Investigating Thermal Conductivity of Ferroﬂ uids

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Introduction
Nanotechnology is the fastest-growing area of modern research due to its broad-spectrum applications: medicine, automobiles, etc. Irrespective of the size or type of industry, a common requirement to all is an ef icient heat-transfer mechanism.Cooling of heavy machinery maintains operational functionality and longevity.
Conventionally coolants like water low through pipes around heated machinery.Nano luids have emerged as potential replacements in such cooling systems.Their versatile properties allow for the manipulation of heat transfer through them.
They possess greater heat-transfer ability and are ef icient in small quantities-vital to cooling of microprocessors and Micro-Electro-Mechanical Systems (MEMS) [1].
To explore one such methodology used to enhance the heat transfer capabilities of speci ic Nano luids, the following research question was derived: How is the thermal conductivity of a model (50 m -100 m) Ferro luid (Fe2O3), contained in a glass test tube of length 0.15 m and diameter 0.036 m and placed axially within 50-turn and 200-turn solenoids, affected when an increasing voltage (0V to 4.5V) increases the magnetic ield strength (0.023 mT to 0.310 mT) across the solenoid?Nano luids can be characterized as nanoparticles of substances like metal or metallic-oxides dispersed in the base luid.Ferro luids (also referred to as Magnetic Nano luids or MNFs) are colloidal solutions containing super-paramagnetic particles [2,3] in a non-magnetic base.Ferro luids thus demonstrate both magnetic characteristics and luid properties.Base luids can be organic or inorganic, however, with regard to heat-transfer properties, luids with relatively higher conductivity and heat capacity are preferred like water and oils.The magnetic particles can be ferromagnetic in nature which includes metals like iron and cobalt, or even metallic oxides like Fe2O3 or Al2O3.
Thermal Conductivity is a characteristic property of any material.A higher thermal conductivity represents a higher heat-transfer rate.In Nano luids, thermal conduction takes place through microscopic collisions of nanoparticles with each other and molecules of base luid.
Originally, it was considered that adding nanoparticles of higher thermal conductivity to an industrially used coolant like water would greatly enhance the thermal conductivity, culminating in volumes of research using TiO2, Cu, and Ag.However, Honk TJ and Choi CJ [4] proved through their investigations that solid materials with higher conductivities weren't always effective.This, along with the idea of controlling the thermal conductivity of luid cooling systems such that a "reversible switchable thermal luid" be created, ushered in a great deal of research into the enhancement of thermal conductivity of nano luids using external magnetic ields.
Works of scientists like Krichler [5] and Li Q. Xuan Y [6] have demonstrated the impact an external magnetic ield has on nano luids.To understand these effects, it's necessary to understand the theoretical methods of heat transfer in such luids.https://doi.org/10.29328/journal.ijpra.1001064a) Brownian motion is the term given to random movements of molecules and particles in luids, i.e. liquids and gases, at a inite temperature [7].Inelastic collisions with molecules of base luid cause nanoparticles to undergo "zigzag" movement.In regard to heat transfer, Brownian-motion theory suggests that when heat energy is to be transferred, the particles closer to the heat-source gain kinetic energy, thereby causing intense movement.Under these conditions, nanoparticles can transfer this heat energy by:They diffuse through luid towards the cooler end where they collide with surrounding particles and increase their kinetic energy, leading to temperature rise.b) Creating micro-convection of base liquid molecules which transfers heat from the region of the energized nanoparticles to the cooler region.These effects were considered to enhance the thermal conductivity of luid as there would be an ef icient convectional mechanism between nanoparticles and luid molecules [8].
Scientists like Li Q, Xuan Y and Philip J [9] further investigated the impact of volume fraction [10] of nanoparticles.Volume fraction refers to the ratio of the volume of constituents added to the volume of the entire solution after mixing.Their investigations demonstrated that decreasing particle sizes enhanced thermal conductivity but only till a certain limit.
Brownian-motion theory would be favored by decreasing particle sizes due to more particles and greater surface area for heat transfer (Figure 1).But these studies showed that Brownian motion accounted for only a certain amount of enhancement.This led to the NanoParticle Clustering Model.
Perhaps the most widely-acclaimed model for heat transfer in Nano luids.In colloidal systems, suspended particles are almost evenly distributed in luids.Nano-particle clustering model works on the aggregate formations of such distributed particles [11].
Aggregation of nanoparticles into isolated clusters, or ideally into long, linear chains is proposed as the main mechanism behind improved thermal conductivity of Nano luids over industrial coolants as seen in Figure 2.
These aggregations form long and highly conductive nanoparticle chains, which are particles of high thermal conductivity themselves, which perform as pathways for heat transfer, causing faster, ef icient heat low over long distances.
Aggregates form due to the superparamagnetic nature of nanoparticles.'Superparamagnetic nature' refers to when particles can form weak, self-induced magnetic ields and can instantly switch their magnetism based on temperaturegradient around [12].
Under such conditions, nanoparticles cling due to magnetic attraction and form structures like chains, rings, or twodimensional, three-dimensional lattice structures [13].
Without these aggregations, the distribution morphology of nanoparticles is disordered and the thermal conductivity is isotropic-even in all directions.However, in these microstructures, thermal conductivity becomes anisotropic (unidirectional).Scientists like Zhu H and Jiang W conducted investigations into the Nanoparticle clustering model and concluded positively that clusters signi icantly enhanced thermal conductivity.Phase model.In the Single Phase model, the luid is considered to be a homogenous mixture while the Two-Phase (or Mixture) model considers the nanoparticles merely suspended in carrier luid.
The synthesized luid is a Two-Phase mixture with a particle size of Fe2O3-powder ranging from 50 m -100 m, greater than nano-scale and hence, model-Ferro luid: One assumption made while modelling the Ferro luid was that the particle size is large enough to prevent the 'clumping' of particles.In an actual Nano luid, clumping of particles due to extremely strong external magnetic ields may alter the shape of the chain or cause a "zippering" effect, which would result in broken micro-structures and the thermal conductivity wouldn't increase.This also occurs because of weak Van der Waal's forces present between molecules along with temporary magnetic dipole that is created due to its superparamagnetic nature.But because these particles aren't of the nano-scale, it would be unlikely for magnetic-ield strength to be large enough to cause clumping.

Carrier-fl uid-w ater
Investigations prove that thermal conductivity enhancement is the greatest in carrier luids with low thermal conductivities themselves.However, absolute thermal conductivity is higher for Nano luids having base luid with high thermal conductivity [16].Considering this, water quali ied as easily-available and best-suited.Distilled water was used to ensure that impurities weren't present which could bring about added conduction or affect the magneticield.

Nano particle-ha ematite
Haematite was used due to the relatively high thermal conductivity of iron and its oxides.Haematite and magnetite are frequently used in Nano luids and studies have investigated their functionality.
Though low volume fraction improved thermal conductivity, because nanoparticles are being modelled, a relatively higher fraction would be ideal.20 g of Fe2O3 was mixed in 40 ml of distilled water for an overall volume of 60 ml.Volume fraction (volume percent) is therefore 33.33%.This adds a suf icient amount of solute that won't settle down completely.× 100 = 33.33%60 a).The Setup/Pro ceduTwo Solenoids: The experiment used two solenoids of varying lengths and turn numbers.Test tubes containing Ferro luids are inserted into hollow tubular regions, along the axis of the solenoid, parallel to the direction of the magnetic ield inside (Figure 5A).The horizontal orientation of tubes inside the solenoid allows the metallic Figure 3 demonstrates these aggregates.Clearly observable that in (a), the particles are dispersed and widespread, however in (b), they cluster together forming connected, chain-like bridge structures.This behavior of nanoparticles stimulated studies into the effects of external magnetic-ields applied on Nano luids.It was experimentally proven that external magnetic ields had powerful effects on micro-structure formations, engendering thermal conductivity enhancement in Nano luids.These effects were guided by the intensity and orientation of the ield.
Experiments were conducted with magnetic ields applied perpendicularly and parallel to the desired direction of heat low (along temperature gradient) [15].Magnetic ields applied perpendicularly negligible effects on the thermal conductivity of Nano luid, irrespective of magnitude.However, when external magnetic ields were applied parallel to the temperature-gradient, the thermal conductivity of the Nano luid greatly increased.Stronger magnetic ields increased heat conduction.Linking to the nanoparticle clustering model, where due to stronger ields, nanoparticles had reduced inter-particle distance and formed compact chains as shown in Figure 4.It was concluded that when the magnetic ield was parallel to the temperature gradient, the aggregate-structures formed were more ef icient in ensuring antistrophic thermal conductivity.

Mo del-ferrofl uid synthesis -Fe2O3
The model-Ferro luid used was a mixture of powdered-Haematite (Fe2O3) and carrier-luid water.Generally, Nano luids are categorized into two types of mixture models based on physical Properties-Single Phase model and Two-  particles (heavier than nanoparticles) to spread out.It minimizes gravitational effects on these particles which could impact the thermal conduction due to vertical movement.The glass test tubes are poor conductors of heat, further ensuring no heat is lost during the process.However, test-tube walls are extremely thin and could lead to radial heat loss by conduction.Initially, it was planned that test tubes be wrapped in insulators like wool but this wasn't done because the thick, insulating layer could cause hindrance between the weak magnetic ield generated by the solenoid and the luid, resulting in lower temperatures measured at End-B.
Length (L), number of turns (N), and calculated turn density (n) of each solenoid is given in Table 1.The turn density is directly proportional to magnetic-ield strength: B = 0 [17] (2) The turn density: b) Power Supply/Ammeter/Multimeter/Magnetic-Probe: A power supply applies the voltage measured by the multimeter (Figure 5B) across the solenoid.An ammeter measures the current (I) and a magnetic probe (Figure 5C) measures the magnetic ield inside the solenoid using Logger-Pro software.The magnetic ield across the solenoid was measured in microteslas (mT) (Tables 2,3).The earth's magnetic ield itself is roughly 25 -65 microteslas (at the surface).However, this external magnetic ield has minimum impact on solenoids.Given the dimensions of the test tube and quantity of luid, it is predicted that the given range will suf iciently in luence the ferro luid.
From Figure 6, there is a signi icant increase in magneticprobe reading after voltage is applied as compared to earth's ield alone, indicated as 0.02mT before the application of voltage.The relationship is not linear and the slope gradually decreases.There are large decreases in slope for both solenoids between the second and third multimeter readings.
Using current readings of the Ammeter, theoretical magnetic ield strength can be calculated using   From  = , an increase in voltage across the solenoid with resistance-R would increase current-I, therefore increasing magnetic-ield strength.Furthermore, higher turn density corresponds to relatively higher magnetic ield strength.Tables 4,5 above indicate that the magnetic probe reading is always lower than the theoretical value of magnetic ield strength.The likely reason is that the solenoid converts some of the electric current to heat.This depends on the ef iciency of solenoids which has been calculated using the ratio of experimental and theoretical magnetic-ield strength.
For Tables 8,9, Ioutput (or current used to create magnetic ield) = % average ef iciency × Iinput (9) = 87.42 % × 0.45 = 0.39A eq. ( 10) Therefore, IH (current converted to heat energy) = Iinput -Ioutput = 0.45 -0.39 = 0.06A Applying P = VI, where P represents power generated (heat energy per unit time) = 0.14W c) Heat-Source-Spirit-Lamp: A spirit lamp is used as a heat source.It is lit and placed close to End-A of the test-tube.For each trial, it's held in place for 2 minutes, measured using a stopwatch (± 0.1s).The drawback of using a spirit lamp is that while it's strong, the temperature cannot be measured directly.A digital thermometer [least-count (± 0.1 °C)] measured temperature change at End-B.
The integrated form of Fourier's Thermal Conduction law: For the experiment, the length (0.15m), cross-sectional area(diameter=0.036m),and the heat supplied by the Spirit-Lamp stay constant.
The heat lows along the temperature gradient, i.e. from hot End-A to relatively cooler End-B.As time passes (2 min), END B increases and therefore, ∆ decreases.From Fourier's law, it is inferred that decreasing ∆ results in the thermal conductivity constant 'k' increasing.But because nanoparticles are being modelled, the rate of change of END B can be interpreted as a measure of the rate of increase of 'k'.

Enhancement of thermal conductivity
The enhancement factor of ther mal conductivity of Nano luid can be quanti ied: The dependent variable is the temperature which is measured at End-B at regular intervals of 10s.Therefore, the equation is:

Sample raw data-tables
First, the experiment was conducted under controlled conditions, where no voltage was applied across the so lenoid and the test tube contained the ferro luid and water.Three trials were carried out using each solenoid and Tables 10  N represents the number of voltages, xi represents each data value; σ 2 represents the standard deviation (Table 14).

Processing of data
The irst step in data processing is inding average temperatures recorded after every 10s interval in 6 trials at each voltage and each solenoid (Tables 15,16).50-Turn solenoid, voltage=0.66V,B=0.12mT, at the end of 2-minutes: Sum of temperatures at that time interval Average temperature measured = number of intervals (16) 29.7 29.3 29.8 30.0 29.9 29.9 Average temperature measured = 6 = 29.8 ± 0.1 ℃ Using average initial and inal temperatures measured for each voltage, the rate of temperature change will be measured, which is the change in temperature over total time (120s) (Tables 17,18).
We can calculate the enhancement factor in the rate of change of temperature, which is theoretically proportional to the enhancement factor in the thermal conductivity of the luid.

Thermal conduction higher in modelled-ferrofl uid
Table 12 clearly indicates the thermal-conducting superiority ferro luids have over water.For both solenoids, the temperature change at End-B was higher when model-Fe2O3-solution was used, even without a magnetic ield.In the absence of voltage, the rate of change of temperature for 50 turn-solenoid with water was 0.013 °Cs-1 while it was 0.024 °Cs-1 with Fe2O3-solution.This empirically veri ies the fundamental notion of increased heat transfer by a stationary luid on the dispersion of particles.

Magnetic fi eld's impact on the temperature measured
Figure 6 demonstrates decreasing trend in B with increasing voltage.For voltage rise 0.66  1.42V, magneticprobe displayed an increase from 0.12m  0.19mT, with ∆B = 0.07mT.But for voltage rise 2.04 2.23V, B rose from 0.24m  0.25mT only, with ∆B = 0.01mT.While these are signi icantly less than corresponding theoretical B-values due The experiment was irst conducted under controlled conditions, where no voltage was applied and test tubes contained only water and then the Fe2O3-particles with water.Three trials were conducted for each solenoid and Tables 19-21 in the processed data section show the results.Now that we have the '  ∆ 1' for each https://doi.org/10.29328/journal.ijpra.1001064 to the inef iciency of the solenoid, the decrease in magneticield strength could be because of the fact that as the voltage applied across the solenoid increased, larger current began lowing through th e coils as indicated by Tables 2,3.The larger current would, in time, generate heat energy that would cause the temperature of the coils to increase, thereby increasing the effective resistance of the solenoid.With an increasing variable resistance and constant voltage applied across, the solenoid would tend to decrease the current lowing ( = v).From B = nI, a decrease in I would thus result in decreasing magnetic ield strength.This could have been experimentally veri ied by maintaining a magnetic probe inside the solenoid for the duration of the trials along with a multimeter.The heating of the solenoid was qualitatively observed as the coils were extremely hot to handle after trials taken for larger voltages.
Figure 7 demonstrates that the inal temperature of the readings constantly increased with rising B. Rise in temperature can be justi ied by nanoparticle clustering which supports the magnetic enhancement of thermal conduction.The increase in B would cause the formation of Fe2O3-particle chains which formed conducting bridges, increasing the heat energy transferred from End EndB.Although this has been con irmed in prior studies by Choi and other scientists for iron-oxides of the nano-scale, the model here uses powdered particles ranging in size from 50 m -100 m.Given the greater mass and volume of these particles, the magnetic ield strength may not have had the same clustering effect.And there is merit in believing that the temperature rise measured was otherwise caused.The inef iciency of both solenoids generated a weakermagnetic ield with heat energy in coils.In fact, the amount of power-generated as per Tables 8,9 increased with voltage, i.e.B. This heat could have caused a rise in the temperature of the luid.However, the inner lining of the solenoid was wooden and would have restricted the heat conduction from the coils to the tube.As a result, it cannot be conclusively justi ied if the temperature rise was due to the magnetic properties of the model ferro luid or the dissipation of heat.
Figure 7 shows that with every increase in magnetic ield strength, ∆T-value constantly increased.
Although it was expected that trend of ∆T would follow that of the magnetic ield-strength, the parabolic relation in Figure 7 indicates that although ∆B is decreasing, ∆T increases with a rising slope, indicating the strong effect the magnetic ield has on thermal conduction.This could be because the low volume of Fe2O3-particles would tend to align faster even with minor changes in B, thereby increasing the rate of change of temperature as indicated by Table 17,18.However, the last two readings indicate a constant B value (0.25 mT) where the ∆T rises from 17.1 °C  19 °C.This rise in temperature would be due to heat generated by the current in the coils.Further, Figures 8,9 demonstrates a rise in ∆T for every 10s, indicated by an increasing gradient.This means that for every consequent 10s interval, the change in temperature is larger.Since 'k' varies inversely with temperature gradient, a decrease in the gradient as temperatures at End-B rise would increase conducting ability of the luid.Also considering conduction by Fe2O3-particles, aggregation and cluster-formation under a magnetic-ield would take time, especially in the model where particles are of the micro-scale in size.Applying the Brownian motion theory, it is perceived that the random motion gradually spreads from End A B. During this time, the kinetic energy of particles closer to End-A would constantly increase, causing    a gradual rise in the number of collisions per unit of time.Yet another explanation could be the strength of convection currents developed in water molecules.As the spirit lamp is left lit, the temperature at End-A would also constantly rise, possibly faster than at End-B.Therefore, increasing differences in temperature would gradually strengthen the convectional currents.
For the 50-turn solenoid, the gradient of the curves of 2.23V and 2.32V readings in Figure 8 start decreasing after 100s, when temperatures reach 40 °C.This could be credited to Fe2O3-particles cramping-analogous to the "zipperingeffect" due to the clumping of nanoparticles as demonstrated by Figure 2(e)-causing heat conduction in different directions, opposed to the unidirectional heat-low occurring in linear structures.However, the "clumping" wouldn't be due to the magnetic ield strength but because of the large mass and volume of the Fe2O3-particles.

Conclusion
The results agreed with empirical conclusions drawn up by Wensel J, who used Fe3O4-nano luids to demonstrate the chain formation using electrostatic forces, working along the Nano-Particle Clustering model.The works of Choi support this chain formation using magnetic ields.The increase in magnetic ield observably caused an increase in the rate of temperature-change at the cooler end, with an enhancement factor of the thermal conduction reaching 6 and 7.The variable resistance of solenoids possibly in luenced the effective current, thereby affecting the strength of produced magnetic ield and heat-dissipated.Therefore, conclusively determined that the enhanced conduction was due to nanoparticle theories and, in part, due to the solenoid's heat.

Figure 1 :
Figure 1: Random Movement of Particles and molecules in Brownian Motion [28].Figure 2: Types of Aggregate Cluster Nanoparticles tend to form [29].

Figure 2 :
Figure 1: Random Movement of Particles and molecules in Brownian Motion [28].Figure 2: Types of Aggregate Cluster Nanoparticles tend to form [29].

Figure 6 :
Figure 6: Magnetic Probe Reading and Multimeter Reading for 50 turns and 200 turns Solenoids.

Q=
Amount of heat supplied ∆ = Time-duration for which heat is supplied A = Cross-sectional area (of the tube) L = Length of tube ∆ = Temperature-gradient k = Thermal-conductivity constant Can be written as,
-13 below show the average initial and inal temperatures, the average change, and the rate of temperature change.Those readings are shown when extreme voltages were applied.Standard Deviation of Raw Temperature Change Trials at each 10s Interval: μ represents the mean average temperature at End-B for a given temperature;

3 cFigure 7 :
Figure 7: Change in Temperature versus Magnetic Field Strength as measured by the probe for the 50-turn solenoid.

Figure 8 :
Figure 8: Average Temperature measured at End B versus Time for diff erent magnetic fi eld strengths in the 50-turn solenoid.

Figure 9 :
Figure 9: Average Temperature measured at End B versus Time for diff erent magnetic fi eld strengths in the 200 turns solenoid.

Table 1 :
Length of each solenoid.

Table 2 :
Voltage v Magnetic Field for 50 turns solenoid with turn density 555.56 N/m.

Table 3 :
Voltage v Magnetic Field for 200 turns solenoid with turn density 1052.63N/m.

Table 4 :
Theoretical and Experimental values of Magnetic Field Strength for 50-turn solenoid.

Table 5 :
Theoretical and Experimental values of the Magnetic Field Strength for 200-turn solenoid.

Table 10 :
Temperature Measurements for the 1.05V and 0.12mT readings using a 200-turn solenoid.

Table 11 :
Temperature Measurements for the 4.20V and 0.31mT readings using a 200-turn solenoid.

Table 12 :
Temperature Measurements for the 0.66V and 0.12mT readings using a 50-turn solenoid.

Table 13 :
Temperature Measurements for the 2.32V and 0.25mT readings using a 50-turn solenoid.

Table 14 :
Standard Deviation for 6 trials at voltage = 2V for both solenoids.

Table 15 :
Average Temperature Measurements for each voltage for the 50-turn solenoid.

Table 17 :
Rate of Change of Temperature at End B for diff erent voltages applied across the 200-Turn solenoid.

Table 18 :
Rate of Change of Temperature at End B for diff erent voltages applied across the 50-Turn solenoid.

Table 19 :
Rate of Change of Temperature for both solenoids when no voltage is applied.

Table 20 :
Rates of Change of Temperature and Enhancement factors for the 200-Turn solenoid -with their uncertainties.

Table 21 :
Rates of Change of Temperature and Enhancement factors for the 50-Turn solenoid -with their uncertainties.