ORIGINAL_ARTICLE
Investigation of pore-scale random porous media using lattice boltzmann method
The permeability and tortuosity of pore-scale two and three-dimensional random porous media were calculated using the Lattice Boltzmann method (LBM). Effects of geometrical parameters of medium on permeability and tortuosity were investigated as well. Two major models of random porous media were reconstructed by computerized tomography method: Randomly distributed rectangular obstacles in a unit-cell as two-dimensional porous media, and random granular media in a cubic unit-cell as three-dimensional porous media. Results were validated using available theoretical, experimental, and numerical results from the literature. It is observed that permeability is a weak function of porosity in low porosity regions, but a strong function of porosity at high porosities. It also depends on the aspect ratio and hydraulic diameter of obstacles.Permeability results were obtained regarding to 73 random two-dimensional samples with different porosities and obstacle aspect ratios. Also 29 random sphere-packings including three different cases with three different sphere diameters were investigated as three-dimensional cases. Employing nonlinear regression based on the “least-squares” method, two permeability correlations were proposed with minimum curve-fitting errors. Besides, the effect of porosity on required time-steps to reach the converged solutions was investigated. It is concluded that an increase in the required time-steps to convergence is seen with reaching both high and low ends of porosity.© 2015 Published by Semnan University Press. All rights reserved.
http://jhmtr.journals.semnan.ac.ir/article_326_7fdf84f647e1c30bf59cf27849427f31.pdf
2015-04-01T11:23:20
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1
12
10.22075/jhmtr.2015.326
Lattice Boltzmann
pore-scale simulation
Creeping flow
Random porous media
Alireza
Azhdari Heravi
a.azhdari85@gmail.com
true
1
Semnan University
Semnan University
Semnan University
LEAD_AUTHOR
Farhad
Talebi
ftalebi@semnan.ac.ir
true
2
Semnan University
Semnan University
Semnan University
AUTHOR
Mohmmad Sadegh
Valipour
msvalipour@semnan.ac.ir
true
3
Semnan University
Semnan University
Semnan University
AUTHOR
[1]. R.B. Bird, W.E. Stewart, and E.N. Lightfoot, Transport Phenomena, Wiley, New York, P. 199 (1960).
1
[2]. Ergun S 1952 Fluid ﬂow through packed columns Chemical Engineering Progress, 48, 89-94, 1952.
2
[3]. Macdonald I F, EL-Sayed M S, Mow K and Dullien F A L 1979 Flow through porous media—the Ergun equation revisited Industrial & Engineering Chemistry Fundamentals, 18 199-208, 1979.
3
[4]. R. M. Fand, B.Y.K Kim, A.C.C. Lam, and R.T. Phan, Resistance to the ﬂow of ﬂuids through simple and complex porous media whose matrices are composed of randomly packed spheres, Journal of Fluids Engineering, 109, 268, 1987.
4
[5]. A. S. Sangani, A. Acrivos, Slow flow through a periodic array of spheres, International Journal of Multiphase Flow, 8(4), 343-360, 1982.
5
[6]. S. Liu, A. Afacan, and J. Masliyah, Steady incompressible laminar ﬂow in porous media, Chemical Engineering Science, 49, 3565, 1994.
6
[7]. R. E. Larson, and J.J.L. Higdon, A periodic grain consolidation model of porous media, Physics of Fluids A, 1, 38-46, 1989.
7
[8]. S. Kim, W.B. Russel, Modeling of porous media by renormalization of the Stokes equations, Journal of Fluids Mechanics, 154, 269-286, 1985.
8
[9]. A. Nakayama, F. Kuwahara, Y Kawamura, and H. Koyama, Three-dimensional numerical simulation of ﬂow through a microscopic porous structure Proc. ASME/JSME Thermal Engineering Conference, 3, 313, (1995).
9
[10]. D.H. Rothman, Cellular-automaton ﬂuids: a model for ﬂow in porous media, Geophysics, 54, 509, 1988.
10
[11]. S. Chen, K. Diemer, G.D. Doolen, K. Eggert, C. Fu, S. Gutman, and B.J. Travis, Lattice gas automata for ﬂow through porous media, Physica D, 47, 72-84, 1991.
11
[12]. S. Succi, E Foti, and F. Higuera, Three-dimensional ﬂows in complex geometries with the lattice Boltzmann method Europhysics Letter, 10, 433-438, 1989.
12
[13]. A. Cancelliere, C. Chang, E. Foti, D.H. Rothman, and S. Succi, The permeability of a random medium: comparison of simulation with theory, Physics of Fluids, A 2, 2085-2088, 1990.
13
[14]. R.S. Maier, D.M. Kroll, Y.E. Kutovsky, H.T. Davis, and R.S. Bernard, simulation of flow-through bead packs using the lattice boltzmann method, Physics of Fluids, 10 (1), 60-74, 1998.
14
[15]. T. Inamuro, M. Yoshino, and F. Ogino, Lattice Boltzmann simulation of ﬂows in a three-dimensional porous structure, International Journal for Numerical Methods in Fluids, 29, 737-748, 1999.
15
[16]. C. Manwart, U. Aaltosalmi, A. Koponen, R. Hilfer, and J. Timonen, Lattice-Boltzmann and ﬁnite-difference simulations for the permeability for three-dimensional porous media, Physical Review E, 66, 016702, 2002.
16
[17]. M.A. van der Hoef, R. Beetstra, and J.A.M. Kuipers, Lattice-Boltzmann simulations of low-Reynolds-number flow past mono- and bidisperse arrays of spheres: results for the permeability and drag force, Journal of Fluids Mechanic, 528, 233-254, 2005.
17
[18]. D. Coelho, J.F. Thovert, and P.M. Adler, Geometrical and transport properties of random packings of spheres and aspherical particles, Physical Review, E 55, 1959-1978, 1997.
18
[19]. M.L. Stewart, A.L. Ward, and D.R. Rector, A study of pore geometry effects on anisotropy in hydraulic permeability using the lattice-Boltzmann method, Advanced Water Resources, 29, 1328-1340, 2006.
19
[20]. X. Garcia, L.T. Akanji, M.J. Blunt, S.K. Matthai, and J.P. Latham, Numerical study of the effects of particle shape and polydispersity on permeability , Physical Review E 80(2), 222, 145–197, 2009.
20
[21]. N. Jeon, D.H., Choi, and C.L. Lin, Prediction of Darcy-Forchheimer drag for micro-porous structures of complex geometry using the lattice Boltzmann method, Journal of Micromechanics and Microengineering, 16, 2240–2250, 2006a.
21
[22]. P.L. Bhatnagar, E.P. Gross, and M. Krook, A model for collisional processes in gases I: small amplitude processes in charged and in nutral one-component systems, Physical Review, 94, 511-525, 1954.
22
[23]. A.A. Mohammad, Lattice Boltzmann Method, Fundamentals and Engineering Application With Computer Codes, Springer, London, (2011).
23
[24]. S. Succi, The Lattice Boltzmann Equation for Fluid Dynamics and Beyond, Oxford University Press, Oxford, UK, pp288, (2001).
24
[25]. Y.H. Qian, D. d’Humières, and P. Lallemand, Lattice BGK models for Navier–Stokes equation. Europhysics Letter, 17, 479–484, 1992.
25
[26]. E.W. Llewellin, LBﬂow: An extensible lattice Boltzmann framework for the simulation of geophysical ﬂows. Part I: theory and implementation”. Computers & Geosciences, 36, 115–122, 2010.
26
[27]. P.C. Carman, Fluid flow through granular beds, Transactions of the Institution of Chemical Engineers, 15, 150–166, 1937.
27
[28]. A. Koponen, M. Kataja, and J. Timonen, Permeability and effective porosity of porous media, Physical Review E, 56 (3), 3319- 3325, 1997.
28
[29]. A. Koponen, M. Kataja, and J. Timonen, Tortuous flow in porous media, Physical Review E, 54 (1), 406-410, 1996.
29
[30]. A. Duda, Z. Koza, and M. Matyka, Hydraulic tortuosity in arbitrary porous media flow, Physical Review E 84, 036319, 2011.
30
[31]. H. Rumpf, A.R. Gupte, The influence of porosity and grain size distribution on the permeability equation of porous flow, Chemie Ingenieur Technik (Weinheim), 43 (6) , 367-375, 1975.
31
[32]. E. Mauret, M. Renaud, Transport phenomena in multi-particle systems—I. Limits of applicability of capillary model in high voidage beds-application to fixed beds of fibers and fluidized beds of spheres, Chemical Engineering Science, 52, 1807-1817, 1997.
32
[33]. F.G. Ho, W. Strieder, A variational calculation of the effective surface diffusion coefficient and tortuosity, Chemical Engineering Science, 36, 253–258, 1981.
33
[34]. H. Pape, L. Riepe, and J.R. Schopper, Interlayer conductivity of rocks-a fractal model of interface irregularities for calculating interlayer conductivity of natural porous mineral systems, Colloids and Surfaces, 27, 97–122, 1987.
34
[35]. M.R. Riley, F.J. Muzzio, H.M. Buettner, and S.C. Reyes, A simple correlation for predicting effective diffusivities in immobilized cell systems, Biotechnology and Bioengineering, 49, 223–227, 1996.
35
[36]. M. Mota, J.A. Teixeira, and A. Yelshin, Binary spherical particle mixed beds: porosity and permeability relationship measurement, Transactions of the filtration Society, 1, 102–106, 2001.
36
[37]. K. Klusáček, P. Schneider, Effect of size and shape of catalyst microparticles on pellet pore structure and effectiveness, Chemical Engineering Science, 36, 523–527, 1981.
37
[38]. R.J. Millington, J.P Quirk, Permeability of porous solids, Transactions of the Faraday Society, 57, 1200–1207, 1961.
38
[39]. T.C. Zhang, P.L. Bishop, Evaluation of tortuosity factors and effective diffusivities in biofilms, Water Research, 28, 2279–2287, 1994.
39
[40]. A. Yelshin, M. Mota, and J. Teixeira, Proceedings of the International Conference on Filtech Europa-97, Dusseldorf, Filtration Society, Horsham, UK, October 14–16, 327–334 (1997).
40
[41]. M. Mota, J.A. Teixeira, and A. Yelshin, Ed. Feyo de Azevedo, E. Ferreira, K. Luben, O Osseweijer (Eds.), Proceedings of the Second European Symposium on Biochemical Engineering Science, Univ. of Porto, Porto, Portugal, September 16–19, 93–98, 1998.
41
[42]. J.C. Maxwell, A treatise on electricity and magnetism, Clarendon Press, Oxford, UK (1873).
42
[43]. M. Barrande, R. Bouchet, and R. Denoyel, Tortuosity of Porous Particles, Analytical Chemistry, 79, 9115-9121, 2007.
43
[44]. Q Zou, X. He, On pressure and velocity boundary conditions for the lattice Boltzmann BGK model, Physics of Fluids, 9, 1591-1598, 1997.
44
ORIGINAL_ARTICLE
Investigation of purge time in cathodic dead-end mode PEMFC
Recently, special type of fuel cells has been developed that operates in a Dead End mode. Working in this condition, the Dead-End fuel cell is supplied withhydrogen almost at the same rate of consumption. It is noteworthy to mention thatall of the water transport mechanisms have been considered in this simulation.Water accumulation that is directly proportional to the cell current is of a greatimportance and has a negative impact on the cell voltage and its performance.Hence, water and gas management in Dead-End mode should be handled properly.To do so, determining the suitable time of purge and its duration is valuable with adirect impact on cell performance. In this paper, the channel and gas diffusion layerhave been considered as a single control volume and the blockage effect has beeninvestigated by means of thermodynamic analysis. In order to obtain a reasonableassumption, we have studied three different scenarios: GDL flooding, channelflooding and GDL-channel flooding simultaneously. The influence of blockageeffect rate of gas diffusion layer and channel on cell voltage drop, performance andpurge time have been studied. Voltage drop curves in different operating conditionshave been presented and the results show an acceptable agreement withexperimental studies. These curves have been investigated for different currentdensities (0.5, 1 and 1.5 A/cm2), active areas (25, 50 and 100 cm2) andtemperatures (60-80 °C).An Increase in temperature and in current density, reducespurge time interval, while increasing active area has an inverse impact. In highcurrent densities, the effect of temperature variation can be neglected.
http://jhmtr.journals.semnan.ac.ir/article_335_a714ca51bfcb47ddf3ca631d5e40f566.pdf
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13
19
10.22075/jhmtr.2015.335
Dead-End Mode
PEMFC
Thermodynamic
Analysis
Voltage Losses
Purge Time
Temperature
Amirmohammad
Khazaee Pool
amirm.khazaee@yahoo.com
true
1
School of Mechanical Engineering, Babol Noshirvani University of Technology, Iran
School of Mechanical Engineering, Babol Noshirvani University of Technology, Iran
School of Mechanical Engineering, Babol Noshirvani University of Technology, Iran
LEAD_AUTHOR
Rouzbeh
Shafaghat
rshafaghat@nit.ac.ir
true
2
School of Mechanical Engineering, Babol Noshirvani University of Technology, Iran
School of Mechanical Engineering, Babol Noshirvani University of Technology, Iran
School of Mechanical Engineering, Babol Noshirvani University of Technology, Iran
AUTHOR
Qadir
Esmaili
qesmaili@iauamol.ac.ir
true
3
School of Mechanical Engineering, Amol Islamic Azad University, Iran
School of Mechanical Engineering, Amol Islamic Azad University, Iran
School of Mechanical Engineering, Amol Islamic Azad University, Iran
AUTHOR
Abbas
Ramiar
aramiar@nit.ac.ir
true
4
School of Mechanical Engineering, Amol Islamic Azad University, Iran
School of Mechanical Engineering, Amol Islamic Azad University, Iran
School of Mechanical Engineering, Amol Islamic Azad University, Iran
AUTHOR
[1]. F. Barbir, PEM Fuel Cells Theory And Practice, International Centre for Hydrogen Energy Technologies, Turkey, (2005).
1
[2]. S. Asghari, An investigation into the effect of anode purging on the fuel cell performance, International Of Journal Of Hydrogen Energy, 35, 9276-9282, (2010).
2
[3]. J.W. Choi, An experimental study on the purge characteristics of the cathodic dead-end mode PEMFC for the submarine or aerospace applications and performance improvement with the pulsation effects, International Of Journal Of Hydrogen Energy, 35, 3698-3711, (2010).
3
[4]. A.J. del Real, Development and experimental validation of a PEM fuel cell dynamic model, Journal of Power Sources, 173, 310-324, (2007).
4
[5]. J.W. Choi, Experimental study on enhancing the fuel efficiency of an anodic dead-end mode polymer electrolyte membrane fuel cell by oscillating the hydrogen, International Of Journal Of Hydrogen Energy, 35, 12469-12479, (2010).
5
[6]. A.S. Mujumdar, Performance evaluation of a polymer electrolyte fuel cell with a dead-end anode: A computational fluid dynamic study, International Of Journal Of Hydrogen Energy, 36, 10917-10933, (2011)
6
[7]. Y. Kim, An experimental study on water transport through the membrane of a PEFC operating in the dead-end mode, International Of Journal Of Hydrogen Energy, 34(18), 7768-7779, (2009).
7
[8]. C. Y. Wang, Two-phase transport and the role of micro-porous layer in polymer electrolyte fuel cells, Journal of Electrochemical Acta, 49, 4359-4369, (2004).
8
[9]. C. Y. Wang, Liquid Water Transport in Gas Diffusion Layer of Polymer Electrolyte Fuel Cells, Journal of The Electrochemical Society, 151(3), A399-A406, (2004).
9
[10]. S. Jayanti,Effect of air flow on liquid water transport through a hydrophobic gas diffusion layer of a polymer electrolyte membrane fuel cell, International Of Journal Of Hydrogen Energy, 35, 6872-6886, (2010).
10
[11]. J. Larminie, Fuel Cell Systems Explained, Second ed,Wiley, England, (2003).
11
[12]. M. Mench,Fuel Cell Engines, Wiley, United State of America,(2008).
12
[13]. J.T. Pukrushpan, Modeling And Control Of Fuel Cell Systems And Fuel Processors, PhD Thesis, University of Michigan, Michigan, (2003).
13
[14]. J.B. Siegel,Experiments and Modeling of PEM Fuel Cells for Dead-Ended Anode Operation, PhD Thesis, University of Michigan, Michigan, (2010).
14
[15]. A. Pulung Sasmito, Modeling Of Transport Phenomena In Polymer Electrolyte Fuel Cell Stacks: Thermal, Water And Gas Management, PhD Thesis, National University of Singapore, Singapore, (2010).
15
[16]. Ch. Quick,Characterization of water transport in gas diffusion media, Journal of Power Sources, 190, 110-120, (2009).
16
[17]. Z. Lu,Water management studies in PEM fuel cells, part III: Dynamic breakthrough and intermittent drainage characteristics from GDLs with and without MPLs, International Journal Of Hydrogen Energy, 35, 4222-4233, (2010).
17
[18]. J. Benziger, ,. “Water flow in the gas diffusion layer of PEM fuel cells”. Journal of Membrane Science, 261, May, pp. 98-106, (2005).
18
[19]. M.C. Potter, Fluid Mechanics, United State of America, (2008).
19
[20]. M.M. Abdollahzadeh, Quasi two dimensional modeling of multi-component two phase flow in PEM fuel cathode, High Technology and Environmental science, First annual energy conference on International Center for Science, (2011).
20
ORIGINAL_ARTICLE
Numerical study of fluid flow and heat transfer in a gas-tank water heater
Influence of a vent hood at the exit of exhaust flue gas and flue baffles in the firetube on the temperature and flow fields of a gas tank water heater, as well as thestructure and amount of heat transferred to the water tank has been studiednumerically using two-dimensional steady state finite element simulation.Observations show that without a vent hood, there is a downward gas flow in theflue and a strong vortex in the lower burner chamber. Using a vent hood preventsthe gas back flow into the flue, and placing the flue baffles increases the heatdelivered to the water
http://jhmtr.journals.semnan.ac.ir/article_336_01c9d6c4577988c156e1a1b1acb36516.pdf
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21
29
10.22075/jhmtr.2015.336
Fluid flow
Heat transfer
Tank water heater
Computer simulation
Mohammad Hossein
Tavakoli
true
1
Physics Department, Bu-Ali Sina University, Hamedan, Iran
Physics Department, Bu-Ali Sina University, Hamedan, Iran
Physics Department, Bu-Ali Sina University, Hamedan, Iran
LEAD_AUTHOR
Khatereh
Moharramkhani
h.moharamkhani@yahoo.com
true
2
Physics Department, Bu-Ali Sina University, Hamedan, Iran
Physics Department, Bu-Ali Sina University, Hamedan, Iran
Physics Department, Bu-Ali Sina University, Hamedan, Iran
AUTHOR
[1]. M. Krarti, Energy Auditing of Building Systems – An Engineering Approach, CRC Press, (2000).
1
[2]. http://oee.nrcan.gc.ca/equipment/heating/806?attr=4
2
[3]. K.F. Michaelsen, K. Taudorf, Danger of Gas Water Heaters, the Lancet, 322,229-230, (1983).
3
[4]. W.R. Chang, C.L. Cheng, Carbon monoxide transport in an enclosed room with sources from a water heater in the adjacent balcony, Building and Environment, 43,861-870, (2008).
4
[5]. O. Aydin, Y.E. Boke, An experimental study on carbon monoxide emission reduction at a fire tube water heater, Applied Thermal Engineering, 30, 2658-2662, (2010).
5
[6]. G. Gutierrez, F. Hincapie, J.A. Duffie, W.A. Beckman, Simulation of forced circulation water heaters; effects of auxiliary energy supply, load type and storage capacity, Solar Energy, 15,287-298, (1974).
6
[7]. G.N. Tiwari, N.K. Dhiman, Effect of the baffle plate on transient performance of built-in-storage water heater, Energy Conversion and Management,23,151-155, (1983).
7
[8]. T.W. Abou-Arab, M.O. Othman, Y.H. Najjar, N.T. Ahmad, Combustion and heat transfer characteristics for a dual-fuel cylindrical water heater model,Fuel,69,485-489, (1990).
8
[9]. A.K. Kar, K.M. Al-Dossary, Thermal performances of water heaters in series, Applied Energy,52,47-53, (1995).
9
[10]. A.A. Hegazy, M.R. Diab, Performance of an improved design for storage-type domestic electrical water-heaters, Applied Energy,71,287-306, (2002).
10
[11]. M. Kim, M.S. Kim, J.D. Chung, Transient thermal behavior of a water heater system driven by a heat pump, International Journal of Refrigeration,27,415-421, (2004).
11
[12]. A.A. Hegazy Effect of inlet design on the performance of storage-type domestic electrical water heaters, Applied Energy, 84, 1338-1355, (2007).
12
[13]. D.S. Sowmy, R.T.A. Prado Assessment of energy efficiency in electric storage water heaters, Energy and Buildings, 40, 2128-2132, (2008).
13
[14]. S. Tajwar, A.R. Saleemi, N. Ramzan, S. Naveed Improving thermal and combustion efficiency of gas water heater, Applied Thermal Engineering,31,1305-1312, (2011).
14
[15]. M. MoeiniSedeh, J.M. Khodadadi Energy efficiency improvement and fuel savings in water heaters using baffles, Applied Energy, 102,520-533, (2013).
15
[16]. http://www.atlantarealestateinspection.com/
16
[17]. F.P. Incropera, D.P. De Witt Introduction to Heat Transfer, John Wiley and Sons,(1996).
17
[18]. I.H. Shames, Mechanics of Fluids, Mc-Graw-Hill, New York, (1982).
18
[19]. J.P. Holman, Heat Transfer, Mc-Graw-Hill, New York, (1990).
19
[20]. http://www.Pdesolutions.com
20
[21]. K. Moharramkhani, M.Sc. Thesis, Bu-Ali Sina University, (2010).
21
[22]. Technical Manual, T.M. 5-650Central Boiler Plants, Publications of the Headquarters, United States Army Corps of Engineers, (1989).
22
[23]. S.J. Craig, J.F. McMahon, The effects of draft control on combustion, ISA Transactions,35,345-349, (1996).
23
ORIGINAL_ARTICLE
Determination of stationary region boundary in multiple reference frames method in a mixing system agitated by Helical Ribbon Impeller using CFD
The multiple reference frames (MRF) method is the most suitable method tosimulate impeller rotation in mixing systems. Precise determination of stationaryand moving zones in MRF method leads to accurate results in mixing performance.In this research, the entire volume of mixing system was divided into two zones.The kinetic energy values were used to distinguish the zones with differentvelocities. The low-velocity zones, close to zero, were considered as the stationaryzone and higher velocities were considered as the moving zone. The standardgeometrical parameters were used for mixing system. The axial velocity and axialflow number were compared with literatures for validation. The values fordimensionless diameter of stationary zone at different Reynolds numbers wereachieved for Newtonian and non-Newtonian fluids that are in agreement withvalues applied in literatures. The results show that the dimensionless diameter ofstationary zone decreases as Reynolds number increases.
http://jhmtr.journals.semnan.ac.ir/article_337_c1fb0b4dd682ef3e3a9c15f02706dcab.pdf
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31
37
10.22075/jhmtr.2015.337
CFD
MRF
Helical Ribbon
Impeller
Mixing
Non-Newtonian fluid
Maryam
Sanaie-Moghadam
true
1
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
AUTHOR
Mansour
Jahangiri
mjahangiri@semnan.ac.ir
true
2
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
LEAD_AUTHOR
Faramarz
Hormozi
fhormozi@semnan.ac.ir
true
3
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
School of Chemical& Petroleum and Gas Engineering, Semnan University, Semnan, Iran.
AUTHOR
[1]. P.J. Carreau, I. Patterson, C.Y. Yap, "Mixing of viscoelastic fluids with helical-ribbon agitators - I. Mixing time and flow patterns," Can. J. Chem. Eng. 54 (1976) pp. 135-142.
1
[2]. S.M. Shekhar, S. Jayanti, "Mixing of Pseudoplastic Fluids Using Helical Ribbon Impellers," AIChE J. 49 (2003) pp. 2768-2772.
2
[3]. M. Jahangiri, "Velocity distribution of helical ribbon impeller in mixing of polymeric liquids in the transition region," Iranian Polymer J. 16 (2007) pp. 731-739.
3
[4]. M. Jahangiri, "Shear Rates in Mixing of Viscoelastic Fluids by Helical Ribbon Impeller," Iranian Polymer J. 17 (2008) pp. 831-341.
4
[5]. K. Takahashi, Y. Takahata, T. Yokota, H. Konno, "Mixing of two miscible highly viscous Newtonian liquid in a helical ribbon agitator," J. Chem. Eng. Japan. 18 (1985) pp. 159-162.
5
[6]. P. J. Carreau, R.P. Chhabra, J. Cheng, "Effect of rheological properties on power consumption with helical ribbon agitators," AIChE J. 39 (1993) pp. 1421-1430.
6
[7]. G. Delaplace, J.C. Leuliet, V. Relandeau, "Circulation and mixing times for helical ribbon impellers. Review and experiments," Experiments in Fluids. 28 (2000) pp. 170–182.
7
[8]. I. Ihejirika, F. Ein-Mozaffari, "Using CFD and Ultrasonic Velocimetry to Study the Mixing of Pseudoplastic Fluids with a Helical Ribbon Impeller," Chem. Eng. Technol. 30 (2007) pp. 606-614.
8
[9]. W.I. Patterson, P.J. Carreau, C.Y. Yap, "Mixing with helical ribbon agitators, Part II. Newtonian fluids," AIChE J. 25 (1979) pp. 508-516.
9
[10]. K.V. Vyakaranam, J.L. Kokini, "Advances in 3D Numerical Simulation of Viscous and Viscoelastic Mixing Flows," in: J.M. Aguilera, Simpson R, Welti-Chanes J, Bermudez Aguirre D, Baebosa-Canovas G (Eds.) Food Engineering interfaces, Springer Science, Business Media, (2011), pp. 19-44.
10
[11]. P.M. Armenante, C. Luo, C.C. Chou, I. Fort, J. Medek, "Velocity profiles in a closed, unbaffled vessel: comparison between experimental LDV data and numerical CFD prediction," Chem. Eng. Sci. 52 (1997) pp. 3483-3492.
11
[12]. D. Anne-Archard, M. Marouche, H.C. Boisson, "Hydrodynamics and Metzner-Otto correlation in stirred vessels for yield stress fluids," Chem. Eng. J. 125 (2006) pp. 15-24.
12
[13]. J. Aubin,I. Naude, C. Xuereb, J. Bertrand, "Blending of Newtonian and Shear‐Thinning Fluids in a Tank Stirred with a Helical Screw Agitator," Cherd Trans. IChemE. 78 (2000) pp. 1105‐1114.
13
[14]. J. Aubin, I. Naude, C. Xuereb, "Design of Multiple Impeller Stirred Tanks for the Mixing of Highly Viscous Fluids Using CFD," Chem. Eng. Sci. 61 (2006) pp. 2913-2920.
14
[15]. B. Letellier, C. Xuereb, P. Swaels, P. Hobbes, J. Bertrand, "Scale-up in laminar and transient regimes of a multi-stage stirrer, a CFD approach,"Chem. Eng. Sci. 57 (2002) pp. 4617-4632.
15
[16]. R. Sanjuan-Galindo, M. Heniche, G. Ascanio, P.A. Tanguy, "CFD investigation of new helical ribbon mixers bottom shapes to improve pumping," Asia-Pac. J. Chem. Eng. 6 (2011) pp.181–193.
16
[17]. H. Ameur, M. Bouzit, M. Helmaoui, "Numerical study of fluid and power consumption in a stirred vessel with a Scsbs 6SRGT impeller," Chem. Process Eng. 32 (2011) pp.351-366.
17
[18]. H. Ameur, M. Bouzit, "Agitation of Yield Stress Fluids by Two-Blade Impellers," Canadian J. on Chem. Eng. Technol. 3 (2012) pp. 93-99.
18
[19]. H. Ameur, M. Bouzit, M. Helmaoui, "Hydrodynamic study involving a maxblend impeller with yield stress fluids," J. Mech. Sci. Technol. 26 (2012) pp. 1523-1530.
19
[20]. S. Youcefi, M. Bouzit, H. Ameur, Y. Kamla, A. Youcefi, "Effect of some design parameters on the flow fields and power consumption in a vessel stirred by a Rushton Turbine," Chem. process Eng. 34 (2013) pp. 293-307.
20
[21]. J.Y. Luo, I. Issar, A.D. Gosman, "Prediction of impeller induced flows in mixing vessels using multiple frames of reference," Proceeding Institution Chem. Eng. 136 (1993) 549-556.
21
[22]. M. Zhang, L. Zhang, B. Jiang, Y. Yin, X. Li, "Calculation of Metzner Constant for Double Helical Ribbon Impeller by Computational Fluid Dynamic Method," Chinese J. Chem. Eng. 16 (2008) pp. 686-692.
22
[23]. M. Rahimi, A. Kakekhani, A. AbdulazizAlsairafi, "Experimental and computational fluid dynamic (CFD) studies on mixing characteristics of a modified helical ribbon impeller," Korean J. Chem. Eng. 27 (2010) pp.1150-1158.
23
[24]. Y. Tsui, Y. Hu, Eng. "Flow characteristics in mixers agitated by helical ribbon blade impeller," Application of Computational Fluid Mechanics. 5 (2011) pp.416-429.
24
[25]. L.W. Adams, "Experimental and computational study of non-Turbulent flow regimes and cavern formation of non-Newtonian fluids in a stirred tank,' PhD thesis, Birmingham, 2009, B15 2TT.
25
[26]. V.V. Chavan, R.A. Mashelkar, "Mixing of viscous Newtonian and non-Newtonian fluids," in: A.S. Mujumdar (Ed.) Advances in Transport Processes, Wiley Eastern/Wiley Halsted, 1980, pp. 210-252.
26
ORIGINAL_ARTICLE
2D Numerical Simulation of a Micro Scale Ranque-Hilsch Vortex Tube
In this study, fluid flow and energy separation in a micro-scale Ranque-HilschVortex Tube are numerically investigated. The flow is assumed as 2D, steady,compressible ideal gas, and shear-stress-transport SST k-W is found to be a bestchoice for modeling of turbulence phenomena. The results are in a good agreementwith the experimental results reported in the literature. The results show that fluidflow and energy separation inside the micro-scale vortex tube is quite similar tothose of traditional ones. Moreover, it is found that non-dimensional forms of coldtemperature difference and refrigerating capacity are only dependent on cold massfraction. In addition, two correlations have been proposed to estimate nondimensional forms of cold temperature difference and refrigeration capacity in themicro-scale vortex tube.
http://jhmtr.journals.semnan.ac.ir/article_338_31dbf3d180072138c0c88629c4094a57.pdf
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48
10.22075/jhmtr.2015.338
Micro-Scale Vortex Tube
energy separation
cold-temperature difference
refrigeration capacity
Nader
Rahbar
nrahbar@gmail.com
true
1
Islamic Azad University, Semnan Branch
Islamic Azad University, Semnan Branch
Islamic Azad University, Semnan Branch
AUTHOR
Mostafa
Shateri
mostafashateri@gmail.com
true
2
Semnan Branch, Islamic Azad University
Semnan Branch, Islamic Azad University
Semnan Branch, Islamic Azad University
AUTHOR
Mohsen
Taherian
m.taheriyan@gmail.com
true
3
Semnan Branch, Islamic Azad University
Semnan Branch, Islamic Azad University
Semnan Branch, Islamic Azad University
AUTHOR
Mohammad Sadegh
Valipour
msvalipour@semnan.ac.ir
true
4
Semnan University
Semnan University
Semnan University
AUTHOR
[1]. Ranque G. Experiments on expansion in a vortex with simultaneous exhaust of hot air and cold air. Le Journal de Physique et le Radium (Paris). 1933;4:112-4.
1
[2]. Ranque G. Method and apparatus for obtaining from a fluid under pressure two outputs of fluid at different temperatures. US1934.
2
[3]. Hilsch R. The use of the expansion of gases in a centrifugal field as cooling process. Review of Scientific Instruments. 1947;18(2):108-13.
3
[4]. Fröhlingsdorf W, Unger H. Numerical investigations of the compressible flow and the energy separation in the Ranque-Hilsch vortex tube. International Journal of Heat and Mass Transfer. 1999;42(3):415-22.
4
[5]. Behera U, Paul PJ, Kasthurirengan S, Karunanithi R, Ram SN, Dinesh K, et al. CFD analysis and experimental investigations towards optimizing the parameters of Ranque-Hilsch vortex tube. International Journal of Heat and Mass Transfer. 2005;48(10):1961-73.
5
[6]. Aljuwayhel NF, Nellis GF, Klein SA. Parametric and internal study of the vortex tube using a CFD model. International Journal of Refrigeration. 2005;28(3):442-50.
6
[7]. Skye HM, Nellis GF, Klein SA. Comparison of CFD analysis to empirical data in a commercial vortex tube. International Journal of Refrigeration. 2006;29(1):71-80.
7
[8]. Eiamsa-ard S, Promvonge P. Numerical investigation of the thermal separation in a Ranque-Hilsch vortex tube. International Journal of Heat and Mass Transfer. 2007;50(5-6):821-32.
8
[9]. Farouk T, Farouk B. Large eddy simulations of the flow field and temperature separation in the Ranque-Hilsch vortex tube. International Journal of Heat and Mass Transfer. 2007;50(23-24):4724-35.
9
[10]. Behera U, Paul PJ, Dinesh K, Jacob S. Numerical investigations on flow behaviour and energy separation in Ranque-Hilsch vortex tube. International Journal of Heat and Mass Transfer. 2008;51(25-26):6077-89.
10
[11]. Farouk T, Farouk B, Gutsol A. Simulation of gas species and temperature separation in the counter-flow Ranque-Hilsch vortex tube using the large eddy simulation technique. International Journal of Heat and Mass Transfer. 2009;52(13-14):3320-33.
11
[12]. Ameri M, Behnia B. The study of key design parameters effects on the vortex tube performance. Journal of Thermal Science. 2009;18(4):370-6.
12
[13]. Dutta T, Sinhamahapatra KP, Bandyopdhyay SS. Comparison of different turbulence models in predicting the temperature separation in a Ranque-Hilsch vortex tube. International Journal of Refrigeration. 2010;33(4):783-92.
13
[14]. Nezhad AH, Shamsoddini R. Numerical three-dimensional analysis of the mechanism of flow and heat transfer in a vortex tube. Thermal Science. 2009;13(4):183-96.
14
[15]. Shamsoddini R, Nezhad AH. Numerical analysis of the effects of nozzles number on the flow and power of cooling of a vortex tube. International Journal of Refrigeration. 2010;33(4):774-82.
15
[16]. Dutta T, Sinhamahapatra K, Bandyopadhyay S. Numerical investigation of gas species and energy separation in the Ranque-Hilsch vortex tube using real gas model. International Journal of Refrigeration. 2011.
16
[17]. Baghdad M, Ouadha A, Imine O, Addad Y. Numerical study of energy separation in a vortex tube with different RANS models. International Journal of Thermal Sciences. 2011;50(12):2377-85.
17
[18]. Khazaei H, Teymourtash A, Jafarian M. Effects of gas properties and geometrical parameters on performance of a vortex tube. Scientia Iranica B. 2012;19(3):454-62.
18
[19]. Dyskin L, Kramarenko P. Energy characteristics of vortex microtubes. Journal of Engineering Physics and Thermophysics. 1984;47(6):1394-5.
19
[20]. Hamoudi A, Fartaj A, Rankin G. Performance Characteristics of a Microscale Ranque–Hilsch Vortex Tube. Journal of Fluids Engineering. 2008;130:101206.
20
[21]. Rahbar N, taherian M, Shateri M, valipour MS. Numerical investigation on flow behavior and energy separation in a micro-scale vortex tube. Thermal Science. 2012.
21
[22]. Hamoudi AF. An Investigation of a Micro-Scale Ranque-Hilsch Vortex Tube: University of Windsor,Windsor, ON, Canada, 2006.
22
[23]. Zhang Z. Nano/microscale heat transfer. 1st ed: McGraw-Hill Professional, 2007.
23
[24]. Cebeci T. Turbulence models and their application: efficient numerical methods with computer programs: Horizons Pub. and Springer, 2004.
24
[25]. Menter FR. Two-equation eddy-viscosity turbulence models for engineering applications. AIAA journal. 1994;32(8):1598-605.
25
[26]. Cebeci T. Analysis of turbulent flows. 2nd ed: Elsevier, 2004.
26
[27]. Patankar SV. Numerical heat transfer and fluid flow: Hemisphere Pub, 1980.
27
[28]. Versteeg HK, Malalasekera W. An introduction to computational fluid dynamics: the finite volume method: Prentice Hall, 2007.
28
[29]. Valipour MS, Niazi N. Experimental Modeling of a Curved Ranque-Hilsch Vortex Tube Refrigerator. International Journal of Refrigeration. 2011;34(4):1109–16.
29
ORIGINAL_ARTICLE
Unsteady free convection flow between two vertical plates with variable temperature and mass diffusion
The unsteady free convection flow between two long vertical parallel plates withvariable temperature and mass diffusion in the presence of the thermal radiation hasbeen presented. The governing dimensionless coupled linear partial differentialequations on the flow are solved by using the Laplace transform technique. TheExact solutions have been obtained for the fluid velocity, temperature and the massconcentration. The Representative numerical results for the fluid velocity,temperature, mass concentration and the shear stresses at the plate are presentedgraphically for the various pertinent flow parameters such as the radiationparameter, buoyancy forces, Schmidt number and time and studied in detail. Thestudy shows that these parameters have significant impact on the velocity,temperature, mass concentration and the shear stresses at the plates.
http://jhmtr.journals.semnan.ac.ir/article_334_691621b40aa0afe20999172ef224d14f.pdf
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58
10.22075/jhmtr.2015.334
Free convection
mass diffusion
vertical channel
thermal radiation
Sanatan
Das
tutusanasd@yahoo.co.in
true
1
Department of Mathematics, University of Gour Banga, Malda 732 103, India
Department of Mathematics, University of Gour Banga, Malda 732 103, India
Department of Mathematics, University of Gour Banga, Malda 732 103, India
AUTHOR
Rabindera
Jana
true
2
Department of Applied Mathematics, Vidyasagar University, Midnapore 721 102, India
Department of Applied Mathematics, Vidyasagar University, Midnapore 721 102, India
Department of Applied Mathematics, Vidyasagar University, Midnapore 721 102, India
AUTHOR
Ali
Chamkha
achamkha@yahoo.com
true
3
Manufacturing Engineering Department, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al-Khobar 31952, Saudi Arabia
Manufacturing Engineering Department, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al-Khobar 31952, Saudi Arabia
Manufacturing Engineering Department, Prince Mohammad Bin Fahd University, P.O. Box 1664, Al-Khobar 31952, Saudi Arabia
LEAD_AUTHOR
[1]. Cussler, E. L. (1998). Diffusion Mass Transfer in Fluid Systems, Cambridge University Press, Cambridge, UK.
1
[2]. Lee, T.S., Parikh, P.G., Acrivos, A., Bershadar, D. (1982). Natural convection in a vertical channel with opposing buoyancy forces. Int J Heat Mass Transf 25(4), 499-511.
2
[3]. Yan, W.M., Lin, T.F., Chang, C.J. (1988). Combined heat and mass transfer in natural convection vertical parallel plates. Warme-Stoffübertrag 23,69-76.
3
[4]. Nelson, D.J., Wood, B.D. (1989). Combined heat and mass transfer natural convection between vertical parallel plates. Int. J. Heat Mass Transf. 32(9), 1779-1787.
4
[5]. Nelson, D.J., Wood, B.D. (1989). Fully developed combined heat and mass transfer natural convection between vertical parallel plates with asymmetric boundary conditions. Int. J. Heat Mass Transf. 32, 1789-1792.
5
[6]. Yan, W.M., Lin, T.F. (1990). Combined heat and mass transfer natural convection between vertical parallel plates with film evaporation. Int J Heat Mass Transf 33(3), 529-541.
6
[7]. Yan, W.M., Lin, T.F. (1991). Evaporative cooling of liquid film through interfacial heat and mass transfer in a vertical channel - II. Numerical study. Int J Heat Mass Transf 34(4-5), 1113-1124.
7
[8]. Yan, W.M., Lin, T.F. (1991). Evaporative cooling of liquid film through interfacial heat and mass transfer in a vertical channel - I. Experimental study. Int. J. Heat Mass Transf. 34(4-5), 1105-1111.
8
[9]. Desrayaud, G., Lauriat, G. (2001). Heat and mass transfer analogy for condensation of humid air in vertical channel. Heat Mass Transf. 37, 67-76.
9
[10]. Salah El-Din, M.M. (2003). Effect of thermal and mass buoyancy forces on the development of laminar mixed convection between vertical parallel plates with uniform wall heat and mass fluxes. Int. J. Therm. Sci. 42, 447-453.
10
[11]. Cheng, C-Y. (2006). Fully developed natural convection heat and mass transfer of a micropolar fluid in a vertical channel with asymmetric wall temperatures and concentrations. Int Commun. Heat Mass Transf. 33,627-635.
11
[12]. Narahari, M. (2008). Transient free convection flow between two long vertical parallel plates with constant temperature and mass diffusion. In: Proceedings of the world congress on engineering 2008, vol II, WEC 2008, July 2-4, London, UK, pp 1614-1619
12
[13]. Rosseland, S. (1936). Theoretical Astrophysics, Oxford University, New York, NY, USA.
13
ORIGINAL_ARTICLE
Effects of the rectangular groove dimensions on the thermal features of the turbulent Al2O3-water nanofluid flow in the grooved tubes
The forced convection heat transfer of turbulent Al2O3-water nanofluid flow inside the grooved tubeswith the different aspect ratio of the rectangular grooves is numerically investigated. The governingequations have been solved using finite volume method (FVM) coupled with SIMPLE algorithm. It isassumed the heat flux is constant on the grooved walls. The Single-phase approach is applied for thecomputation of the nanofluid flow. The Nanoparticles volume fraction is in the range of 0-5% and flowReynolds number is in the range of 10,000-35,000. Comparisons between the numerical results andavailable experimental data show that among different turbulence models, k-ε model with enhanced walltreatment gives the better results. The results show that the heat transfer coefficient increases withnanoparticles volume fraction and Reynolds number but it is accompanied by pressure dropaugmentation. From the results, it is concluded that the grooved tubes with Al2O3-water nanofluid floware thermodynamically advantageous. The Correlations for heat transfer coefficients have been presentedfor grooved tubes in different aspect ratios using the numerical results. The optimum geometric ratios inwhich the entropy generation is minimized are also determined.
http://jhmtr.journals.semnan.ac.ir/article_339_c63e2c4b931cd91b0d44cbcfd6caa5b2.pdf
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59
70
10.22075/jhmtr.2015.339
Nanofluid
Grooved tube
Turbulent flow
forced convection
Entropy generation minimization
Komayl
Mohebbi
komaylmohebbi@gmail.com
true
1
Faculty of Mechanical Engineering, Semnan University, Semnan
Faculty of Mechanical Engineering, Semnan University, Semnan
Faculty of Mechanical Engineering, Semnan University, Semnan
AUTHOR
Roohollah
Rafee
rafee@semnan.ac.ir
true
2
Faculty of Mechanical Engineering, Semnan University, Semnan
Faculty of Mechanical Engineering, Semnan University, Semnan
Faculty of Mechanical Engineering, Semnan University, Semnan
LEAD_AUTHOR
Farhad
Talebi
ftalebi@semnan.ac.ir
true
3
Faculty of Mechanical Engineering, Semnan University, Semnan
Faculty of Mechanical Engineering, Semnan University, Semnan
Faculty of Mechanical Engineering, Semnan University, Semnan
AUTHOR
[1]. Cheng, L. “Nanofluid heat transfer technologies,” Recent Pat. Eng. 3 (2009) 1-7.
1
[2]. Duangthongsuk, W., Wongwises, S. “An experimental study on the heat transfer performance and pressure drop of TiO2–water nanofluids flowing under a turbulent flow regime,” International Journal of Heat and Mass Transfer, 53 (2010) 334–344.
2
[3]. Webb, R.L., Robertson, G.F., “Shell-side evaporators and condensers used in the refrigeration industry,” in: R.K. Shah, E.C. Subbarao, R.A. Mashelkar (Eds.), Heat Equipment Design, (Hemisphere Pub. Corp., Washington), pp. 559-570 (1988).
3
[4]. Dalle Donne, M., Meyer, L. “Turbulent convective heat transfer from rough surfaces with two-dimensional rectangular ribs,” International Journal Heat and Mass Transfer 20 (1977) 583–620.
4
[5]. Naphon, P., Nuchjapo, M., Kurujareon, J., “Tube side heat transfer coefficient and friction factor characteristics of horizontal tubes with helical rib,” Energy Conversion and Management 47 (2006) 3031–3044.
5
[6]. San, J.Y., Huang, W.C. “Heat transfer enhancement of transverse ribs in circular tubes with consideration of entrance effect,” International Journal of Heat and Mass Transfer 49 (17, 18) (2006) 2965–2971.
6
[7]. Bilen, K., Cetin, M., Gul, H., Balta, T. “The investigation of groove geometry effect on heat transfer for internally grooved tubes,” Applied Thermal Engineering 29 (2009) 753–761.
7
[8]. Pingan, L., Ye, G., Hairong, M., Liu, H. “Numerical simulation of heat transfer and resistance pattern in channels with different ribs,” in: 2010 International Conference on Computer Design and Applications (ICCDA 2010) p. V3-507-V3-11.
8
[9]. Choi, S.U.S. "Enhancing thermal conductivity of fluids with nanoparticles," ASME Publications FED-Vol. 231/MD-Vol. 66, (1995)99- 105,
9
[10]. Keblinski, P., Phillpot, S.R., Choi, S.U.S., Eastman, J.A. “Mechanisms of heat flow in suspensions of nano-sized particles (nanofluid).” International Journal of Heat and Mass Transfer, 45 (2002) 855-863.
10
[11]. Das, S., Putra, N., Thiesen, P., Roetzel, W. Temperature dependence of thermal conductivity enhancement for nanofluids, Journal of Heat Transfer 125 (2003) 567–574.
11
[12]. Pak, B.C., Cho, Y.I. Hydrodynamic and heat transfer study of dispersed fluids with submicron metallic oxide particles, Experimental Heat Transfer 11 (1998) 151–170.
12
[13]. Xuan, Y.M., Li, Q. Investigation on convective heat transfer and flow features of nanofluids, Journal of Heat Transfer 125 (2003) 151–155.
13
[14]. Maiga, S.E.B., Nguyen, C.T., Galanis, N., Roy, G., Mare, T., Coqueux, M. “Heat transfer enhancement in turbulent tube flow using Al2O3 nanoparticle suspension,” International Journal of Numerical Methods for Heat and Fluid Flow 16 (2006) 275–292.
14
[15]. Fotukian, S.M.,Nasr Esfahany, M. Experimental investigation of turbulent convective heat transfer of dilute γ-Al2O3/water nanofluid inside a circular tube, International Journal of Heat and Fluid Flow, 31 (2010) 606–612.
15
[16]. Wongcharee, K., Eiamsa-ard, S. Heat transfer enhancement by using CuO/water nanofluid in corrugated tube equipped with twisted tape, International Communication of Heat and Mass Transfer 39 (2) (2012) 251–257.
16
[17]. Manca, O., Nardini, S., Ricci, D. A numerical study of nanofluid forced convection in ribbed channels, Applied Thermal Engineering 37 (2012) 280–292.
17
[18]. Vatani, A., Mohammed, H.A. Turbulent nanofluid flow over periodic rib-grooved channels, Engineering Applications of Computational Fluid Mechanics 7(3) (2013) 369-381.
18
[19]. Haghighi, E.B., Utomo, A.T., Ghanbarpour, M., Zavareh, A.I.T., Poth, H., khodabandeh, R., Pacek, A., Palm, B.E. Experimental study on convective heat transfer of nanofluids in turbulent flow: Methods of comparison and their performance, Experimental thermal and Fluid Sciences, 57 (2014) 378-387.
19
[20]. Al-Shamani, A.N., Sopian, K., Mohammed, H.A., Mat, S., Ruslan, M.H., Abed, A.M. “Enhancement heat transfer characteristics in the channel with trapezoidal rib-groove using nanofluids, Case Studies in Thermal Engineering, 5, (2015) 48-58.
20
[21]. Bejan, A. Entropy Generation Minimization, CRC Press, Boca Taron (1996).
21
[22]. Maxwell, J.C. A treatise on Electricity and Magnetism, Carendon Press, Oxford UK (1873).
22
Xuan, Y.M., Roetzel, W. “Conceptions for heat transfer correlation of nanofluids,” International Journal of Heat and Mass Transfer 43 (2000) 3701–3707.
23
[24]. Corcione, M. “Empirical correlating equations for predicting the effective thermal conductivity and dynamic viscosity of nanofluids,” Energy Conversion Management. 52 (2011) 789-793.
24
[25]. Chon, C.H., Kihm, K.D., Lee, S.P., Choi, S.U.S. “Empirical Correlation Finding the Role of Temperature and Particle Size for Nanofluid (Al2O3) Thermal Conductivity Enhancement,” Appl. Phys. Lett., 87 (2005) 153107.
25
[26]. White, F.M. “Fluid Mechanics”, 7th ed. McGraw-Hill, New York (2011).
26
www.US-Nano.com.
27
[28]. White, F.M. “Viscous fluid Flow,” 3rd ed., McGraw-Hill, New York (2003).
28
[29]. Versteeg, H., Malalasekera, W. An introduction to computational fluid dynamics: the finite volume method, 2nd ed. Pearson Education Limited (2007).
29
[30]. Eckert, E.R.G., Drake, R.M. Heat and Mass Transfer, McGraw-Hill, New York (1959).
30
[31]. Petukhov, B.S. “Heat transfer and friction in turbulent pipe flow with variable physical properties,” Adv. Heat Transfer 6 (1970) 503–564.
31
[32]. Gnielinski, V. “New Equations for Heat and Mass Transfer in Turbulent Pipe and Channel Flow,” International Chemical Engineering 16 (1976) 359–368.
32