfer enhancement in (A). We need more detailed experiment in the future to clarify the heat transfer phenomena in (A). 615

5 Fig. 9. Change in the standard deviation of streamwise velocity by applying magnetic field in (A) and (V) Turbulent flow regime Figure 7 shows the results of the streamwise variation of the heat transfer in the turbulent flow. As shown in this figure, the heat transfer is suppressed at the region where the magnetic field exists in all directions as already reported in our previous study in the case of (V) [14]. The suppression in (V) and (P) is similar level, but the suppression level by applying the magnetic field in (A) is smaller than that in (V) and (P). This is because turbulent diffusion is suppressed by applying the magnetic field in all magnetic field directions. Moreover, Fig. 8 shows the same as Fig. 7 for (V) and (P), but stronger magnetic field is applied. The suppression of the heat transfer becomes large for both (V) and (P) with increasing the intensity of magnetic field. Regarding the difference of heat transfer downstream of magnetic field, although suppressed heat transfer recovers downstream of the region of magnetic field in the case of applying weak magnetic field as shown in Fig. 7, it does not recover but continue to be suppressed downstream of the magnetic field area by applying strong magnetic field as shown in Fig. 8. This fact means that the turbulent diffusion of magnetic fluid is suppressed strongly by applying strong magnetic field. Consequently, the suppression of turbulent diffusion in magnetic fluid is related to flow velocity and magnetic field intensity. Figure 9 shows the change in the standard deviation of streamwise velocity of magnetic fluid flow by applying the magnetic field. In the UVP measurement, because the spatial and temporal resolution are low comparing with PIV measurement, it is difficult to measure the turbulent fluctuation precisely. However, UVP displays the standard deviation of measured streamwise velocity at each positions. Although the result is not clear as shown in Fig. 9, this figure indicates that the standard deviation of streamwise velocity decreases by applying the strong magnetic field (i.e. 300 mt) throughout half of the rectangular duct. However, it Fig. 10. Change in the frictional coefficient by applying magnetic field in (A) and (V). is difficult to discuss the change in the standard deviation of streamwise velocity under weak magnetic field (i.e 50 mt). Considering Fig. 7, the fact, that is the suppression level in (A) is weaker than that in other direction, shows the possibility that there is characteristic anisotropy of the suppression of turbulent diffusion in relation to the magnetic field direction. Only when the magnetic field is applied in (A) (i.e. streamwise direction of magnetic fluid flow), it seems that the velocity fluctuation normal to the heater plate is not suppressed so strongly. For discussion of this unique turbulent suppression, we will measure the turbulent fluctuation more precisely in the future. 3.2 Frictional coefficient Figure 10 shows the Reynolds number dependence of change in the frictional coefficient by applying the magnetic field for (A) and (V). In this case, the influence of magnetic field on the flow resistance for (P) is the same as (V), because the cross section of the test section is square in this study. Frictional coefficient is calculated by the pressure difference ( p). In this figure, the vertical axis is the ratio of the frictional coefficient with magnetic field to that without magnetic field. This figure clearly indicates that the increment ratio of frictional coefficient increases in (V) with increasing the magnetic field intensity, but slightly increases in (A) in the laminar flow case. However, this increment ratio decreases with increasing Reynolds number in (V). Moreover, the flow resistance hardly changes in (A) under high Reynolds number. Previously, Kamiyama et al. [19] investigated the influence of non-uniform magnetic field on pipe frictional coefficient and made more detailed discussion. They reported that the flow resistance increases in laminar flow, but the magnetic field hardly influences on flow resistance in turbulent flow, namely the similar result is obtained in this study. It is well known that the apparent viscosity increases when the magnetic field is applied to the magnetic fluid. Therefore, this increment of apparent viscosity causes 616

6 the increment of flow resistance. In the case of (A), as the magnetic field is applied to the magnetic fluid flow along the streamwise direction, skin friction in (A) does not significantly increase comparing with (V). Therefore, the flow resistance slightly increases by the increase of apparent viscosity. This difference of increment of flow resistance between (V) and (A) indicates that there is also characteristic anisotropy of the change in the apparent viscosity related to the magnetic field direction. 4. Conclusion We investigated the forced convective heat transfer of magnetic fluid by applying magnetic field in a vertical, a parallel and an axial direction against heat transfer direction by using a rectangular duct. In the case of laminar flow, heat transfer is enhanced by applying the magnetic field in the order by the vertical direction and the axial direction. However, the heat transfer hardly changes by applying the magnetic field in the parallel direction even if strong magnetic field is applied. In contrast, in the case of turbulent flow, the heat transfer is suppressed by applying magnetic field in all directions. The suppression of heat transfer is similar level for applying the magnetic field in the vertical direction and the parallel direction. However, the suppression level by applying the magnetic field in the axial direction is much smaller than that in other directions. On the other hand, the flow resistance by applying the magnetic field in the vertical direction (same as the parallel direction) largely increases with increasing the magnetic field in laminar flow regime, but that by applying the magnetic field in the axial direction slightly increases. Acknowledgment This study was partly supported by a Grant-in-Aid for Young Scientists (B) Number of the Japan Society for Promotion of Science. References [1] S. K. Das, S. U. S. 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