Theoretical Investigation Heat Transfer Mechanisms in Nanofluids and the Effects of Clustering on Thermal Conductivity

Transcription

1 International Journal o Bioscience, Biochemistry an Bioinormatics, Vol., No., March 01 Theoretical Investigation Heat Transer Mechanisms in Nanoluis an the Eects o Clustering on Thermal Conuctivity Mohamma Hai irahmaian, Azaeh Ebrahimi Abstract Nanoluis are suspensions o particles in luis that show signiicant enhancement o their properties at moest particle concentrations. Nanoluis, ue to anomalously high thermal conuctivity, are important in heat transer. Regaring the various moels o thermal conuctivity, we show that thermal ispersion moel or explaining lui heat transer results have better agreement with experimental results. Relationships between thermal conuctivity an various actors such as temperature, concentration, an particle size are also isplaye along with a iscussion on clustering. There is a brie iscussion on convection where the number o stuies is limite. There is research currently being perorme on the manipulation o the properties governing the thermal conuctivity o luis the particle size, shape, an surace area. Other actors that aect heat transer are the material o the particle, particle volume concentration, an the lui use. Although the interest in this relatively new class o luis has generate many experimental stuies, there is still isagreement over several aspects o heat transer in luis, primarily concerning the mechanisms behin the increase thermal conuctivity. Investigation o the eect o lui particle size an temperature on heat transer results in complicate trens ue to the opposing eects o thermal conuctivity an thermal ispersion on heat transer in terms o particle size epenence. Numerical results are compare with experimental an numerical ata in the literature an goo agreement is observe especially with experimental ata. Inex Terms Nanoluis, ispersion moel, heat transer, bounary conition. I. INTRODUCTION The growth o technology oun in high-tech inustries, such as microelectronics, transportation, an manuacturing, has create a cornucopia o ieas that woul have wie ranging eects on many obstacles acing toay s scientiic worl incluing energy eiciency, pollution, an reusability. However, there are many actors hinering urther evelopment in these inustries, one being the ability to rapily cool the proucts being use. Cooling is necessary or maintaining the operational perormance an reliability o new proucts, an as a result o increase heat loas an heat luxes cause by the increase in power an ecrease in eature sizes present in new proucts, the eman or a more eicient cooling process has increase ramatically in Manuscript receive January 3, 01; revise February 7, 01. Mohamma Hai irahmaian is with the Neyriz Branch, Islamic Aza University, Neyriz, Iran ( pirahmaian@gmail.com). Azaeh Ebrahimi is with the Department o physics, Shiraz Branch, Islamic Aza University, Shiraz, Iran. the last ecae. Consequently, more companies are beginning to invest more capital into the research o more eicient heat transer processes. The conventional metho or enhancing heat transer in a thermal system consists o increasing the heat transer surace area as well as the low velocity o the working lui [1]. The ispersion o soli particles in heat transer luis is a relatively new metho. Extene suraces such as ins an microchannels (with <100 μm) have alreay been use to increase the heat transer surace area. Their perormance in eectively removing as much as 1000 W/cm has shown a great improvement in the area o cooling. Heat transer can be enhance by employing various techniques an methoologies, such as increasing either the heat transer surace or the heat transer coeicient between the lui an the surace, that allow high heat transer rates in a small volume. Cooling is one o the most important technical challenges acing many iverse inustries, incluing microelectronics, transportation, solistate lighting, an manuacturing. Fluis behavior an spatial structure in the scale unamentally are ierent rom behavior an structure in micron an larger imensions. A lui is the suspension o particles in a base lui.. Stuies show that the lui has been conine or low in channels has non-continuum behavior an phenomena such as lux elaminate an unconventional ensity luctuation appear. Furthermore, the role o interaction between lux an channel is prominent an channel wall ynamic can be unamentally aect lui ynamics. With the recent improvements in technology, the prouction o particles with sizes on the orer o meters can be achieve with relative ease. As a consequence, the iea o suspening these particles in a base liqui or improving thermal conuctivity has been propose recently [], [3]. II. IMROVING HEAT TRANSFER EFFICIENCY Heat transer plays an important role in numerous applications. For example, in vehicles, heat generate by the prime mover nees to be remove or proper operation. Similarly, electronic equipments issipate heat, which requires a cooling system. Heating, ventilating, an air conitioning systems also inclue various heat transer processes. Heat transer is the key process in thermal power stations. In aition to these, many prouction processes 90

2 International Journal o Bioscience, Biochemistry an Bioinormatics, Vol., No., March 01 inclue heat transer in various orms; it might be the cooling o a machine tool, pasteurization o oo, or the temperature ajustment or triggering a chemical process. In most o these applications, heat transer is realize through some heat transer evices; such as, heat exchangers, evaporators, conensers, an heat sinks. Increasing the heat transer eiciency o these evices is esirable, because by increasing eiciency, the space occupie by the evice can be minimize, which is important or applications with compactness requirements. Furthermore, in most o the heat transer systems, the working lui is circulate by a pump, an improvements in heat transer eiciency can minimize the associate power consumption. Researches show that, there is signiicant iscrepancy in lui thermal conuctivity ata in the literature. There are several mechanisms propose to explain the thermal conuctivity enhancement o luis, such as Brownian motion o particles [4], clustering o particles [5] an liqui layering aroun particles. Due to the lack o systematic experimental ata in the literature, it is iicult to analyze the relative signiicance o these mechanisms. Most o the theoretical moels base on these mechanisms inclue some empirical constants. The eect o parameters such as temperature, particle volume raction an particle size istribution o particles stuie to heat transer enhancement with luis. It is possible to correctly preict experimental results to some extent by ajusting the values o these constants accoringly. On the other han, at present, a complete theoretical moel o thermal conuctivity that takes all o the parameters into account is not available. Fig. 1. Schematic illustration representing the clustering phenomenon. High conuctivity path results in ast transport o heat along large istances. It was shown that the thermal conuctivity was aecte by actors such as temperature, particle size, an ph level. Several theoretical moels have been propose to explain the behavior o particles. Many o these moels can be categorize as either static or ynamic moels. Static moels assume that the particles are stationary in the base lui, orming a composite material. In these moels, the thermal properties o luis are preicte through conuction base moels such as that o Maxwell. One such moel is the moiie Maxwell theory o Hamilton an Crosser which gives the enhancement o thermal conuctivity as where ( ) n (1) ( ) n, p an are the thermal conuctivity o the lui, particles an base lui, respectively. is the volume raction o particles in the mixture. Density o luis can be etermine by using the ollowing expression 1 ) () n ( An we can erive speciic heat o luis by c, n c 1 c n Dynamic moels assume that particles are in constant, ranom motion in the base lui (i.e., Brownian motion), as shown in Fig.. In the ynamic moels, it is believe that this ranom motion may be the main cause o the increase thermal properties associate with luis. Taking Brownian motion to be a key mechanism in the thermal properties o luis, Jang an Choi evelope a moel that portraye the relationship between conuctivity, temperature, concentration, an particle size. However, there is isagreement with the assumption that ranom motion plays a key role in the transer o heat in a lui. eblinski et al. propose an explanation o our possible actors or the heat transer mechanism in luis one o which was Brownian motion. However, the stuy conclue that the movement o particles ue to Brownian motion was too slow in transporting heat through a lui. To travel rom one point to another, a particle moves a large istance over many ierent paths in orer to reach a estination that may be a short istance rom the starting point. Thereore, the ranom motion o particles, no matter how agitate or energetic they may be, cannot be a key actor in the improvement o heat transer. Jang an Choi also came to a similar conclusion. Here, it was etermine that the collision between particles ue to ranom motion was a very slow process an coul, thereore, be neglecte in the calculation o thermal conuctivity. Although they contribute to the iea that collisions resulting rom Brownian motion i not contribute to the overall conuction o heat, Jang an Choi were able to evelop a ynamic moel that takes into account convection heat transer inuce by Brownian particles. The general expression erive in this stuy introuce our moes o energy transport in luis: 1) collision between base lui molecules (i.e., thermal conuctivity o base lui). ) thermal iusion in particles in luis. 3) collision between particles ue to Brownian motion (neglecte because it is a very slow process). 4) thermal interactions o ynamic particles with base lui molecules (once overlooke, this moe is now consiere to be a key actor in the relationship between conuctivity, temperature, an particle size). The major aspect o this moel was the introuction o (3) 91

3 International Journal o Bioscience, Biochemistry an Bioinormatics, Vol., No., March 01 the iea that particles can prouce a convection-like eect in a lui. The thermal conuctivity or their moel is given by B ke k B (1 ) k 3C1 k B Re r (4) where k e is the eective thermal conuctivity o the lui, k B is the base lui conuctivity, is the volume raction o the particles, k is the thermal conuctivity o the particles, C 1 is an empirical constant, B is the iameter o the base lui molecule, an is the iameter o a particle [1]. Re is the Reynols number eine by CR. M. Re (5) v where v is the ynamic viscosity o the base lui, an C R.M. is the ranom motion velocity o particles eine by D0 CR. M. (6) I B where I B is the mean-ree path o a base lui molecule. D 0 is the particle iusion coeicient given by D k T 3 b 0 (7) where μ is the viscosity o the base lui, T is the temperature o the base lui, an k b is the Boltzmann constant. The preictions presente by this moel are in excellent agreement with temperature-epenent conuctivity ata rom experiments involving luis containing Al O 3 particles. Moels erive rom Maxwell s equations ail to correlate with this type o experimental ata. Fig.. Interpretation o brownian motion III. CLUSTERING IN NANOFLUIDS One o the main obstacles encountere in microlui experiments was the agglomeration o particles. Even though research, such as that ocumente in [10, 11], shows a substantial increase in the thermal conuctivity o the base lui with the aition o particles, the movement towars practical applications has been hampere by the rapi settling o the particles. The settling o particles not only ecrease the overall heat transer o the lui (by ecreasing the eective surace area use or heat transer), but also le to the abrasion o suraces, clogging o microchannels, an a ecrease in pressure which resulte in an increase in pumping power. Although size particles have greatly reuce the problem o agglomerate particles, it still occurs an can hiner the thermal conuctivity o the lui, especially at concentrations over 5% agglomeration is more apparent when using oxie particles because they require a higher volume concentration compare to metallic particles in orer to achieve the same thermal conuctivity enhancement [1]. The tenency o particles to group together beore they are isperse in the lui is ue to the van er Waals orces. This is particularly seen in metallic particles since ipoles can occur easily in the molecules o these particles. The creation o ipoles prompts the attraction o other ipoles in the vicinity. The van er Waals orces stem rom the attraction o these ipoles, which can be inuce even in neutral particles. This attractive orce is consiere to be the main culprit behin the agglomeration o particles, especially in powers. To alleviate this problem, there have been various proposals or the manuacture an ispersion o particles in luis. One proposal involves aing surace treatments to the particles. It was seen that when copper particles were coate with a 10 nm thick organic layer a stable suspension woul be achieve in ethylene glycol [13]. There is research currently being conucte towars improving the two-step process to prouce well-isperse luis. Moreover, there exist a ew one-step processes that result in particles being uniormly isperse an stably suspene in the base lui. One such metho involves conensing copper powers irectly rom the vapor phase into lowing ethylene glycol in a vacuum chamber [14]. Documents [15 17] also show stable, well isperse suspensions in luis containing TiO, CuO, an Cu. In these experiments, a one-step process calle submerge arc particle synthesis was use to create the particles. Various techniques have been implemente to reuce the clustering o particles once they are in the lui [18, 19]. Usually, they involve some sort o agitation within the lui to separate the clusters into iniviual particles an keep them rom settling. These methos inclue the use o ispersants, changing the ph value o the base lui, an using ultrasonic vibration to excite the particles [16]. Among these methos, the most commonly use ones are ultrasonic vibration an the use o ispersants. Both techniques are relatively eective, but when using ispersants, the amount ae to the lui must be a very low percentage (usually 1% or less). This is one so as to minimize its eects on the thermal conuctivity o the lui. However, it shoul be note that loose particle chains may be responsible or some o the high thermal conuctivities o luis; see rasher et al. [19]. The Argonne National Laboratory also evelope the single-step an two-step processes or the ispersion o particles in a lui [1]. The single-step process consists o simultaneously making an ispersing the particles in the lui. The two-step metho separates the manuacture an ispersion o particles into two steps (particles are manuacture irst an then isperse into the base lui). 9

4 International Journal o Bioscience, Biochemistry an Bioinormatics, Vol., No., March 01 The two-step process is the more commonly use metho an is usually use in conjunction with ultrasonic vibration to reuce the amount o clustere particles in the lui. Analysis o the reviewe literature shows that there is still no conclusive theory concerning the prevention o clustering in the particle suspensions. Beore using luis in practical applications, the problem o clustering must be consistently kept to a minimum. When looking at long-term eects, clustering o the particles will eventually cause a ecrease in the thermal conuctivity o the lui an may also cause wear in the pipes or pumps through which it is lowing. Thereore, luis cannot be use in systems esigne or long-term use until this problem is solve. Otherwise, the use o luis may ecrease the lie expectancy o a system, even i it improves the overall eiciency. In the mean time, an optimization an esign problem persists when luis are use in the iel. associate calculations [6]. Fig. an Fig. 3 show the parameter o particle size in the lui thermal conuctivity that is observe with increasing particle size, thermal conuctivity increases, which results rom compliance with the experimental results is well. Investigation o the eect o lui particle size on heat transer results in complicate trens ue to the opposing eects o thermal conuctivity an thermal ispersion on heat transer in terms o particle size epenence. It is seen that i empirical constant C in isperse thermal conuctivity expression is suiciently small, the eect o thermal conuctivity ominates particle size epenence which results in increasing heat transer with ecreasing particle size. On the other han, i C is large, heat transer increases with increasing particle size. IV. CONCLUSION Convection heat transer is recognize within luis, but there is not enough research results publishe to evelop a moel that ully explains this behavior in luis. Furthermore, several o the research papers available seem to contraict each other as some ata shows an increase in convection as the particle volume raction is increase, while other ata shows eterioration in convective heat transer as the particle ensity an concentration were increase. Clustering still poses a problem in luis even though the occurrence o agglomeration has ecrease rom the previous micrometer-size particles suspensions. Various methos are currently use to keep particles rom clustering together, but in the long run, it is inevitable. Clustering is a problem thatmust be solve beore luis can be consiere or long-term practical uses. Although the increase in thermal conuctivity woul increase the eiciency o the systems where luis are use, the lie o the system may be ecrease over time i particles begin to orm clusters. In Fig. an Fig. 3 result o the numerical analysis or the hyroynamically ully evelope, thermally eveloping laminar low o Al O 3 /water lui insie a straight circular tube uner constant wall temperature an constant wall heat lux bounary conitions are presente. Numerical results are compare with experimental an numerical ata available in the literature. Eects o particle size, heating an cooling on heat transer enhancement are investigate. It is seen that application o the thermal ispersion moel to the governing energy equation provies meaningul results which are in agreement with the available experimental ata in the literature [4]. This can be consiere as an inication o the valiity o the thermal ispersion moel or lui heat transer analysis. Furthermore, it can be conclue that single phase analysis o lui heat transer is suiciently accurate or practical applications as long as variation o thermal conuctivity with temperature is taken into account in the Fig. 3. Comparison o the experimental results o the thermal conuctivity ratio or Al O /water lui. Fig. 4. Comparison o the experimental results o the thermal conuctivity ratio or Al O 3 /water lui. Fig. 3 an Fig. 4 show that the lui heat transer reveale that or the constant wall heat lux bounary conition. Investigation o the eects o cooling an heating on lui heat transer reveale that or the constant wall heat lux bounary conition, heat transer an associate enhancement is higher when low temperature is higher. When it comes to the constant wall temperature bounary conition, the ominant parameter that aects the heat transer is the wall temperature. As the wall temperature increases, the heat transer an the associate enhancement increases. These acts shoul be taken into account or the practical application o luis in heat transer evices. 93

5 International Journal o Bioscience, Biochemistry an Bioinormatics, Vol., No., March 01 the practical arenas o science in a more meaningul way. Fig. 5. Comparison o the experimental results o the thermal conuctivity ratio or Al O /water lui. Fig. 6. Comparison o the experimental results o the thermal conuctivity ratio or Al O /water lui. Nanoluis have the potential to open the oors to major avancements in many high-tech inustries where limits on cooling have pose limits on innovation. Since all other cooling options have been exhauste, luis are the only option let with the possibility o increasing heat transer capabilities o current systems. However, a ull unerstaning o the mechanisms behin the enhancement o thermal conuctivity in luis has not been reache an there is still isagreement between some o the experimental results. This lack o agreement has le to the generation o various moels. Once a general moel that ully explains the behavior o particle suspensions has been evelope, steps can be taken towars practical uses. Moreover, better techniques or the ispersion o particles in luis must be create so as to minimize clustering. When these objectives have been reache, luis will enter REFERENCES [1] S.. Das, S. U. S. Choi, W. Yu, an T. raeep, Nanoluis:Science an Technology, John Wiley an Sons,NJ, 008. [] H. Masua, A. Ebata,. Teramae, an N. Hishinuma, Netsu Bussei, vol. 4, no. 4, pp. 7-33, [3] S. U. S. Choi, The American Society o Mechanical Engineers, New York, FED-Vol. 31 / MD-Vol. vol. 66, pp , 1995 [4] Y. Li, W. Qu an J. Feng, Chinese hys. Lett., vol. 5, no. 9, pp , 008. [5] S.. Jang an S. U. S. Choi, Appl. hys. Lett., vol. 84, no. 1, pp , 004. [6] R. rasher,. Bhattacharya, an. E. helan, hys. Rev. Lett., vol. 94, no., 05901, 005. [7] C. H. Chon,. D. ihm, S.. Lee, an S. U. S. Choi, Appl. hys. Lett., vol. 87, no. 15, , 005. [8] S.. Das, N. utra,. Thiesen, an W. Roetzel, J. Heat Transer, vol. 15, no. 4, pp , 003. [9] C. H. Li an G.. eterson, J. Appl. hys., vol. 99, no. 8, pp , 006. [10] S. Lee, S. U.-S. Choi, S. Li, an J. A. Eastman, Measuring thermal conuctivity o luis containing oxie particles, Journal o Heat Transer, vol. 11, no., pp , [11] H. Xie, J.Wang, T. Xi, Y. Liu, F. Ai, an Q. Wu, Thermal conuctivity enhancement o suspensions containing size alumina particles, Journal o Applie hysics, vol. 91, no. 7, pp , 00. [1] W. Yu, D. M. France, J. L. Routbort, an S. U. S. Choi, Review an comparison o lui thermal conuctivity an heat transer enhancements, Heat Transer Engineering, vol. 9, no. 5, pp , 008. [13]. S. Suslick, M. Fang, an T. Hyeon, Sonochemical synthesis o iron collois, Journal o the American Chemical Society, vol. 118, no. 47, pp , [14] J. A. Eastman, S. U. S. Choi, S. Li, W. Yu, an L. J. Thompson, Anomalously increase eective thermal conuctivities o ethylene glycol-base luis containing copper particles, Applie hysics Letters, vol. 78, no. 6, pp , 001. [15] H. Chang, T. T. Tsung, an Y. C. Yang, et al., Nanoparticle suspension preparation using the arc spray particle synthesis system combine with ultrasonic vibration an rotating electroe, International Journal o Avance Manuacturing Technology, vol. 6, no. 5-6, pp , 005. [16] C.-H. Lo, T.-T. Tsung, L.-C. Chen, C.-H. Su, an H.-M. Lin, Fabrication o copper oxie lui using submerge arc particle synthesis system (SANSS), Journal o Nanoparticle Research, vol. 7, no. -3, pp , 005. [17] C.-H. Lo, T.-T. Tsung, an L.-C. Chen, Shape-controlle synthesis o Cu-base lui using submerge arc particle synthesis system (SANSS), Journal o Crystal Growth, vol. 77, no. 1 4, pp , 005. [18] Q. Cao an J. Tavares, Dual-lasma Synthesis o Coate Nanoparticles an Nanoluis, November 006, [19] S. M. S. Murshe,. C. Leong, an C. Yang, Thermophysical an electrokinetic properties o luis a critical review, Applie Thermal Engineering, vol. 8, no , pp ,