Natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation

Transcription

1 Natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation Zuo-Sheng Lei, Sheng-Yang Song, Chun-Long Xu, Jia-Hong Guo To cite this version: Zuo-Sheng Lei, Sheng-Yang Song, Chun-Long Xu, Jia-Hong Guo. Natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation. 8th International Conference on Electromagnetic Processing of Materials, Oct 2015, Cannes, France. EPM2015. <hal > HAL Id: hal Submitted on 21 Jun 2016 HAL is a multi-disciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

2 Natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation Zuo-Sheng Lei 1*, Sheng-Yang Song 1, Chun-Long Xu 1, Jia-hong Guo 2 1 State Key Laboratory of Advanced Special Steel, Shanghai University, , Shanghai, China 2 Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, 20072, Shanghai, China *Corresponding author : lei_zsh@staff.shu.edu Abstract The experimental studies on natural convection of magnetic fluid inside a cubical enclosure under magnetic gravity compensation are presented. The bottom wall of the enclosure was uniformly heated by a heating element from a DC power supply while the top wall was cooled by ice water flowing from a container. The cubical enclosure was positioned in the center of the Helmholtz-Maxwell coils, which can provide a uniform gradient magnetic field. The magnetic force applied to the magnetic fluid was large enough to compensate gravitational force of the magnetic fluid, which was the driven force of natural convection. The Nusselt number was calculated by measuring the heat flux on the bottom wall and the temperature of both walls. Heat transfer efficiency of natural convection of magnetic fluid under different effective gravitational accelerations was compared in this study. Key words : natural convection, magnetic fluid, magnetic gravity compensation Introduction Experimental and numerical studies have been carried out on natural convection. Enhancements or suppressions of natural convection heat transfer have been long-term research topics investigated by many researchers. The driving force for natural convection is the buoyancy force caused by the density difference between hot and cold regions of the fluid in terrestrial conditions. And controlling natural convection may be difficult as the gravitational acceleration is constant and uniform on the earth. In recent years, another option for flow control has appeared the magnetic buoyancy force. One of the first works on magnetic convection was carried out by Carruthers and Wolfe [1]. They found that when an insulating paramagnetic fluid such as gaseous oxygen was subjected to combined thermal and magnetic field gradients, a magnetic body force was shown to exist which was analogous to that of gravity. The possibility of magnetic control of thermal convection was discussed for several instances. Braithwaite et al. [2] used a magnetic field both to enhance and suppress buoyancy-driven convection in a solution of gadolinium nitrate, and showed that the effect depended on the relative orientation of magnetic field and temperature gradient. Quantitative treatment of air convection under magnetic fields was initiated by Bai et al. [3]. Huang et al. [4] studied the effect of a static, nonuniform magnetic field on a laterally unbounded nonconducting paramagnetic fluid layer heated from below or above using a linear stability analysis of the Navier- Stokes equations supplemented by Maxwell s equations and the appropriate magnetic body force. Tagawa et al. [5] employed a procedure similar to the Boussinesq approximation and developed model equations for convection resulting from a gradient magnetic field. Ozoe et al. [6] installed a four-poles magnet to apply the cusp-shaped magnetic field to air in the cubic enclosure. A simple model equation was derived for magnetizing force and numerically computed for the system. Bednarz et al. [7-10] investigated natural convection of paramagnetic fluids in a differentially heated cubic enclosure under magnetic fields. It was shown in their works that by using a strong magnetic field they can enhance, suppress or invert the usual gravitational convection with different combinations of the two main body forces (gravitational and magnetic buoyancy forces) that act together to drive thermo-magnetic convection of paramagnetic fluids. In this present study, we develop an apparatus made of two pairs of Helmholtz-Maxwell coils, which can generate a uniform magnetic gradient field for ferro-fluid filled inside a cubical enclosure, so as to produce a uniform magnetic volume force to compensate the gravity. Then natural convection of water-based magnetic fluid inside the cubical enclosure under magnetic gravity compensation is studied experimentally. Experimental apparatus and the working fluid The experimental setup is presented in Fig. 1, here the magnetic gravity compensation was realized by combining the two pairs of Helmholtz-Maxwell coils and ferro-fluid [11]. The specifications of the coil system and the configuration of the Helmholtz-Maxwell coil system is described in our other work [12]. The experimental cell consisted of a cubical enclosure filled with magnetic fluid placed in the centre of the Helmholtz-Maxwell coils, a heater control system, a cooling system, a heat flux meter and a portable data acquisition module connected to a personal computer. The details of experimental cell is shown schematically in Fig. 2. Six separate elements were designed to assemble the final

3 experimental model. Those are: two copper plates (one for the cooling side and the other for the heating side) with one hole in each to place two K-type thermocouples, a quartzose cubic cavity, the cooling chamber is made of stainless steel, the base is made of polytetrafluoroethylene. There were a heat flux sensor and a heater between the heating plate and the base. The heater was connected to a DC power supply (KXN-305D). The cooling copper plate was cooled by water pumped from a container which is full of ice water. The cubic cavity had an internal dimension of 40mm on each side. Fig. 1: Experimental setup Fig. 2: Schematic view of the experimental apparatus In the present experiment a water-based magnetic fluid which contains magnetic nanoparticles was used as the working fluid. The major properties of the working fluid are listed in Table 1. Table 1 Important properties of the working fluid at room temperature Property Value Unit α(thermal diffusivity) m 2 /s β(thermal expansion coefficient) /K λ(thermal conductivity) 0.59 W/(m K) ν(kinematic viscosity) m 2 /s ρ(density at room temperature) kg/m 3 When all parts of the experimental setup were assembled, it was possible to fill the enclosure with the working fluid. This was done with a syringe and a thin needle. There was a hole through the cooling copper plate and the cooling chamber. When the enclosure was filled, the hole was sealed by hot glue and the experimental apparatus was placed in the center of the Helmholtz-Maxwell coils. The environmental temperature was kept constant. The electric current to the Helmholtz coils was 130A while the electric current to the Maxwell coils increased from 0A to 93A in order to modulate the gravity level. The heater power was set to 2W at the beginning of every group of experiments. The temperature of heated and cooled side walls were monitored continuously. After about 1 hour, when the system had

4 reached a steady state, the temperatures and the heat flux were recorded. Then the heater power gradually increased by 2W until it reached 20W. Results and Discussion Fig. 3: The Nusselt number at different heating power under normal gravity and a uniform magnetic field In Fig. 3, the natural convection Nusselt numbers are plotted against the heating power. As seen in Fig. 3, the Nusselt number increases with the heating power no matter under normal gravity or under a uniform magnetic field. Because the temperature gradient increases with the heating power, natural convection heat transfer is enhanced. The viscosity of magnetic fluid increases under a uniform magnetic field, so the natural convection heat transfer efficiency under a uniform magnetic field is lower than that under normal gravity consequently. As we can see in Fig. 3, the Nusselt number is less under a uniform magnetic field at the same heating power. Fig. 4: The Nusselt number at different heating power under different effective gravitational accelerations Fig. 4 shows natural convection heat transfer of magnetic fluid under different effective gravitational accelerations. It is clear in the figure that the Nusselt number decreases with the decrease of effective gravitational acceleration. In order to figure out the effect of magnetic force to natural convection, we calculate the magnetic Grashof number. The Nusselt numbers are plotted against the magnetic Grashof numbers in Fig. 5. The Nusselt number increases with the magnetic Grashof number under the same effective gravitational acceleration but decreases with the increase of effective gravitational acceleration. The magnetic force acting on the magnetic fluid applied by the gradient magnetic field causes the magnetic acceleration. The magnetic force will suppress natural convection of magnetic fluid when the direction of

5 the magnetic acceleration is contrary to the direction of the gravitational acceleration. The magnetic acceleration increases with the increase of magnetic force, so does the suppression of natural convection. Fig. 5 The Nusselt number at different magnetic Grashof number under different effective gravitational accelerations Conclusions In this paper, natural convection of magnetic fluid under magnetic gravity compensation in a cubical enclosure has been investigated experimentally. The enclosure is placed in the center of the Helmholtz-Maxwell coils. The heat transfer measurements show that, as the magnetic field increases, the effective gravitational acceleration decreases, the Nusselt number decreases, indicating that convection is suppressed. Acknowledgment This project financially supported by National Science Foundation of China (No and NO ). References [1] Carruthers J, Wolfe R(1968),Journal of Applied Physics, 39(12): [2] Braithwaite D, Beaugnon E, Tournier R(1991), Natural, 354 (14): [3] Bai B, Yabe A, Qi J, Wakayama NI(1999), AIAA journal, 37(12): [4] Huang J, Gray DD, Edwards BF(1998), Physical Review E, 57(5): 5564 [5] Tagawa T, Shigemitsu R, Ozoe H(2002), International journal of heat and mass transfer, 45(2): [6] Kaneda M, Tagawa T, Ozoe H(2002), Journal of heat transfer, 124(1): [7] Bednarz T, Fornalik E, Tagawa T, Ozoe H, Szmyd JS(2005), International Journal of Thermal Sciences, 44(10): [8] Bednarz T, Fornalik E, Tagawa T, Ozoe H, Szmyd JS(2006), Thermal Science and Engineering, 14(4): [9] Bednarz T, Fornalik E, Ozoe H, Szmyd JS, Patterson JC, Lei C(2008), International Journal of Thermal Sciences, 47(6): [10] Bednarz TP, Lei C, Patterson JC, Ozoe H(2009), International Journal of Thermal Sciences, 48(1): [11] Zuo-Sheng L, Chao-Yue C, Li-Jie Z, Zhong-Ming R(2012), The 7th International Conference on Electromagnetic Processing of Materials, Beijing. Journal of Iron and Steel Research International [12] Zuo-Sheng Lei, Song-Bao Wang, Yong-Chao Shi(2015), The 8th International Conference on Electromagnetic Processing of Materials, France, (In this volume)