ORIGINAL_ARTICLE
Simulation of Micro-Channel and Micro-Orifice Flow Using Lattice Boltzmann Method with Langmuir Slip Model
Because of its kinetic nature and computational advantages, the Lattice Boltzmann method (LBM) has been well accepted as a useful tool to simulate micro-scale flows. The slip boundary model plays a crucial role in the accuracy of solutions for micro-channel flow simulations. The most used slip boundary condition is the Maxwell slip model. The results of Maxwell slip model are affected by the accommodation coefficient significantly, but there is not an explicitly relationship between properties at wall and accommodation coefficient. In the present wok, Langmuir slip model is used beside LBM to simulate micro-channel and micro-orifice flows. Slip velocity and nonlinear pressure drop profiles are presented as two major effects in such flows. The results are in good agreement with existing results in the literature.
http://tpnms.usb.ac.ir/article_2858_c4f0739951c5403457253fd383ef8d73.pdf
2016-12-24T11:23:20
2018-09-21T11:23:20
1
8
10.7508/tpnms.2017.01.001
Lattice Boltzmann method
Langmuir slip model
Micro-channel
Micro-orifice
A. R.
Rahmati
true
1
Department of Mechanical Engineering, University of Kashan, Kashan, I. R.Iran
Department of Mechanical Engineering, University of Kashan, Kashan, I. R.Iran
Department of Mechanical Engineering, University of Kashan, Kashan, I. R.Iran
AUTHOR
R.
Ehsani
true
2
Department of Mechanical Engineering, University of Kashan, Kashan, I. R.Iran
Department of Mechanical Engineering, University of Kashan, Kashan, I. R.Iran
Department of Mechanical Engineering, University of Kashan, Kashan, I. R.Iran
AUTHOR
[1] M. Gad-el Hak: The fluid mechanics of micro devices, ASME journal of fluid engineering 121 (1999) 5-33.
1
[2] G. Karniadakis, A. Beskok, N. Aluru, (2005), Microflows and nano-flows, Springer, New York.
2
[3] D.A. Perumal, G.V.S. Kumar, A.K. Daas: Application of Lattice Bpltzmann method to fluid flows in micro-geometries, CFD letters 2-2 (2009) 75-83.
3
[4] C.M. Ho, Y.C. Tai: Micro-electro-mechanical system (MEMS) and fluid flows, Annual review of fluid mechanics 30 (1998) 579-612.
4
[5] J. Zhang: Lattice Boltzmann method for microfluidics: models and applications, Micro fluid nanofluid 10 (2011) 1-28.
5
[6] Z.W. Tian, C. Zho, H.J. Liu, Z.L. Guo: Lattice Boltzmann scheme for simulating thermal microflow, Physica A 385 (2007) 59-68.
6
[7] C.Y. Lim, X.D. Niu, T.T. Chew: Application of Lattice Boltzmann method to simulate microchannel flows, Physics of fluids 14-7 (2002) 2299-2308.
7
[8] C. Cercignani, S. Lorenzani: Variational approach to gas flows in micro-channels, Journal of physics of fluids 16 (2004) 3426-3737.
8
[9] W.M. Zhang, G. Meng, X. Wei: A review on slip models for gas micro-flows, Micro-fluidics and nano-fluidics 13-6 (2012) 845-882.
9
[10] H.M. Kim, D. Kin, W.T. Kim: Langmuir slip model for air bearing simulation using the Lattice Boltzmann method, IEEE transactions on magnetic 43-6 (2007) 2244-2246.
10
[11] H.I. Choi, D.H. Lee: Complex micro-scale flow simulations using Langmuir slip condition, Numerical heat transfer A 48 (2005) 407-425.
11
[12] E. Fathi, I.Y. Akkutlu: Lattice Boltzmann method for simulation of shale gas transport in kerogen, Society of Petroleum Engineers conference (2013), Colorado, USA.
12
[13] R.S. Myong: Gaseous slip models based on the Langmuir adsorption isotherm, Physics of fluids 16-1 (2004) 104-117.
13
[14] X. Nie, G.D. Doolen, Sh. Chen: Lattice Boltzmann simulation of fluid flows in MEMS, Journal of statistical physics 107-112 (2001) 279-289.
14
[15] G.H. Tang, W.Q. Tao, Y.I. He: Lattice Boltzmann method for simulating gas flows in micro-channels, International journal of modern physics C 15-2 (2004) 335-347.
15
[16] Y. Zhang, R. Qin, D.R. Emerson: Lattice Boltzmann simulation of rarefied gas flows in micro-channels,Physical review E 71 (2005) 1-4.
16
[17] E. Shirani, S. Jafari: Application of LBM in simulation of flow in simple micro-geometries and micro-porous media, African physical review 1 (2007).
17
[18] R.S. Myong, J.M. Reese, R.W. Barber, D.R. Emerson: Velocity slip in micro-scale cylindrical qouette flow: the Langmuir model, Physics of fluids 17-8 (2005) 1-11.
18
[19] Sh. Chen, Zh. Tian: Simulation of micro-channel flow using the lattice Boltzmann method, Physica A388 (2009) 4803-4810.
19
[20] Sh. Chen, Zh. Tian: Simulation of thermal microchannel flow using the lattice Boltzmann method with Langmuir slip model, International journal of heat and fluid flow 31 (2010) 227-235.
20
[21] S. Succi, (2001), The Lattice Boltzmann equation: for fluid dynamics and beyond, Oxford university press,New York.
21
[22] X. Liu, Zh. Guo, A Lattice Boltzmann study of gas flows in a long micro-channel, Computers and mathematics with applications 65 (2013) 186-193.
22
[23] R.S. Myong, D.A. Lockerby, J.M. Reese, The effect of gaseous slip on micro-scale heat transfer: an extended Gratz problem, International journal of heat and mass transfer 49 (2006) 2502-2513.
23
[24] A. Beskok, G.E. Karniadakis, W. Trimmer: Rarefaction and compressibility effects in gas microflows, Journal of fluid engineering 118-3 (1996) 448-456.
24
[25] E.B. Arkilic, M.A. Schmidt, K.S. Breuer, Gaseous slip flow in long micro-channels, Journal of Microelectro-mechanical systems 6-2 (1997) 167-178.
25
[26] T. Reis, P.J. Dellar: Lattice Boltzmann simulations of pressure-driven flows in microchannels using Navier–Maxwell slip boundary conditions, Physics of Fluids 24 (2012) 1-18.
26
[27] M. Wang, Zh. Li: Simulations for gas flows in microgeometries using the direct simulation Monte Carlo method, International Journal of Heat and Fluid Flow 25 (2004) 975–985.
27
ORIGINAL_ARTICLE
MHD boundary layer flow and heat transfer of Newtonian nanofluids over a stretching sheet with variable velocity and temperature distribution
Laminar boundary layer flow and heat transfer of Newtonian nanofluid over a stretching sheet with the sheet velocity distribution of the form (Uw=CXβ) and the wall temperature distribution of the form (Tw= T∞+ axr) for the steady magnetohydrodynamic(MHD) is studied numerically. The governing momentum and energy equations are transformed to the local non-similarity equations using the appropriate transformations. The set of ODEs are solved using Keller–Box implicit finite-difference method. The effects of several parameters, such as magnetic parameter, volume fraction of different nanoparticles (Ag, Cu, CuO, Al2O3 and TiO2), velocity parameter, Prandtl number and temperature parameter on the velocity and temperature distributions, local Nusselt number and skin friction coefficient are examined. The analysis reveals that the temperature profile increases with increasing magnetic parameter and volume fraction of nanofluid. Furthermore, it is found that the thermal boundary layer increases and momentum boundary layer decreases with the use of water based nanofluids as compared to pure water. At constant volume fraction of nanoparticles, it is also illustrated that the role of magnetic parameter on dimensionless temperature becomes more effective in lower value.
http://tpnms.usb.ac.ir/article_2859_0a3f50221b07415cc4613b1b823ec9f5.pdf
2016-12-24T11:23:20
2018-09-21T11:23:20
9
22
10.7508/tpnms.2017.01.002
Boundary Layer Flow
MHD
Nanofluid
Stretching Sheet
P.
Elyasi
true
1
Mechanical Engineering Department,Faculty of Mechanical Engineering, Shahrekord University, Shahrekord, I. R.Iran
Mechanical Engineering Department,Faculty of Mechanical Engineering, Shahrekord University, Shahrekord, I. R.Iran
Mechanical Engineering Department,Faculty of Mechanical Engineering, Shahrekord University, Shahrekord, I. R.Iran
AUTHOR
A. R.
Shateri
true
2
Mechanical Engineering Department,Faculty of Mechanical Engineering, Shahrekord University, Shahrekord, I. R.Iran
Mechanical Engineering Department,Faculty of Mechanical Engineering, Shahrekord University, Shahrekord, I. R.Iran
Mechanical Engineering Department,Faculty of Mechanical Engineering, Shahrekord University, Shahrekord, I. R.Iran
AUTHOR
[1] U.S. Choi: Enhancing thermal conductivity of fluids with nanoparticle Developments and Applications of Non-Newtonian Flows 231 (1995) 99-105.
1
[2] S. Choi, Z. Zhang, W. Yu, F. Lockwood, E. Grulke: Anomalously thermal conductivity enhancement in nanotube suspensions, Journal of Applied Physics Letters 79 (2001) 2252–2254.
2
[3] S. Z. Heris, M. N. Esfahany, S. Gh. Etemad: Experimental Investigation of Convective Heat Transfer of Al2O3/Water Nanofluid in Circular Tube, International Journal of Heat and Fluid Flow 28 (2006) 203–210.
3
[4] M. Hojjat, S. Etemad, R. Bagheri: Laminar heat transfer of non-Newtonian nanofluids in a circular tube, Korean Journal of Chemical Engineering 27 (2010) 1391–1396.
4
[5] B.C. Pak, Y. Cho: Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Experimental Heat Transfer 11 (1998) 151-170.
5
[6] Y. Xuan, Q. Li: Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer 125 (2003) 151-155.
6
[7] A. Ahuja: Augmentation of heat transport in laminar flow of polystyrene suspensions, Journal of Applied Physics 46 (1975) 3408-3425.
7
[8] J. Buongiorno: Convective transport in nanofluids, Journal of Heat Transfer 128 (2006) 240-250.
8
[9] MA Fadzilah, R Nazar, M. Arifin, I. Pop: MHD boundary-layer flow and heat transfer over a stretching sheet with induced magnetic field. Journal of Heat Mass Transfer 47 (2011) 155–162.
9
[10] A. Ishak, R. Naza, I. Pop: MHD boundary-layer flow due to a moving extensible surface, Journal of Engineering Mathematics 62 (2008) 23–33.
10
[11] A.V. Kuznetsov, D.A Nield: Natural convective boundary-layer flow of a nanofluid past a vertical plate, International Journal of Thermal Sciences 49 (2010) 243-247.
11
[12] N. Bachok, A.Ishak, I.Pop: Boundary-layer flow of nanofluids over a moving surface in a flowing fluid, International Journal of Thermal Sciences 49 (2010) 1663-1668.
12
[13] W.Ibrahim, B. Shanker: Unsteady MHD boundarylayer flow and heat transfer due to stretching sheet in the presence of heat source or sink, International Journal of Computers & Fluids 70 (2012) 21-28.
13
[14] A. Ishak, R. Naza, I. Pop: Heat transfer over a stretching surface with variable heat flux in microplar fluids. Physics Letters A 5 (2008) 559–61.
14
[15] A. Noghrehabadi, R. Pourrajab, M. Ghalambaz: Effect of partial slip boundary condition on the flow and heat transfer of nanofluids past stretching sheet prescribed constant wall temperature, International Journal of Thermal Sciences 54 (2012) 253-261
15
[16] M. Narayana, P. Sibanda: Laminar flow of a nanoliquid film over an unsteady stretching sheet, International Journal of Heat and Mass Transfer 55 (2012) 7552-7560.
16
[17] A. Aziz, W.A. Khan: Natural convective boundary layer flow of a nanofluid past a convectively heated vertical plate, International Journal of Thermal Sciences 52 (2012) 83-90.
17
[18] L. Zheng, C. Zhang, X. Zhang, J. Zhang: Flow and radiation heat transfer of a nanofluid over a stretching sheet with velocity slip and temperature jump in porous medium, Journal of the Franklin Institute 350 (2013) 990–1007.
18
[19] P. Rana, R. Bhargava: Flow and heat transfer of a nanofluid over a nonlinearly stretching sheet: A numerical study, Communications in Nonlinear Science and Numerical Simulation 17 (2012) 212–226.
19
[20] A. Mahdy: Unsteady mixed convection boundary layer flow and heat transfer of nanofluids due to stretching sheet, Nuclear Engineering and Design 249 (2012) 248– 255.
20
[21] K.V. Prasad, P.S. Pal Dulal, Datti: MHD power-law fluid flow and heat transfer over a non-isothermal stretching sheet, Communications in Nonlinear Science and Numerical Simulation 14 (2009) 2178–2189.
21
[22] H. Xu, S. Liao: Laminar flow and heat transfer in the boundary-layer of non-Newtonian fluids over a stretching flat sheet, Computers and Mathematics with Applications 57 (2009) 1425_1431.
22
[23] N. Masoumi, N. Sohrabi, A.A. Behzadmehr: New model for calculating the effective viscosity of nanofluids, Journal of Physics D: Applied Physics 42 (2009) 055501–055506.
23
[24] C.H. Chon, K.D. Kihm, S.P. Lee, S.U. Choi: Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement, Journal of Applied Physics Letters 87 (2005) 153107–153110.
24
[25] H.A. Mintsa, G. Roy, C.T. Nguyen, D. Doucet: temperature dependent thermal conductivity data for water-based nanofluids, International Journal of Thermal Sciences 48 (2009) 363–371.
25
[26] C.T Nguyen., F. s Desgrange, G. Roy, T. Galanis, S. Boucher, H.A.n Mintsa: Temperature and particlesize dependent viscosity data for waterbased nanofluids–hysteresis phenomenon, International Journal of Heat Fluid Flow 28 (2009) 1492–1506.
26
[27] Kh. Khanafer, K. Vafai: A critical synthesis of thermophysical characteristics of nanofluids, International Journal of Heat Mass Transfer 54 (2011) 4410–4428.
27
[28] D.A.G. Bruggeman: Berechnung verschiedener physikalischer konstanten von heterogenen substanzen, I. Dielektrizitatskonstanten und leitfahigkeiten der mischkorper aus isotropen substanzen, Annals of Physics 24 (1935) 636– 679.
28
[29] J.C. Maxwell Garnett: Colours in metal glasses and in metallic films, Philos. Trans. R. Soc. Lond. A203 (1904). 385–420.
29
[30] H.C. Brinkman: The viscosity of concentrated suspensions and solutions. Journal of Chemical Physics 20 (1952) 571–581.
30
[31] S.E.B. Maiga, S.J. Palm, C.T.Nguyen, G. Roy, N. Galanis: Heat transfer enhancement by using nanofluids in forced convection flow, International Journal of Heat and Fluid Flow 26 (2005) 530–546.
31
[32] E. Abu-Nada: Application of nanofluids for heat transfer enhancement of separated flows encountered in a backward facing step, International Journal of Heat Fluid Flow 29 (2008) 242–249.
32
[33] A. Akbarinia, A. Behzadmehr: Numerical study of laminar mixed convection of a nanofluid in horizontal curved tubes, Journal of Applied Thermal Engineering 27 (2007) 1327–1337.
33
[34] T. Cebeci, J. Cousteix: Modeling and Computation of Boundary-Layer Flows, Second Edition, Horizons Publishing Inc., Long Beach, California-Springer-Verlag, (2005).
34
[35] A. Ishak, R. Nazar, I. Pop: Boundary layer flow and heat transfer over an unsteady stretching vertical surface Meccanica 44 (2009) 369–375.
35
[36] M.E.Ali: Heat transfer characteristics of a continuous stretching surface, Journal of Heat Mass Transfer 29 (1904) 227–234.
36
[37] L.J. Grubka, K.M. Bobba: Heat transfer characteristics of a continuous, stretching surface with variabletemperature, ASME Journal of Heat Transfer 107 (1985) 248–250.
37
ORIGINAL_ARTICLE
An experimental investigation on the performance of a symmetric conical solar collector using SiO2/water nanofluid
One of the effective methods to improve the thermal efficiency of solar collectors is using nanofluids as the coolant. The present study experimentally investigated the effect of SiO2/water nanofluid with 1% mass fraction on the performance of a symmetric collector, i.e. conical solar collector. The conical solar collector with 1 m2 area and normal to the earth was tested in Ahvaz, a city in the southwest of Iran. The experiments performed under ASHRAE standard without any surfactants based on the solar radiation, mass flow rate, and temperatures variation. Results demonstrated that the thermal efficiency and the temperature performance can be enhanced through SiO2/water nanofluid in comparison with pure water. The maximum efficiency and outlet-inlet difference temperature of conical collector using nanofluid was about 62% and 6.8 0C respectively. Moreover, the collector behaviors are more efficient with the nanofluid than with pure water in the higher values of the flow rate and sun radiation.
http://tpnms.usb.ac.ir/article_2860_059da64dcb086e86f51c921462ec21e8.pdf
2016-12-24T11:23:20
2018-09-21T11:23:20
23
29
Conical solar collector
SiO2/water nanofluid
Solar radiation
Flow rate
efficiency
A.R.
Noghrehabadi
true
1
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
AUTHOR
E.
Hajidavalloo
true
2
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
AUTHOR
M.
Moravej
true
3
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
Department of Mechanical Engineering, Shahid Chamran University of Ahvaz, Ahvaz, Iran
AUTHOR
[1] M. Abdolzadeh, M. A. Mehrabian: The optimal slope angle for solar collectors in hot and dry parts of Iran,Energy Sources 34 (2012) 519-530.
1
[2] Y. Tian, C. Y. Zhao, A review of solar collectors and thermal energy storage in solar thermal applications, Applied Energy 104 (2013) 538-553.
2
[3] S. Riffat, X. Zhao P. S. Doherrty: Developing a theoretical model to investigate thermal performance of a thin membrane heat-pipe solar collector, Applied Thermal Engineering 25(2005) 899-91.
3
[4] JA. Duffie, WA. Beckman: Solar Engineering of Thermal Processes, New York Wiley (2013).
4
[5] S. Kalogirou: Solar thermal collectors and applications, Progress in Energy and Combustion Science 30 (2004) 231-295.
5
[6] S. Kalogirou: Prediction of flat plate collector performance parameters using artificial neural networks, Solar Energy 80 (2006) 248-259.
6
[7] Z. Chen, S. Furbo, B. Perers, J. Fan A. Andersen: Efficiencies of flat plate solar collectors at different flow rates, Energy Procedia 30 (2012) 65-72.
7
[8] N. Kumar, T. Chavda, HN. Mistry: A truncated pyramid non tracking type multipurpose solar cooker/hot water system, Applied Energy 87 (2010) 471-477.
8
[9] LM. Ayompe, A. Duffy: Analysis of the thermal performance of a solar water heating systemwith flat plate collectors in a temperate climate, Applied Thermal Engineering 58 (2013) 447-454.
9
[10] T. Yousefi, E. Shojaeizadeh, F. Veysi, S. Zinadini: An experimental investigation on the effect of pH variation of MWCNT-H2O nanofluid on the efficiency of flat plate solar collector, Solar Energy 86 (2012) 771-779.
10
[11] D. Han, Z. Meng, D. Wu, C. Zhang, H. Zhu: Thermal properties of carbon black aqueous nanofluids for solar absorption, Nanoscale Research Letter 6 (2011) 1-7.
11
[12] H. Tyagi, P. Phelan, R. Prasher: Predited efficiency of a low-temperature nanfluid-based direct absorption solar collector, Journal of Solar Energy Engineering 131 (2009) 1-7.
12
[13] RA. Taylor, PE. Phelan, TP. Otanicar, CA. Walker, M. Nguyen, S. Trimble, RS. Parsher: Applicability of nanofluids in high flux solar collectors, Journal of Renewable and Sustainable Energy 3 (2011) 023104.
13
[14] SU. Choi, ZG. Zhang: Anomalous thermal conductivity enhancement in nanotube suspensions, Applied Physics Letter 79(2001) 2252-2254.
14
[15] TP. Otanicar, PE. Phelan, RS. Parsher, G. Rosengarten, RA. Taylor: Nanofluid-based direct absorption solar collector, Journal of Renewable and Sustainable Energy 2 (2010) 033102.
15
[16] TP. Otanicar, J. Golden: Comparative environmental and economic analysis of conventional and nanofluid solar hot water technologies, Environmental Science and Technology 43 (2009) 6082-6087.
16
[17] T. Yousefi, E. Shojaeizadeh, F. Veysi, S. Zinadini: An experimental investigation on the effect of Al2O3-H2O nanofluid on the efficiency of flat plate solar collector, Renewable Energy 39 (2012) 293-298.
17
[18] T. Yousefi, E. Shojaeizadeh, F. Veysi, S. Zinadini: An experimental investigation on the effect of MWCNT-H2O nanofluid on the efficiency of flatplate solar collectors, Experimental Thermal and Fluid Science 39 (2012) 207-212.
18
[19] L. Lu, ZH. Liu, HS. Xiao: Thermal performance of an open thermosyphon using nanofluids for hightemperature evacuated tubular solar collectors: Part 1: Indoor experiment, Solar Energy 85 (2011) 379-387.
19
[20] O. Mahian, A. Kianifar, AZ. Sahin, S. Wongwises: Performance analysis of a minichannel-based solar collector using different nanofluids, Energy Conversion and Management 88 (2014)129-138, 2014.
20
[21] R. Nasrin, MA. Alim: Modeling of a Solar Water Collector with Water-Based Nanofluid Using Nanoparticles, Heat Transfer-Asian Research 43 (2014) 270-287.
21
[22] K. Goudarzi, E. Shojaeizadeh, F. Nejati: An experimental investigation on the simultaneous effect of CuO–H2O nanofluid and receiver helical pipe on the thermal efficiency of a cylindrical solarcollector, Applied Thermal Engineering 73 (2014) 1236-1243.
22
[23] E. Shojaeizadeh, F. Veysi, A. Kamandi: Exergy efficiency investigation and optimization of an Al2O3–water nanofluid based Flat-plate solar collector, Energy and Building 101 (2015) 12-23.
23
[24] HK. Gupta, GD. Agrawal, J. Mathur: Investigation for effect of Al2O3-H2O nanofluid flow rate on the efficiency of direct absorption solar collector, Solar Energy 118 (2015) 390-396.
24
[25] ASHRAE Standard 93-86, Methods of testing and determine the thermal performance of solar collectors, ASHRAE: Atlanta (2003).
25
[26] D. Rojas, J. Beermann, SA. Klein, DT. Reindl: Thermal performance testing of flat-plate collectors, Solar Energy 82 (2008) 746-757.
26
[27] TL. Bergman, T. L, Effect of reduced specific heats of nanofluids on single phase, laminar internal forced convection, International Journal of Heat and Mass Transfer 52 (2009) 1240-1244.
27
[28] SQ. Zhou, R. Ni: Measurement of the specific heat capacity of water-based Al2O3 nanofluid, Applied Physics Letter 92 (2008) 1-3.
28
[29] M. Faizal, R. Saidur, S. Mekhilef, MA. Alim: Energy economic and environmental analysis of metal oxides nanofluid for flat-plate solar collector, Energy Conversion and Management 76 (2013)162-168.
29
[30] RB. Abernethy, RP. Benedict, RB. Dowdell: ASME measurement uncertainty, ASME paper (1983) 83- WA/FM-3.
30
[31] AC. Mintsa, M. Medale, C. Abid: Optimization of the design of a polymer flat plate solar collector, Solar Energy 87 (2013) 64-75.
31
[32] SK. Das, N. Putra, P. Thiesen, W. Roetzel: Temperature dependence of thermal conductivity enhancement for nanofluids, Journal of Heat Transfer, vol. 125 (2003) 567-574.
32
[33] P. Keblinski, P., SR. Phillpot, SU. Choi, JA. Eastman: Mechanisms of heat flow in suspensions of nano-sized particles (nanofluids), International Journal of Heat and Mass Transfer 45 (2002) 855-863.
33
[34] Y. Xuan, Q. Li: Heat transfer enhancement of nanofluids, International Journal of Heat and Fluid Flow 21 (2000) 58-64.
34
[35] C. Cristofari, G. Notton, P. Poggi, A. Louche: modeling and performance of a copolymer solar water heating collector, Solar Energy 72 (2002) 99-112.
35
[36] Y. Xuan, Q. Li, W. Hu: Aggregation structure and thermal conductivity of nanofluids, AIChE Journal, vol. 49 (2003) 1038-1043.
36
[37] P. Bhattacharya, SK. Saha, A. Yadav, PE. Phelan, RS. Parsher: Brownian dynamics simulation to determine the effective thermal conductivity of nanofluids, Journal of Applied Physics 95 (2004) 6492-6494.
37
[38] J. Koo, C. Kleinstreuer: A new thermal conductivity model for nanofluids, Journal of Nanoparticle Research 6 (2004) 577-588.
38
ORIGINAL_ARTICLE
Mixed convection fluid flow and heat transfer and optimal distribution of discrete heat sources location in a cavity filled with nanofluid
Mixed convection fluid flow and heat transfer of water-Al2O3 nanofluid inside a lid-driven square cavity has been examined numerically in order to find the optimal distribution of discrete heat sources on the wall of a cavity. The effects of different heat source length, Richardson number and Grashof number on optimal heat source location has been investigated. Moreover, the average Nusselt number on the heat source for two models of nanofluid, constant properties and variable properties, are compared. The obtained results showed that by decreasing the Richardson number and increasing the Grashof number, heat transfer rate decreases. Also by reducing the Richardson number, optimal heat source location move to the top of the wall and with augmentation of Richardson number, heat source optimal location move to the middle of the wall. Furthermore, the overall heat transfer increases by increasing nanoparticles volume fraction. Moreover, it was found that for two different models of nanofluids and in Ri=1, the values of the average Nusselt number are close together.
http://tpnms.usb.ac.ir/article_2861_36e0aadbff3320fa12c993e320991c4a.pdf
2016-12-24T11:23:20
2018-09-21T11:23:20
30
43
10.7508/tpnms.2017.01.004
Mixed convection
Nanofluids
Heat sources
Optimization
A. A
Abbasian Arani
true
1
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
AUTHOR
M.
Abbaszadeh
true
2
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
AUTHOR
A.
Ardeshiri
true
3
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
Mechanical Engineering Department, University of Kashan, Kashan, I. R.Iran
AUTHOR
[1] T. Basak, S. Roy, P.K. Sharma, I. Pop: Analysis of mixed convection flows within a square cavity with uniform and non-uniform heating of bottom wall, International Journal of Thermal Science 48 (2009) 891–912.
1
[2] G. Guo, M.A.R. Sharif: Mixed convection in rectangular cavities aspect ratios with moving isothermal sidewalls and constant flux heat source on the bottom wall, International Journal of Thermal Science 43 (2004) 465–475.
2
[3] A. Fattahi, M. Alizadeh: Numerical Investigation of Double- Diffusive Mixed Convective Flow in a Lid-Driven Enclosure Filled with Al2O3-Water Nanofluid, Transport Phenomena in Nano and Micro Scales 2 (2014) 65-77.
3
[4] A. Zare Ghadi, M. Sadegh Valipour: Numerical Study of Hydro-Magnetic Nanofluid Mixed Convection in a Square Lid-Driven Cavity Heated From Top and Cooled From Bottom, Transport Phenomena in Nano and Micro Scales 2 (2014) 29-42.
4
[5] B. Jafarian, M. Hajipour, R. Khademi: Conjugate Heat Transfer of MHD non-Darcy Mixed Convection Flow of a Nanofluid over a Vertical Slender Hollow Cylinder Embedded in Porous Media, Transport Phenomena in Nano and Micro Scales 4 (2016) 1-10.
5
[6] H. R. Ehteram, A. A. Abbasian Arani, G. A. Sheikhzadeh, A. Aghaei, A. R. Malihi: The effect of various conductivity and viscosity models considering Brownian motion on nanofluids mixed convection flow and heat transfer, TransportPhenomena in Nano and Micro Scales 4 (2016) 19-28.
6
[7] F. Vahidinia, M. Rahmdel: Turbulent Mixed Convection of a Nanofluid in a Horizontal Circular Tube with Non-Uniform Wall Heat Flux Using a Two-Phase Approach, Transport Phenomena in Nano and Micro Scales 3 (2015) 106-117.
7
[8] A. Aghaei, H. Khorasanizadeh, G. Sheikhzadeh, M. Abbaszadeh: Numerical study of magnetic field on mixed convection and entropy generation of nanofluid in a trapezoidal enclosure, Journal of Magnetism and Magnetic Materials 403 (2016) 133–145.
8
[9] A. Rahmati, A. R. Roknabadi, M. Abbaszadeh: Numerical simulation of mixed convection heattransfer of nanofluid in a double lid-driven cavity using lattice Boltzmann method, Alexandria Engineering Journal Available online 20 September 2016, http://dx.doi.org/10.1016/j.aej.2016.08.017.
9
[10] M.A.R. Sharif: Laminar mixed convection in shallow inclined driven cavities with hot moving lid on top and cooled from bottom, Applied Thermal Engineering 27 (2007) 1036–1042.
10
[11] R.K. Tiwari, M.K. Das: Heat transfer augmentation in a two-sided lid-driven differentially heated square cavity utilizing nanofluids, International Journal Heat and Mass Transfer 50 (2007) 2002–2018.
11
[12] M. Muthtamilselvan, P. Kandaswamy, J. Lee: Heat transfer enhancement of Copper–water nanofluids in a lid-driven enclosure, Communications in Nonlinear Science Numerical Simulation 15 (2010) 1501–1510.
12
[13] A. Arefmanesh, M. Mahmoodi: Effects of uncertainties of viscosity models for Al2O3–water nanofluid on mixed convection numerical simulations, International Journal of Thermal Sciences 50 (2011) 1706–1719.
13
[14] P. Kandaswamy, S. Sivasankaran, N. Nithyadevi: Buoyancy-driven convection of water near its density maximum with partially active vertical walls, International Journal of Heat and Mass Transfer 50 (2007) 942-948.
14
[15] M. Mahmoodi: Mixed convection inside nanofluid filled rectangular enclosures with moving bottom wall, Thermal Science 15 (2011) 889–903.
15
[16] S. Mazrouei Sebdani, M. Mahmoodi, S.M. Hashemi: Effect of nanofluid variable properties on mixed convection in a square cavity, International Journal of Thermal Sciences 52 (2012) 112–126.
16
[17] A.M. Amiri, Kh.M. Khanafer, I. Pop: Numerical simulation of combined thermal and mass transport in a square lid-driven cavity, International Journal of Thermal Sciences 46 (2007) 662-671.
17
[18] A. Arefmanesh, A. Aghaei, H. Ehteram: Mixed convection heat transfer in a CuO–water filled trapezoidal enclosure, effects of various constant and variable properties of the nanofluid, Applied Mathematical Modelling 40 (2016) 815–831.
18
[19] A. Aghaei, GA. Sheikhzadeh, H. Ehteram, M. Hajiahmadi: Numerical Investigation of Mixed Convection Fluid Flow, Heat Transfer and Entropy Generation in Triangular Enclosure Filled with a Nanofluid, Journal of Applied Fluid Mechanics 9 (2016) 147-156.
19
[20] M. Najafi, M. Nikfar, A. Arefmanesh: Inclination angle implications for fluid flow and mixed convection in complex geometry enclosure-meshless numerical analyses, Journal of Theoretical and Applied Mechanics 53 (2015) 519-530.
20
[21] A. Saha, T. Malik: Mixed convection flow and heat transfer through a horizontal channel with surface mounted obstacles, Journal of Enhanced Heat Transfer 19 (2012) 313-329.
21
[22] S. H. Hussain, Q.R. Abd-Amer: Mixed convection heat transfer flow of air inside a sinusoidal corrugated cavity with a heat conducting horizontal circular cylinder, Journal of Enhanced Heat Transfer 18 (2011) 433-447.
22
[23] P. Shiang-Wuu, W. Horng-Wen: Heat transfer enhancement for turbulent mixed convection in reciprocating channel by various rib installation, Journal of Enhanced Heat Transfer 20 (2013) 95-114.
23
[24] T. Hayat, M. Bilal Ashraf, H.H. Alsulami: On mixed convection flow of Jeffrey fluid over an inclined stretching surface with thermal radiation, Heat Transfer Research 46 (2015) 515-539.
24
[25] M. Hemmat Esfe, A.H. Refahi, H. Teimouri, M.J. Noroozi, M. Afrand, A. Karimiopour: Mixed convection fluid flow and heat transfer of the Al2O3-water nanofluid with variable properties in a cavity with an inside quadrilateral obstacle, Heat Transfer Research 46 (2015) 465-482.
25
[26] M. Hemmat Esfe, M. Akbari, D.Toghraei Semiromi, A. Karimiopour, M. Afrand: Effect of nanofluid variable properties on mixed convection flow and heat transfer in an inclined two-sided lid-driven cavity with sinusoidal heating on side walls, Heat Transfer Research 45 (2014) 409-432.
26
[27] M. Hemmat Esfe, S.S. Mirtalebi Esforjani, M. Akbari, A. Karimiopour: Mixed-convection flow in a lid-driven square cavity with a nanofluid with variable properties: effect of the nanoparticle diameter and of the position of a hot obstacle, Heat Transfer Research 45 (2014) 563-578.
27
[28] S. Shehzad, F. E. Alsaadi, T. Hayat, S. J. Monaquel: MHD mixed convection flow of Thixo tropic fluid with thermal radiation, Heat Transfer Research 45 (2014) 569-676.
28
[29] M. Hemmat Esfe, S. Niazi, S.S. Mirtalebi Esforjani, M. Akbari: Mixed convection flow and heat transfer in a ventilated inclined cavity containing hot obstacles subjected to a nanofluid, Heat Transfer Research 45 (2014) 309-338.
29
[30] M. Hemmat Esfe, S.S. Mirtalebi Esforjani, M. Akbari: Mixed convection flow and heat transfer in a lid-driven cavity subjected to nanofluid: effect of temperature, concentration and cavity inclination angles, Heat Transfer Research 45 (2014) 453-470.
30
[31] F. Bazdadi-Tehrani, A. Safakish: Mixed-convection and thermal radiation heat transfer in a three dimensional asymmetrically heated vertical channel, Heat Transfer Research 45 (2014) 541-561.
31
[32] M. Mollamahdi, M. Abbaszadeh, G. Sheikhzadeh: Flow field and heat transfer in a channel with a permeable wall filled with Al2O3-Cu/water micropolar hybrid nanofluid, effects of chemical reaction and magnetic field, Journal of Heat andMass Transfer Research Available online from 2 September 2016.
32
[33] M. Abbaszadeh, A. Ababaei, A. A. Abbasian Arani, A. Abbasi Sharifabadi: MHD forced convection and entropy generation of CuO‑water nanofluid in a microchannel considering slip velocity and temperature jump, The Brazilian Society of Mechanical Sciences and Engineering First Online: 7 June 2016, DOI 10.1007/s40430-016-0578-7.
33
[34] G. Sheikhzadeh, A. Aghaei, H. Ehteram, M. Abbaszadeh: Analytical study of parameters affecting entropy generation of nanofluid turbulent flow in channel and micro-channel, Thermal Science (2016) Online-First Issue, DOI: 10.2298/TSCI151112070S.
34
[35] G.A. Sheikhzadeh, H. Khorasanizadeh, S.P. Ghaffari: Mixed Convection of Variable Properties Al2O3-EG-Water Nanofluid in a Two-Dimensional Lid-Driven Enclosure, Transport Phenomena in Nano and Micro Scales 1 (2013) 75-92.
35
[36] G. A. Sheikhzadeh, H. Teimouri, M. Mahmoodi: Numerical Study of Mixed Convection of Nanofluid in a Concentric Annulus with Rotating Inner Cylinder, Transport Phenomena in Nano and Micro Scales 1 (2013) 26-36.
36
[37] A. Muftuoglu, E. Bilgen: Conjugate heat transfer in open cavities with a discrete heater at its optimized position, International Journal of Heat and Mass Transfer 51 (2007) 779-788.
37
[38] Y. Liu, N.P. Thien: An optimum placing problem for three chips mounted on a vertical substrate in an enclosure, Numerical Heat Transfer Part A 37 (2000) 613–630.
38
[39] S. Chen, Y. Liu, S.F. Chan, C.W. Leung, T.L. Chan: Experimental study of optimum spacing in the cooling of simulated electronic package, Heat and Mass Transfer 37 (2001) 251–257.
39
[40] Tito Dias Jr., L.F. Milanez: Optimal location of heat sources on a vertical wall with natural convection and genetic algorithm, International Journal of Heat and Mass Transfer 49 (2006) 2090–2096.
40
[41] J.C. Maxwell, A Treatise on Electricity and magnetism, second ed., clarendon press, Oxford, UK. (1881).
41
[42] Kh. Khanafer, K, Vafai: A critical synthesis of thermophysical characteristics of nanofluids, International journal of heat and mass transfer 54 (2011) 4410-4428.
42
[43] A. Bejan, Convection Heat Transfer. John Wiley & Sons, Inc., Hoboken, New Jersey, USA, 2004.
43
[44] G. Sheikhzadeh, H. Ghasemi, M. Abbaszadeh: Investigation of natural convection boundary layer heat and mass transfer of MHD water-AL2O3 nanofluid in a porous medium, International Journal of Nano Studies & Technology (IJNST) 5 (2) 110-122.
44
[45] K. Khanafer, K. Vafai, M. Lightstone: Buoyancydriven heat transfer enhancement in a twodimensional enclosure utilizing nanofluid, International journal of heat and mass transfer 46 (2003) 3639-3653.
45
[46] A.K. da Silva, S. Lorente, A. Bejan: Optimal distribution of discrete heat sources on a wall with natural convection, International journal of heat and mass transfer 47 (2004) 203-214.
46
[47] V. Sivakumar, S. Sivasankaran, P. Prakash, Jinho lee: Effect of heating and size on mixed convection in lid-driven cavities, Computers and Mathematics With Application 59 (2010) 3053-3065.
47
[48] H.C. Brinkman: The viscosity of concentrated suspensions and solutions, The Journal of Chemical Physic 20 (1952) 571.
48
ORIGINAL_ARTICLE
Dissipative Particle Dynamics simulation hydrated Nafion EW 1200 as fuel cell membrane in nanoscopic scale
The microphase separation of hydrated perfluorinated sulfonic acid membrane Nafion was investigated using Dissipative Particle Dynamics (DPD). The nafion as a polymer was modelled by connecting coarse grained beads which corresponds to the hydrophobic backbone of polytetrafluoroethylene and perfluorinated side chains terminated by hydrophilic end particles of sulfonic acid groups [1, 2]. Each four water molecule coarse grained in a bead to obtain the same bead size as built in Nafion model. The morphology of hydrated Nafion is studied for branching density of 1144, an example of Nafion EW1200, water content of 10%, 20% and 30% and polymer molecular weight of 5720, 11440 and 17160. The results show water particles and hydrophilic particles of Nafion side chains spontaneously form aggregates and are embedded in the hydrophobic phase of Nafion backbone. The averaged water pore diameter and the averaged water clusters distance were found to rises with water volume fraction.
http://tpnms.usb.ac.ir/article_2862_01bb64bc71e6bd67afff862dabe2ee38.pdf
2016-12-24T11:23:20
2018-09-21T11:23:20
44
53
10.7508/tpnms.2017.01.005
Fuel Cell
Membrane
Nafion
Microphase separation
water network
DPD
H.
Hassanzadeh Afrouzi
true
1
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
AUTHOR
A.
Moshfegh
true
2
School of Aerospace, Mechanical, and Mechatronic Eng., The University of Sydney, NSW 2006, Australia
School of Aerospace, Mechanical, and Mechatronic Eng., The University of Sydney, NSW 2006, Australia
School of Aerospace, Mechanical, and Mechatronic Eng., The University of Sydney, NSW 2006, Australia
AUTHOR
M.
Farhadi
true
3
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
AUTHOR
K.
Sedighi
true
4
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
Department of Mechanical Engineering, Babol Noshirvani University of Technology, Babol, I. R.Iran
AUTHOR
[1] K.A. Mauritz, R.B. Moore: State of understanding of Nafion, Chemical reviews 104 (2004) 4535-4586.
1
[2] B. Smitha, S. Sridhar, A. Khan: Solid polymer electrolyte membranes for fuel cell applications—a review, Journal of membrane science 259 (2005) 10-26.
2
[3] K.D. Kreuer: On Solids with Liquidlike Properties and the Challenge To Develop New Proton‐Conducting Separator Materials for Intermediate‐Temperature Fuel Cells, ChemPhysChem 3 (2002) 771-775.
3
[4] T.A. Zawodzinski Jr, M. Neeman, L.O. Sillerud, S. Gottesfeld: Determination of water diffusion coefficients in perfluorosulfonate ionomeric membranes, The Journal of Physical Chemistry 95 (1991) 6040-6044.
4
[5] J. T. Hinatsu, M. Mizuhata, H. Takenak: Water uptake of perfluorosulfonic acid membranes from liquidwater and water vapor, Journal of the Electrochemical Society 141 (1994) 1493-1498.
5
[6] R. B. Moore III, C.R. Martin: Morphology and chemical properties of the Dow perfluorosulfonate ionomers, Macromolecules 22 (1989) 3594-3599.
6
[7] S. Kumar, M. Pineri: Interpretation of small‐angle xray and neutron scattering data for perfluorosulfonated ionomer membranes, Journal of Polymer Science Part B: Polymer Physics 24 (1986) 1767-1782.
7
[8] P.A. Cirkel, T. Okada: A Comparison of Mechanicaland Electrical Percolation during the Gelling of Nafion Solutions, Macromolecules 33 (2000) 4921-4925.
8
[9] T. Gierke, G. Munn, F. Wilson: The morphology in nafion perfluorinated membrane products, as determined by wide‐and small‐angle x‐ray studies, Journal of Polymer Science: Polymer Physics Edition 19 (1981) 1687-1704.
9
[10] H.-G. Haubold, T. Vad, H. Jungbluth, P. Hiller: Nano structure of NAFION: a SAXS study, Electrochimica Acta 46 (2001) 1559-1563.
10
[11] Z.e. Porat, J.R. Fryer, M. Huxham, I. Rubinstein: Electron microscopy investigation of the microstructure of nafion films, The Journal of Physical Chemistry 99 (1995) 4667-4671.
11
[12] M. Ludvigsson, J. Lindgren, J. Tegenfeldt: FTIR study of water in cast Nafion films, Electrochimica Acta 45 (2000) 2267-2271.
12
[13] G. Gebel , R.B. Moore: Small-angle scattering study of short pendant chain perfuorosulfonated ionomer membranes, Macromolecules 33 (2000) 4850-4855.
13
[14] F.N. Büchi, G.G. Scherer: Investigation of the transversal water profile in Nafion membranes in polymer electrolyte fuel cells, Journal of The Electrochemical Society 148 (2001) A183-A188.
14
[15] S. Ge, B. Yi, P. Ming: Experimental determination of electro-osmotic drag coefficient in Nafion membrane for fuel cells, Journal of The Electrochemical Society 153 (2006) A1443-A1450.
15
[16] X. Ren, S. Gottesfeld: Electro-osmotic drag of water in poly (perfluorosulfonic acid) membranes, Journal of The Electrochemical Society 148 (2001) A87-A93.
16
[17] M. Fujimura, T. Hashimoto, H. Kawai: Small-angle X-ray scattering study of perfluorinated ionomer membranes. 1. Origin of two scattering maxima, Macromolecules 14 (1981) 1309-1315.
17
[18] L. Rubatat, A.L. Rollet, G. Gebel, O. Diat: Evidence of elongated polymeric aggregates in Nafion, Macromolecules 35 (2002) 4050-4055.
18
[19] K. Kreuer: On the development of proton conducting polymer membranes for hydrogen and methanol fuel cells, Journal of membrane science 185 (2001) 29-39.
19
[20] K. Schmidt-Rohr, Q. Chen: Parallel cylindrical water nanochannels in Nafion fuel-cell membranes, Nature materials 7 (2008) 75-83.
20
[21] M. Eikerling, S.J. Paddison, L.R. Pratt, T.A. Zawodzinski: Defect structure for proton transport in a triflic acid monohydrate solid, Chemical Physics Letters 368 (2003) 108-114.
21
[22] A. Roudgar, S. Narasimachary, M. Eikerling: Hydrated arrays of acidic surface groups as model systems for interfacial structure and mechanisms in pems, The Journal of Physical Chemistry B 110 (2006) 20469-20477.
22
[23] A. Vishnyakov, A.V. Neimark: Molecular dynamics simulation of microstructure and molecular mobilities in swollen Nafion membranes, The Journal of Physical Chemistry B 105 (2001) 9586-9594.
23
[24] S.S. Jang, V. Molinero, T. Cagin, W.A. Goddard: Nanophase-segregation and transport in Nafion 117 from molecular dynamics simulations: effect of monomeric sequence, The Journal of Physical Chemistry B 108 (2004) 3149-3157.
24
[25] D. Seeliger, C. Hartnig, E. Spohr: Aqueous pore structure and proton dynamics in solvated Nafion membranes, Electrochimica Acta 50 (2005) 4234-4240.
25
[26] J.Elliott, A.S. Elliott, G.Cooley: Atomistic simulation and molecular dynamics of model systems for perfluorinated ionomer membranes, Physical Chemistry Chemical Physics 1 (1999) 4855-4863.
26
[27] D.A. Mologin, P.G. Khalatur, A.R. Khokhlov: Structural Organization of Water‐Containing Nafion: A Cellular‐Automaton‐Based Simulation, Macromolecular theory and simulations 11 (2002) 587-607.
27
[28] P.G. Khalatur, S.K. Talitskikh, A.R. Khokhlov: Structural Organization of Water‐Containing Nafion: The Integral Equation Theory, Macromolecular theory and simulations 11 (2002) 566-586.
28
[29] J.T. Wescott, Y. Qi, L. Subramanian, T.W. Capehart: Mesoscale simulation of morphology in hydrated perfluorosulfonic acid membranes, The Journal of chemical physics 124 (2006) 134702.
29
[30] X. Guerrault, B. Rousseau, J. Farago: Dissipative particle dynamics simulations of polymer melts. I. Building potential of mean force for polyethylene and cis-polybutadiene, The Journal of chemical physics 121 (2004) 6538-6546.
30
[31] W. Jiang, J. Huang, Y. Wang, M. Laradji: Hydrodynamic interaction in polymer solutions simulated with dissipative particle dynamics, The Journal of chemical physics 126 (2007) 044901.
31
[32] D. Long, P. Sotta: Nonlinear and plastic behavior of soft thermoplastic and filled elastomers studied by dissipative particle dynamics, Macromolecules 39 (2006) 6282-6297.
32
[33] M.A. Horsch, Z. Zhang, C.R. Iacovella, S.C. Glotzer: Hydrodynamics and microphase ordering in block copolymers: Are hydrodynamics required for ordered phases with periodicity in more than one dimension?, The Journal of chemical physics 121 (2004) 11455-11462.
33
[34] X. Cao, G. Xu, Y. Li, Z. Zhang: Aggregation of poly (ethylene oxide)-poly (propylene oxide) block copolymers in aqueous solution: DPD simulation study, The Journal of Physical Chemistry A 109 (2005) 10418-10423.
34
[35] D. Wu, S.J. Paddison, J.A. Elliott: A comparative study of the hydrated morphologies of perfluorosulfonic acid fuel cell membranes with mesoscopic simulations, Energy & Environmental Science 1 (2008) 284-293.
35
[36] D. Wu, S.J. Paddison, J. A. Elliott: Effect of molecular weight on hydrated morphologies of the shortside - chain perfluorosulfonic acid membrane, Macromolecules 42 (2009) 3358-3367.
36
[37] G.Dorenbos,Y. Suga:Simulation of equivalent weight dependence of Nafion morphologies and predicted trends regarding water diffusion, Journal of Membrane Science 330 (2009) 5-20.
37
[38] Y.G. Kim, Y.C. Bae: A particle dynamic simulation for morphological aspects of proton exchange membranes, Macromolecular Research 21 (2013) 502-510.
38
[39] P.V. Komarov, I.N. Veselov, P.G. Khalatur: Selforganization of amphiphilic block copolymers in the presence of water: A mesoscale simulation, Chemical Physics Letters 605 (2014) 22-27.
39
[40] S.-i. Sawada, T. Yamaki, T. Ozawa, A. Suzuki, T. Terai, Y. Maekawa: Water Transport in Polymer Electrolyte Membranes Investigated by Dissipative Particle Dynamics Simulation, ECS Transactions 33 (2010) 1067-1078.
40
[41] P. Hoogerbrugge, J. Koelman: Simulating microscopic hydrodynamic phenomena with dissipative particle dynamics, EPL (Europhysics Letters) 19 (1992) 155.
41
[42] J. Koelman, P. Hoogerbrugge: Dynamic simulations of hard-sphere suspensions under steady shear, EPL (Europhysics Letters) 21 (1993) 363.
42
[43] P. Espanol, P. Warren: Statistical mechanics of dissipative particle dynamics, EPL (Europhysics Letters) 30 (1995) 191.
43
[44] P. Español: Fluid particle dynamics: A synthesis of dissipative particle dynamics and smoothed particle dynamics, EPL (Europhysics Letters) 39 (1997) 605.
44
[45] R.D. Groot, T.J. Madden: Dynamic simulation of diblock copolymer microphase separation, The Journal of chemical physics 108 (1998) 8713-8724.
45
[46] R.D.Groot, K.Rabone:Mesoscopic simulation of cell membrane damage, morphology change and rupture by nonionic surfactants, Biophysical journal 81 (2001) 725-736.
46
[47] S. Yamamoto, S.-a. Hyodo: A computer simulation study of the mesoscopic structure of the polyelectrolyte membrane Nafion, Polymer journal 35 (2003) 519-527.
47
[48] M. Twister: A 623-dimensionally equidistributed uniform pseudo-random number generator-Matsumoto Nishimura-1998, DOI.
48
[49] B. Dünweg, W. Paul: Brownian dynamics simulations without Gaussian random numbers, International Journal of Modern Physics C 2 (1991) 817-827.
49
[50] X. Fan, N. Phan-Thien, S. Chen, X. Wu, T.Y. Ng: Simulating flow of DNA suspension using dissipative particle dynamics, Physics of Fluids (1994-present) 18 (2006) 063102.
50
[51] R. D.Groot, P.B.Warren: Dissipative particle dynamics: Bridging the gap between atomistic and mesoscopic simulation, Journal of Chemical Physics107 (1997) 4423.
51
[52] M.A. Seaton, R.L. Anderson, S. Metz, W. Smith, DL_MESO: highly scalable mesoscale simulations, Molecular Simulation 39 (2013) 796-821.
52
[53] M.Eikerling, A. Kornyshev, U. Stimming: Electrophysical properties of polymer electrolyte membranes: a random network model, The Journal of Physical Chemistry B 101 (1997) 10807-10820.
53
[54] W.Y. Hsu, T.D. Gierke: Ion transport and clustering in Nafion perfluorinated membranes, Jurnal of Membrane Science 13 (1983) 307-326.
54
ORIGINAL_ARTICLE
Effects of different atomistic water models on the velocity profile and density number of Poiseuille flow in a nano-channel: Molecular Dynamic Simulation
In the current study, five different atomistic water models (AWMs) are implemented, In order to investigate the impact of AWMs treatment on the water velocity profile and density number. For this purpose, Molecular dynamics simulation (MDS) of Poiseuille flow in a nano-channel is conducted. Considered AWMs are SPC/E, TIP3P, TIP4P, TIP4PFQ and TIP5P. To assessment of the ability of each model in prediction of velocity profile, it is compared with analytic velocity profile. Furthermore, MDS results of density number are evaluated by real non-dimensional value for density number of water (Rho*). Based on computational results,predicted velocity profile from MDS is in appropriate accordance to analytic solution based on the Navier–Stokes equations. In addition, SPC/E and TIP4P models prepare the best prediction of the velocity profile, and are recommended where the averaged magnitude of velocity across the nano-channel is essential. Furthermore, a jump in velocity of TIP5P and TIP4P models is revealed in the vicinity of the nano-channel walls. However, approximately similar quantity is detected in the flow velocity of all different AWMs near the nano-channel walls. Finally, numerical results related to density number show, the TIP5P water model has higher compliance with the intended Rho*, and thus this model is suggested, where density number plays an important role in our MDS.
http://tpnms.usb.ac.ir/article_2863_410d1f53e061c02d3b14c364b87cf31d.pdf
2016-12-24T11:23:20
2018-09-21T11:23:20
54
63
10.7508/tpnms.2017.01.006
Molecular dynamics simulation
Atomistic water models
Analytic solution
Velocity profile
Density number
Lennard-Jones
H.
Nowruzi
true
1
Department of Maritime Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, No 424, P.O.
Box 15875-4413, Tehran, I. R. Iran
Department of Maritime Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, No 424, P.O.
Box 15875-4413, Tehran, I. R. Iran
Department of Maritime Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, No 424, P.O.
Box 15875-4413, Tehran, I. R. Iran
AUTHOR
H.
Ghassemi
true
2
Department of Maritime Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, No 424, P.O.
Box 15875-4413, Tehran, I. R. Iran
Department of Maritime Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, No 424, P.O.
Box 15875-4413, Tehran, I. R. Iran
Department of Maritime Engineering, Amirkabir University of Technology (Tehran Polytechnic), Hafez Ave, No 424, P.O.
Box 15875-4413, Tehran, I. R. Iran
AUTHOR
[1] B. Lee, Y. Baek, M. Lee, D. H. Jeong, H .H. Lee, J.Yoon, Y .H. Kim: A carbon nanotube wall membrane for water treatment, Nature Communications 6 (2015).
1
[2] R. Das, M.d. E. Ali, S. B. A. Hamid, S.Ramakrishna, Z. Z. Chowdhury : Carbon nanotube membranes for water purification: A bright future in water desalination, Desalination 36 (2014) 97–109.
2
[3] R. Saidur, K.Y. Leong, H.A. Mohammad : A review on applications and challenges of nanofluids, Renewable and Sustainable Energy Reviews 15(2011) 1646–1668.
3
[4] A. C. Fischer, F. Forsberg, M. Lapisa, S .J. Bleiker,G. S.N. Roxhed, F. Niklaus: Integrating MEMS and ICs, Microsystems & Nanoengineering (2015).
4
[5] S. Yongli, S. Minhua, C.Weidong, M. Congxiao, L. Fang: The examination of water potentials by simulating viscosity, Computational Materials Science 38 (2007) 737–740.
5
[6] Y. Song, L. Dai: The shear viscosities of common water models by non-equilibrium molecular dynamics simulations, Molecular Simulation 36 (2010) 560-567.
6
[7] M. Gonzàlez, J. Abascal: The shear viscosity of rigid water models, J. Chemical Physics 132 (2010)096101.
7
[8] A. P. Markesteijn, R. Hartkamp, S. Luding, J.Westerweel : A comparison of the value of viscosity for several water models using Poiseuille flow in anano-channel , J. Chemical Physics 136 (2012)134104.
8
[9] G. Guevara-Carrion, J. Vrabec, H. Hasse: Prediction of self-diffusion coefficient and shear viscosity of water and its binary mixtures with methanol and ethanol by molecular simulation, J. Chemical Physics 134 (2011) 074508.
9
[10] D. T. W. Lin, C. K. Chen: A molecular dynamics simulation of TIP4P and Lennard-Jones water in nanochannel, Acta Mechanica 173 (2004) 181–194.
10
[11] B. Plankova´,V. Vins, J. Hruby, M. Duska, T.Nemec, D. Celny: Molecular simulation of water vapor–liquid phase interfaces using TIP4P/2005 model,EPJ Web of Conferences 92 (2015).
11
[12] R. d. C. Barbosa, M. C. Barbosa: Hydration shell of the TS-Kappa protein: higher density than bulk water, Physica A: Statistical Mechanics and its Applications 439 ( 2015) 48–58.
12
[13] J.S. Hansen and J. T. Ottesen, Molecular dynamics simulations of oscillatory flows in microfluidic channels, J. of Micro Fluidic and Nano Fluidic 2 (2006) 301-307.
13
[14] D. C. Rapaport: The art of molecular dynamics simulation, Cambridge, New York (2004).
14
[15] G. Karniadakis, A. Beskok, Narayan Aluru:Microflows and nanoflows fundamentals and simulation, Springer, New York (2005).
15
[16] http://www1.lsbu.ac.uk/water/water_models.html.
16
[17] H. J. C. Berendsen, J. R. Grigera, T. P. Straatsma:The missing term in effective pair potentials, J. Physical Chemistery 91 (1987) 6269-6271.
17
[18] W. L. Jorgensen, J. Chandrasekhar, J. D. Madura, R.W. Impey, M. L. Klein: Comparison of simple potential functions for simulating liquid water, J.Chemical Physics 79 (1983) 926-935.
18
[19] W. L. Jorgensen, J. D. Madura: Temperature and size dependence for monte carlo simulations of TIP4P water, Mol. Phys 56 (1985) 1381-1392.
19
[20] M. W. Mahoney, W. L. Jorgensen: A five-site model for liquid water and the reproduction of the density anomaly by rigid, nonpolarizable potential functions,J. Chemical Physics 112 (2000) 8910-8922.
20
[21] S. W. Rick: Simulation of ice and liquid water over a range of temperatures using the fluctuating charge model, J. Chemical Physics 114 (2001) 2276-2283.
21
[22] M .Allen, D. Tildesley: Computer simulation of liquids, Oxford University Press (1987).
22
[23] P.A. Thompson, S.M. Troian: A general boundary condition for liquid flow at solid surfaces, Nature 389 (1997) 360–2.
23
[24] G. B. Macpherson, M. K. Borg, J .M. Reese:Generation of initial molecular dynamics configurations in arbitrary geometries and in parallel, Mol. Simul 33 (2007) 1199–1212.
24
[25] G.B. Macpherson, J. M. Reese: Molecular dynamics in arbitrary geometries: parallel evaluation of pair forces, Mol Simul 34 (2008) 97–115.
25
[26] G .B. Macpherson, N Nordin, H. G. Weller: Particle tracking in unstructured, arbitrary polyhedral meshesmfor use in CFD and molecular dynamics, Commun.Numer. Methods Eng 25 (2009) 263–273.
26
[27] M.K. Borg, G.B. Macpherson, J.M. Reese:Controllers for imposing continuum-to molecular boundary conditions in arbitrary fluid flow geometries, Mol Simul 36 (2010) 745–57.
27
[28] H. J. C. Berendsen, J. R. Grigera, T .P. Straatsma :The missing term in effective pair potentials, J.Physical Chemistry 91(1987) 6269-6271.
28
[29] R. Kamali, P. Radmehr, A. Binesh: Molecular dynamics simulation of electro-osmotic flow in a nanonozzle, Micro & Nano Letters 7 (2012) 1049–1052.
29
[30] J .P. Hansen, I. R. McDonald: Theory of simple liquids, Academic Press (2006).
30
[31] W. A. Khan, M. M. Yovanovich: Analytical Modeling of Fluid Flow And Heat Transfer In Micro/Nano-Channel Heat Sinks: Proceedings of IPACK2007, ASME Interpack ’07, Vancouver,British Columbia, CANADA (2007).
31
[32] A. S. Ziarani, A. A. Mohamad: A molecular dynamics study of perturbed Poiseuille flow in a nanochannel, Microfluid Nanofluid 2 (2005) 12–20.
32
[33] R. B. Bird, W. E. Stewart, E. W. Lightfoot: Transport phenomena, Wiley, New York (1960).
33
[34] D.Y.C. Chan, R.G Horn: The drainage of thin liquid films between solid surfaces, J. Chemical Physics 83(1985) 5311-5324.
34
ORIGINAL_ARTICLE
Experimental investigation on the heat transfer performance and pressure drop characteristics of γ-Al2O3/water nanofluid in a double tube counter flow heat exchanger
In this paper, overall heat transfer coefficient and friction factor of water based γ-Al2O3 nanofluid in a double tube counter flow heat exchanger have been measured experimentally under turbulent flow condition. For better dispersion of γ-Al2O3 nanoparticles in distilled water, magnetic stirrer and ultrasonic vibrator (with a power of 240 kW and frequency of 35 kHz) were implemented. The stabilized γ-Al2O3 /water nanofluid have been examined at the concentrations of 0.05 and 0.15 vol. % with variation of flow rates in the range of 7–9 l/min. Nanofluid enters the inner tube of the heat exchanger at different temperatures including 45, 55,and 65 °C. Results demonstrated that increasing the nanofluid flow rate, concentration and inlet temperature can improve the overall heat transfer coefficient and heat transfer rate. Also, the ratio of the overall heat transfer coefficient of nanofluid to that of pure water decreased with increasing the nanofluid flow rate. Meanwhile, the maximum enhancements of the overall heat transfer coefficient and heat transfer rate and friction factor compared with those of base fluid (distilled water) are respectively equal to 19.3%, 10% and 25% which is occurred at the concentration of 0.15 vol. %.
http://tpnms.usb.ac.ir/article_2864_d25f0966d8df593fa73e464a3c2576a4.pdf
2016-12-24T11:23:20
2018-09-21T11:23:20
64
75
10.7508/tpnms.2017.01.007
Double tube heat exchanger
Nanofluid
Overall heat transfer coefficient
B.
Raei
true
1
Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan 98164-161, I. R.Iran
Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan 98164-161, I. R.Iran
Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan 98164-161, I. R.Iran
AUTHOR
F.
Shahraki
true
2
Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan 98164-161, I. R.Iran
Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan 98164-161, I. R.Iran
Department of Chemical Engineering, University of Sistan and Baluchestan, Zahedan 98164-161, I. R.Iran
AUTHOR
M.
Jamialahmadi
true
3
Petroleum Engineering Department, Petroleum University of Technology, Ahwaz, I. R. Iran
Petroleum Engineering Department, Petroleum University of Technology, Ahwaz, I. R. Iran
Petroleum Engineering Department, Petroleum University of Technology, Ahwaz, I. R. Iran
AUTHOR
S.M.
Peyghambarzadeh
true
4
Department of Chemical Engineering, Mahshahr branch, Islamic Azad University, Mahshahr, I. R.Iran
Department of Chemical Engineering, Mahshahr branch, Islamic Azad University, Mahshahr, I. R.Iran
Department of Chemical Engineering, Mahshahr branch, Islamic Azad University, Mahshahr, I. R.Iran
AUTHOR
[1] SUS. Choi: Enhancing thermal conductivity of fluids with nanoparticles, Proceedings of the ASME International Mechanical Engineering Congress and Exposition (1995) New York, USA.
1
[2] H. Masuda, A. Ebata, K. Teramae, N. Hishinuma:Alteration of Thermal Conductivity and Viscosity of Liquid by Dispersing Ultra-Fine Particles Dispersion of Al2o3, SiO2 and TiO2 Ultra-Fine Particles, Netsu Bussei 7 (1993) 227-33.
2
[3] S. Lee, SUS. Choi, S. Li, JA. Eastman: Measuring Thermal Conductivity of Fluids Containing Oxide Nanoparticles, Journal of Heat Transfer 121(1999)280-9.
3
[4] JA. Eastman, SUS. Choi, S. Li, W. Yu, LJ:Thompson: Anomalously increased effective thermal conductivities of ethylene glycol-based nanofluids containing copper nanoparticles. Applied Physics Letters 78 (2001) 718-20.
4
[5] O. Mahian, A. Kianifar, SA. Kalogirou, I. Pop, S. Wongwises, A review of the applications of nanofluids in solar energy, International Journal of Heat and Mass Transfer 57 (2013) 582-94.
5
[6] O. Mahian, A. Kianifar, C. Kleinstreuer, MdA. Al-Nimr, I. Pop, AZ. Sahin et al: A review of entropy generation in nanofluid flow, International Journal of Heat and Mass Transfer 65 (2013) 514-32.
6
[7] O. Mahian, A. Kianifar, S. Wongwises: Dispersion of ZnO Nanoparticles in a Mixture of Ethylene Glycol–Water, Exploration of Temperature-Dependent Density, and Sensitivity Analysis, J Clust Sci 24 (2013) 1103-14.
7
[8] L. Godson, DM. Lal, S. Wongwises: Measurement of thermo physical properties of metallic nanofluids for high temperature applications, Nanoscale and microscale thermophysical engineering 14 (2010) 152-73.
8
[9] B. Farajollahi, SG. Etemad, M. Hojjat: Heat transfer of nanofluids in a shell and tube heat exchanger, Int J Heat Mass Transfer 53 (2010) 12-7.
9
[10] BC. Pak, YI. Cho: Hydrodynamic and Heat Transfer Study of Dispersed Fluids with Submicron Metallic Oxide Particles, Experimental Heat Transfer 11(1998).
10
[11] CS. Jwo, LY. Jeng, TP. Teng, CC. Chen:Performance of overall heat transfer in multichannel heat exchanger by alumina nanofluid, J Alloys Compd 504 (2010) 385-S8.
11
[12] W. Yu, H. Xie, Y. Li, L. Chen, Q. Wang:Experimental investigation on the heat transfer properties of Al2O3 nanofluids using the mixture of ethylene glycol and water as base fluid, Powder Technology 230 (2012) 14-9.
12
[13] D. Wen, Y. Ding: Experimental investigation into convective heat transfer of nanofluids at the entrance region under laminar flow conditions, Int J Heat Mass Transfer 47 (2004) 5181-8.
13
[14] SM. Peyghambarzadeh, SH. Hashemabadi, MS.Jamnani, SM. Hoseini: Improving the cooling performance of automobile radiator withAl2O3/water nanofluid, Appl Therm Eng 31(10)(2011) 1833-8.
14
[15] SM. Peyghambarzadeh, SH. Hashemabadi, SM.Hoseini, M. Seifi Jamnani: Experimental study of heat transfer enhancement using water/ethylene glycol based nanofluids as a new coolant for car radiators, Int Commun Heat Mass 38 (2011) 1283-90.
15
[16] AR. Sajadi, MH. Kazemi: Investigation of turbulent convective heat transfer and pressure drop of TiO2/water nanofluid in circular tube, Int Commun Heat Mass 38 (2011) 1474-8.
16
[17] R. Lotfi, AM. Rashidi, A. Amrollahi: Experimental study on the heat transfer enhancement of MWNTwater nanofluid in a shell and tube heat exchanger, Int Commun Heat Mass 39 (2012) 108-11.
17
[18] M. Hemmat Esfe, S. Saedodin: Turbulent forced convection heat transfer and thermophysical properties of Mgo–water nanofluid with consideration of different nanoparticles diameter, an empirical study, J Therm Anal Calorim 119 (2014)1205-13.
18
[19] SM. Peyghambarzadeh, SH. Hashemabadi, M.Naraki, Y. Vermahmoudi: Experimental study of overall heat transfer coefficient in the application of dilute nanofluids in the car radiator, Appl Therm Eng 52 (2013) 8-16.
19
[20] M. Hemmat Esfe, S . Saedodin, O. Mahian, S.Wongwises: Heat transfer characteristics and pressure drop of COOH-functionalized DWCNTs/water nanofluid in turbulent flow at low concentrations, Int J Heat Mass Transfer 73 (2014)186-94.
20
[21] AAR. Darzi, M. Farhadi, K. Sedighi: Heat transfer and flow characteristics of AL2O3–water nanofluid in a double tube heat exchanger, Int Commun Heat Mass 47 (2013) 105-12.
21
[22] W. Duangthongsuk, S. Wongwises: An experimental study on the heat transfer performance and pressure drop of TiO2-water nanofluids flowing under a turbulent flow regime, Int J Heat Mass Transfer 53(2010) 334-44.
22
[23] A. Zamzamian, SN. Oskouie, A. Doosthoseini, A.Joneidi, M. Pazouki: Experimental investigation of forced convective heat transfer coefficient in nanofluids of Al2O3/EG and CuO/EG in a double pipe and plate heat exchangers under turbulent flow,Exp Therm Fluid Sci 35 (2011) 495-502.
23
[24] AA. Abbasian Arani, J. Amani: Experimental study on the effect of TiO2–water nanofluid on heat transfer and pressure drop, Exp Therm Fluid Sci 42(2012) 107-15.
24
[25] M. Hemmat Esfe, S. Saedodin, M. Mahmoodi:Experimental studies on the convective heat transfer performance and thermophysical properties of MgO–water nanofluid under turbulent flow, Exp Therm Fluid Sci 52 (2014) 68-78.
25
[26] B.H. Chun, H. Kang, S. Kim: Effect of alumina nanoparticles in the fluid on heat transfer in doublepipe heat exchanger system, Korean J Chem Eng 25(2008) 966-71.
26
[27] R. Aghayari, H. Maddah, F. Ashori, A. Hakiminejad,M. Aghili: Effect of nanoparticles on heat transfer in mini double-pipe heat exchangers in turbulent flow,Heat Mass Transfer (2014) 1-6.
27
[28] AJN. Khalifa, MA. Banwan: Effect of Volume Fraction of γ‐Al2O3 Nanofluid on Heat Transfer Enhancement in a Concentric Tube Heat Exchanger, Heat Transfer Eng 36 (2015) 1387-96.
28
[29] D. Madhesh, S. Kalaiselvam: Experimental study on the heat transfer and flow properties of Ag–ethylene glycol nanofluid as a coolant, Heat Mass Transfer 50 ( 2014) 1597-607.
29
[30] MM. Sarafraz, F. Hormozi: Intensification of forced convection heat transfer using biological nanofluid in a double-pipe heat exchanger, Experimental Thermal and Fluid Science 66 (2015) 279-89.
30
[31] RS. Khedkar, SS. Sonawane, KL. Wasewar: Heat transfer study on concentric tube heat exchanger using TiO2–water based nanofluid, International Communications in Heat and Mass Transfer 57(2014) 163-169.
31
[32] D. Kim, Y. Kwon, Y. Cho, C. Li, S. Cheong, Y.Hwang et al: Convective heat transfer characteristics of nanofluids under laminar and turbulent flow conditions, Curr Appl Phys 9(2, Supplement) (2009)119-23.
32
[33] KB. Anoop, T. Sundararajan, SK. Das: Effect of particle size on the convective heat transfer in nanofluid in the developing region, Int J Heat Mass Transfer 52(9–10) (2009) 2189-95.
33
[34] M. Nasiri, SG. Etemad, R. Bagheri: Experimental heat transfer of nanofluid through an annular duct,International Communications in Heat and Mass Transfer 38 (2011) 958-63.
34
[35] FM . White: Viscous fluid flow, Second Edition ed. New York: McGraw-Hill, Inc (2006).) 151-70.
35
[36] Y. Xuan, W. Roetzel: Conceptions for heat transfer correlation of nanofluids, International Journal of Heat and Mass Transfer 43 (2000) 3701-7.
36
[37] A. Einstein: A new determination of the molecular dimensions, Annphysics. 19 (1906) 289-306.
37
[38] JC. Maxwell: A Treatise on Electricity and Magnetism. Oxford, UK: ClarendonPress (1881).
38
[39] W. Williams, J. Buongiorno, LW. Hu: Experimental Investigation of Turbulent Convective Heat Transfer and Pressure Loss of Alumina/Water and Zirconia/Water Nanoparticle Colloids (Nanofluids) in Horizontal Tubes, Journal of Heat Transfer 130(2008) 412-24.
39
[40] RJ. Moffat: Describing the uncertainties in experimental results, Exp Therm Fluid Sci 1(1)1988 3-17.
40
[41] V. Gnielinski: New equations for heat and masstransfer in turbulent pipe and channel flow, Int Chem Eng 16 (1976) 359-68.
41
[42] AS. Foust, G. Christian: A. Non-Boiling Heat Transfer Co-Efficients in Annuli, AIChE J 36 (1940)541–54.
42
[43] M. Mehrabian, S. Mansouri, G. Sheikhzadeh: The overall heat transfer characteristics of a double pipe heat exchanger: comparison of experimental data with predictions of standard correlations,International Journal of Engineering Transaction B:Applications 15 (2002) 395-406.
43
[44] FM. White:Fluid Mechanics fourth ed ed. New York:McGraw-Hill, Inc (2001).
44
[45] R. Aghayari, H. Maddah, F. Ashori, M. Aghili: The Experimental Study of Nanpparticles Effect on Thermal Efficiency of Double Pipe Heat Exchangers in Turbulent Flow, Transport Phenomena in Nano and Micro Scales 2 (2014) 140-8.
45
[46] Y. Vermahmoudi, SM. Peyghambarzadeh, SH.Hashemabadi, M. Naraki: Experimental investigation on heat transfer performance of /water nanofluid in an air-finned heat exchanger, European Journal of Mechanics - B/Fluids 44 ( 2014) 32-41.
46