Numerical Investigation and Comparison of Thermal Performance of Ferrofluid in Different Closed Loop Configurations

This paper describes the free convection heat transfer capability of kerosene based ferrofluid flowing through a closed loop for assessing the thermal performance. Numerical investigations were performed using COMSOL Multi Physics 5.0 for comparing the heat transfer characteristics of ferrofluid flowing through three different closed loop geometrical configurations. The heat transfer performance of rectangular, oval and circular shape closed loop was evaluated under same input test conditions. Constant magnetic field was applied and time dependent numerical study was conducted for single-phase fluid flow. The fluid moves under the effect of Kelvin Body Force and maximum velocity of 5.68 mm/s has been found for oval shaped configuration. Temperature and velocity plots have been plotted for different lengths of time and results of investigation reveal that oval shaped configuration favors better output in terms of velocity generated and heat transfer.


Introduction
Magnetically controlled fluids have been used for quite a long time for various applications including dynamic sealing of shafts, magnetic drug targeting, for treatment of hyperthermia and magnetic separation of cells [1]. Heat transfer is another challenging area for ferrofluids which has attracted interest of many resarchers in recent years [2][3][4][5][6][7][8]. Over a period of last few decades, unprecedented growth has been observed in the computational power of electronic devices. Reduction in size and generation of high heat flux has been a prominent feature of their working. Smart cooling systems are thus the need of the hour which should be able to dissipate the high heat flux generated by these devices so that they can work 24×7. Ferrofluid driven heat exchangers can provide a potential solution for cooling of such miniaturized devices.
Ferrofluids are a distinct class of magneically controllable fluid and have added advantage over magneto-rheological (MR) fluids in the sense that the fluid maintains their flowability under strong external magnetic fields while MR fluid tends to solidify when subjected to strong magnetic field. Thus, when such a fluid is subjected to temperature gradient in the presence of external magnetic field, due to non-equilibrium magnetization in the fluid, the fluid will experience a magnetic body force, called "Kelvin body force" which results in movement of fluid in the direction of higher temperature section [9]. The flow rate of the fluid, hence, could be controlled as per heating load by varying only The effect of non-uniform magneti was studied by Shakiba and Vahedi pipe heat exchanger and hydrothe increase in the intensity of magn convective heat transfer behavior o was experimentally investigated by tube and behaviour was studied u Convective heat transfer coefficien while reverse trend was observed element method was applied by Sh and heat transfer characteristics of reported with magnetic number, R behaviour of water-based ferroflui under the effect of transverse magne reported with increase in the flow water based ferrofluid was experime Asfer et al. [14]. Temperature m technique. Augmentation in heat t stainless steel tube under the effec experimentally analyzed by Cherie Augmentation in heat transfer coef mass flow rates.
It can be obseved from the report transfer. Although some research w these studies have been conducted paper to numerically investigate the closed loop due to spatially varying to thermo-magnetic convection prin different loop shapes i.e. rectangul constant heat flux and for same vol MultiPhysics 5.0 on 2D closed loop and temperature plots.  ic field on hydrothermal characteristics of water-b i [10]. The fluid was allowed to pass through a hor ermal characteristics were analyzed using ANSYS netic field, increase in Nusselt number was obs of hybrid nanofluid containing magnetite nanoparti Shahsavar et al. [11]. Fully developed fluid flows t under the influence of constant and alternating m t was found to increase with Re in the absence of in the presence of magnetic field. Control volum heikholeslami and Rashidi [12] to numerically inves f water based ferrofluid. Increase in heat transfer c Rayleigh number and nanoparticle volume fraction id flowing through a helical channel was numeric etic field by Aminfar et al. [13]. Augmentation in he rate and velocity gradient.Convective heat transfer entally evaluated under the influence of constant ma measurements of fluid were done using Infrared transfer was observed, when the ferrofluid was fl t of magnetic field. Convective heat transfer chara ef et al. [15] for a ferrofluid that flows through fficient was observed with increase in volume fract ted literature that ferrofluid based cooling systems work has been done on free convection of ferrofluid, for forced circulation of fluid. An attempt has bee ermal performance of kerosene based ferrofluid flow g fluid magnetization with temperaure. The fluid tend nciple solely due to external magnetic field. A comp ar, oval and circular shape have also been present lume of fluid. The ferrofluid is assumed to flow through a copper pipe having having inner diameter 2.5 mm and outer diameter 3.5 mm. A strip heater of size 28 mm × 1 mm is used as a heat source and permanent magnet has ben positioned in between accumulator and heat source such that it cover half of the heated length. A constant heat flux of 2 W/cm 3 has been applied to the fluid as it flows through the heated length. Aluminum fins of width 1mm and height 15 mm have been fixed on the lower loop with distance between them as 2 mm. Fins are used to increase the surface area for better heat dissipation.

Geometry Description
Three closed loop geometries i.e. rectangular, oval and circular shapes have been considered in the problem. The loop length has been fixed in such a way that same volume of fluid should flow in all the three configuartions while subjecting the fluid to same heat flux, same magnetic field intensity and initial temperature. The important properties of ferrofluid used for the simulation are presented in Table 1.  of COMSOL Multiphysics 5.0 and appropriate material properties were assigned to different components. No slip conditions were assumed for the flow at the pipe inner surface and physics controlled fine mesh has been used for predicting the temperature and velocity measuremets accurately. Initial temperature of the ferrofluid in the loop and surrounding medium was considered as 293 K and flow was assumed to be laminar in nature. Since the problem under consideration involve three different physics i.e. magnetic flux, heat transfer and laminar flow, thus MultiPhysics node containing different physics interfaces are used in the simulation study. Magnetic field is treated stationary, while heat transfer and laminar flow are considered as time dependent while solving the model.

Results and Discussions
Temperature profile generated at different length of time for rectangular, oval and circular loop shapes are presented in Figure 3-5 respectively.   The temperature distribution diagrams shown in Figure 3-5 reveal that fluid is heated in close vicinity to its Curie temperature as it passes through heat source region, thus generating temperature gradient at the place where magnet is positioned. Color bar on the right side of graphic shows the temperature(K) reached in different parts of the loop; whilst values placed alongside bottom and top of the color bar shows the minimum and maximum value of temperature attained respectively in the loop at that instant of time. The temperature difference along with non-uniform magnetic field distribution is thus responsible for flow of the fluid. As the fluid flows through the loop, temperature begins to fall as heat loss by convection takes place mainly in the lower loop section. The cold fluid, thus moves towards the accumulator and is ready to perform next cycle.     Velocity profiles shown in Figure 6-8 highlight the augmentation in velocity of ferrofluid with time as it flows through the loop. Lesser velocity is generated in the beginning, as temperature difference in the loop was less. However, as the time progress, fluid was heated in close vicinity to the Curie temperature near the section where magnet was positioned. Thus, higher temperature gradient near the location of magnet along with non-uniform magnetic field led to generation of Kelvin body force that act as driving force.
The variation of velocity shown in Figure 7 for oval shaped configuration is also represented in the form of line graph in Figure 9 across a cross-section when fluid is about to enter heated length. At fluid-pipe interface, velocity of ferrofluid is zero and it reaches its maximum value as centre line of the pipe is being approached.

Conclusion
Following conclusions could be drawn from the numerical study conducted on different loop geometries: (c) Maximum velocity of 5.68 mm/s was generated at t = 35 minutes for oval shaped loop just when the fluid is about to pass through heat source section. Corresponding value for rectangular and circular shaped loop at same time was found to be 2.45 mm/s and 3.58 mm/s respectively.Thermal performance of oval shaped loop is, thus, better in comparison to other two loop profiles as higher force was generated in the loop resulting in higher fluid velocity. The fluid is thus capable of completing the cycle in lesser time, extracting more heat, thus maintaining safe working temperature.  Figure 9 represents the variation in the velocity across the cross section at time t = 5min, 25 min and 50 min, when the fluid is just about to enter heated length for oval shaped loop. Velocity of fluid is zero at the fluid pipe interface due to no slip conditions and it tends to increase towards the centerline of the pipe.
(e) Velocity vectors in Figure 10 shows the direction of fluid flow. Under the influence of Kelvin body force, fluid starts to move in clockwise direction, extracting heat from the heat source and during its passage dissipate thermal energy to the surroundings. Thus low temperature fluid is always available at the end of every cycle in the accumulator region.