Advertisement

Journal of Thermal Analysis and Calorimetry

, Volume 134, Issue 3, pp 1611–1628 | Cite as

The effect of rib shape on the behavior of laminar flow of oil/MWCNT nanofluid in a rectangular microchannel

  • Mohammad Reza Gholami
  • Omid Ali Akbari
  • Ali Marzban
  • Davood Toghraie
  • Gholamreza Ahmadi Sheikh Shabani
  • Majid Zarringhalam
Article

Abstract

In this research, the laminar and forced flow and heat transfer of oil/multi-walled carbon nanotubes nanofluid in a microchannel have been numerically investigated. The studied geometrics is a two-dimensional rectangular microchannel with the proportion of length to height of 150 (L/d = 150). The purpose of this research is to investigate the effect of using rectangular, oval, parabolic, triangular and trapezoidal rib shapes on behavior and heat transfer of nanofluid flow in the rectangular microchannel. This research has been simulated in Reynolds numbers of 1, 10, 50 and 100 and volume fractions of 0, 2 and 4% of nanoparticles by using finite volume method. The results of this research indicate that the existence of ribs enhances the friction factor and Nusselt number, significantly. Also, the shape of rib is one of the most important factors for determining the behavior and heat transfer of cooling fluid flows. Among the investigated rib shapes, the parabolic rib, comparing to the augmentation of friction factor, has the best proportion of Nusselt number enhancement.

Keywords

Nanofluid Rectangular microchannel Laminar flow Rib Multi-walled carbon nanotubes (MWCNT) 

List of symbols

A

Area (m2)

f

Friction factor

Cp

Heat capacity (Jkg−1 K−1)

D

Microchannel height (μm)

H

Ribbed height (m)

k

Thermal conductivity coefficient (Wm−1 K−1)

K

Inlet microchannel length (m)

L

Microchannel length (m)

M

Ribbed length (m)

Nu

Nusselt number

P

Fluid pressure (Pa)

p

Ribbed pitch (m)

Pe

Peclet number

Pr = (υf)/αf

Prandtl number

Re = (ρfu H)/μf

Reynolds number

T

Temperature (K)

U, V

Dimensionless velocity components in x, y directions

X, Y

Cartesian dimensionless coordinates

u, v

Velocity components in x, y directions (ms−1)

uc

Inlet velocity in x directions (ms−1)

us

Brownian motion velocity (ms−1)

W

Outlet microchannel length (m)

Greek symbols

α

Thermal diffusivity (m2 s−1)

φ

Nanoparticles volume fraction

κb

Boltzmann constant (JK−1)

μ

Dynamic viscosity (Pa s)

θ

Dimensionless temperature

ρ

Density (kg m−3)

υ

Kinematics viscosity (m2 s−1)

Super- and subscripts

c

Cold

Eff

Effective

f

Base fluid (oil)

h

Hot

Ave

Average

Nf

Nanofluid

s

Solid nanoparticles

References

  1. 1.
    Kasaeian A, Pourfayaz F, Bahrami L, Khodabandeh E, Yan WM. Experimental studies on the applications of PCMs and Nano-PCMs in buildings: a critical review. Energy Build. 2017;154:96–112.CrossRefGoogle Scholar
  2. 2.
    Kavusi H, Toghraie D. A comprehensive study of the performance of a heat pipe by using of various nanofluids. Adv Powder Technol. 2017;28(11):3074–84.CrossRefGoogle Scholar
  3. 3.
    Moraveji A, Toghraie D. Computational fluid dynamics simulation of heat transfer and fluid flow characteristics in a vortex tube by considering the various parameters. Int J Heat Mass Transf. 2017;113:432–43.CrossRefGoogle Scholar
  4. 4.
    Rezaei M, Azimian A, Semiromi DT. The surface charge density effect on the electro-osmotic flow in a nanochannel: a molecular dynamics study. Heat Mass Transf. 2015;51:661–70.CrossRefGoogle Scholar
  5. 5.
    Rezaei M, Azimian A, Toghraie D. Molecular dynamics study of an electro-kinetic fluid transport in a charged nanochannel based on the role of the stern layer. Phys A. 2015;426:25–34.CrossRefGoogle Scholar
  6. 6.
    Darzi AAR, Afrouzi HH, Moshfegh A, Farhadi M. Absorption and desorption of hydrogen in long metal hydride tank equipped with phase change material jacket. Int J Hydrogen Energy. 2015;41(22):9595–610.CrossRefGoogle Scholar
  7. 7.
    Keshavarz E, Toghraie D, Haratian M. Modeling industrial scale reaction furnace using computational fluid dynamics: a case study in Ilam gas treating plant. Appl Therm Eng. 2017;123:277–89.CrossRefGoogle Scholar
  8. 8.
    Rabinataj AA, Afrouzi HH, Alizadeh E, Shokri V, Farhadi M. Numerical simulation of heat and mass transfer during absorption of hydrogen in metal hydride tank. Heat Transf Asian Res. 2015;46(1):75–90.Google Scholar
  9. 9.
    Noorian H, Toghraie D, Azimian A. The effects of surface roughness geometry of flow undergoing Poiseuille flow by molecular dynamics simulation. Heat Mass Transf. 2014;50:95–104.CrossRefGoogle Scholar
  10. 10.
    Toghraie D. Numerical thermal analysis of water’s boiling heat transfer based on a turbulent jet impingement on heated surface. Phys E. 2016;84:454–65.CrossRefGoogle Scholar
  11. 11.
    Toghraie D, Mokhtari M, Afrand M. Molecular dynamic simulation of copper and platinum nanoparticles Poiseuille flow in a nanochannels. Phys E. 2016;84:152–61.CrossRefGoogle Scholar
  12. 12.
    Farzinpour M, Rasouli S, Toghraie, DS. Experimental and numerical investigations of bubbling fluidized bed apparatus to investigate heat transfer coefficient for different fins. Comput Therm Sci Int J 2017;9(3):243–55.CrossRefGoogle Scholar
  13. 13.
    Esfe MH, Hajmohammad H, Toghraie D, Rostamian H, Mahian O, Wongwises S. Multi-objective optimization of nanofluid flow in double tube heat exchangers for applications in energy systems. Energy. 2017;137(15):160–71.CrossRefGoogle Scholar
  14. 14.
    Ahmadi GhR, Toghraie D. Parallel feed water heating repowering of a 200 MW steam power plant. J Power Technol. 2015;95(4):288–301.Google Scholar
  15. 15.
    Ahmadi GhR, Toghraie D, Azimian A, Akbari OA. Evaluation of synchronous execution of full repowering and solar assisting in a 200 MW steam power plant, a case study. Appl Therm Eng. 2017;112:111–23.CrossRefGoogle Scholar
  16. 16.
    Ahmadi GHR, Akbari OA, Zarrin Ghalam M. Energy and exergy analyses of partial repowering of a natural gas-fired steam power plant. Int J Exergy. 2017;23:149.CrossRefGoogle Scholar
  17. 17.
    Akbari OA, Marzban A, Ahmadi GhR. Evaluation of supply boiler repowering of an existing natural gas-fired steam power plant. Appl Therm Eng. 2017;124:897–910.CrossRefGoogle Scholar
  18. 18.
    Ahmadi GhR, Toghraie D, Akbari OA. Solar parallel feed water heating repowering of a steam power plant: a case study in Iran. Renew Sustain Energy Rev. 2017;77:474–85.CrossRefGoogle Scholar
  19. 19.
    Ahmadi GhR, Toghraie D. Energy and exergy analysis of Montazeri Steam Power Plant in Iran. Renew Sustain Energy Rev. 2016;56:454–63.CrossRefGoogle Scholar
  20. 20.
    Ahmadi GhR, Toghraie D, Akbari OA. Efficiency improvement of a steam power plant through solar repowering. Int J Exergy. 2017;22(2):158–82.CrossRefGoogle Scholar
  21. 21.
    Zarringhalam M, Karimipour A, Toghraie D. Experimental study of the effect of solid volume fraction and Reynolds number on heat transfer coefficient and pressure drop of CuO–water nanofluid. Exp Thermal Fluid Sci. 2016;76:342–51.CrossRefGoogle Scholar
  22. 22.
    Choi J, Zhang Y. Numerical simulation of laminar forced convection heat transfer of Al2O3 water nanofluid in a pipe with return bend. Int J Therm Sci. 2012;55:90–102.CrossRefGoogle Scholar
  23. 23.
    Afrand M, Karimipour A, Ahmadi Nadooshan A, Akbari M. The variations of heat transfer and slip velocity of FMWNT water nano-fluid along the microchannel in the lack and presence of a magnetic field. Phys E. 2016;84:474–81.CrossRefGoogle Scholar
  24. 24.
    Manca O, Nardini S, Ricci D. A numerical study of nanofluid forced convection in ribbed channels. Appl Therm Eng. 2012;37:280–92.CrossRefGoogle Scholar
  25. 25.
    Akbari OA, Toghraie D, Karimipour A. Numerical simulation of heat transfer and turbulent flow of water nanofluids copper oxide in rectangular microchannel with semi attached rib. Adv Mech Eng. 2016;8:1–25.CrossRefGoogle Scholar
  26. 26.
    Safaei MR, Togun H, Vafai K, Kazi SN, Badarudin A. Investigation of heat transfer enchantment in a forward-facing contracting channel using FMWCNT nanofluids. Numer Heat Transf Part A. 2014;66:1321–40.CrossRefGoogle Scholar
  27. 27.
    Zadeh AD, Toghraie D. Experimental investigation for developing a new model for the dynamic viscosity of Silver/Ethylene Glycol nanofluid at different temperatures and solid volume fractions. J Therm Anal Calorim.  https://doi.org/10.1007/s10973-017-6696-3.CrossRefGoogle Scholar
  28. 28.
    Esfahani NN, Toghraie D, Afrand M. A new correlation for predicting the thermal conductivity of ZnO–Ag (50–50%)/water hybrid nanofluid: an experimental study. Powder Technol. 2018.  https://doi.org/10.1016/j.powtec.2017.10.025.CrossRefGoogle Scholar
  29. 29.
    Aghanajafi A, Toghraie D, Mehmandoust B. Numerical simulation of laminar forced convection of water-CuO nanofluid inside a triangular duct. Phys E. 2017;85:103–8.CrossRefGoogle Scholar
  30. 30.
    Sajadifar SA, Karimipour A, Toghraie D. Fluid flow and heat transfer of non-Newtonian nanofluid in a microtube considering slip velocity and temperature jump boundary conditions. Eur J Mech B Fluids. 2017;61:25–32.CrossRefGoogle Scholar
  31. 31.
    Faridzadeh M, Semiromi DT, Niroomand A. Analysis of laminar mixed convection in an inclined square lid-driven cavity with a nanofluid by using an artificial neural network. Heat Transf Res. 2014;45:361–90.CrossRefGoogle Scholar
  32. 32.
    Esfahani MA, Toghraie D. Experimental investigation for developing a new model for the thermal conductivity of Silica/Water–Ethylene glycol (40–60%) nanofluid at different temperatures and solid volume fractions. J Mol Liq. 2017;232:105–12.CrossRefGoogle Scholar
  33. 33.
    Afrand M, Toghraie D, Karimipour A, Wongwises S. A numerical study of natural convection in a vertical annulus filled with gallium in the presence of magnetic field. J Magn Magn Mater. 2017;430:22–8.CrossRefGoogle Scholar
  34. 34.
    Zadkhast M, Toghraie D, Karimipour A. Developing a new correlation to estimate the thermal conductivity of MWCNT-CuO/water hybrid nanofluid via an experimental investigation. J Therm Anal Calorim. 2017;129:859–67.CrossRefGoogle Scholar
  35. 35.
    Behnampour A, Akbari OA, Safaei MR, Ghavami M, Marzban A, Shabani GAS, Zarringhalam M, Mashayekhi R. Analysis of heat transfer and nanofluid fluid flow in microchannels with trapezoidal, rectangular and triangular shaped ribs. Phys E. 2017;91:15–31.CrossRefGoogle Scholar
  36. 36.
    Akbari OA, Karimipour A, Toghraie D, Safaei MR, Alipour Goodarzi MH, Dahari M. Investigation of Rib’s height effect on heat transfer and flow parameters of laminar water–Al2O3 nanofluid in a two dimensional rib-microchannel. Appl Math Comp. 2016;290:135–53.CrossRefGoogle Scholar
  37. 37.
    Akbari OA, Karimipour A, Toghraie D, Karimipour A. Impact of ribs on flow parameters and laminar heat transfer of Water–Aluminum oxide nanofluid with different nanoparticle volume fractions in a three-dimensional rectangular microchannel. Adv Mech Eng. 2016;7:1–11.Google Scholar
  38. 38.
    Karimipour A, Alipour H, Akbari OA, Semiromi DT, Esfe MH. Studying the effect of indentation on flow parameters and slow heat transfer of water–silver nano-fluid with varying volume fraction in a rectangular two-dimensional micro channel. Indian J Sci Technol. 2016;8:2015.Google Scholar
  39. 39.
    Gravndyan Q, Akbari OA, Toghraie D, Marzban A, Mashayekhi R, Karimi R, Pourfattah F. The effect of aspect ratios of rib on the heat transfer and laminar water/TiO2 nanofluid flow in a two-dimensional rectangular microchannel. J Mol Liq. 2017;236:254–65.CrossRefGoogle Scholar
  40. 40.
    Akbari OA, Toghraie D, Karimipour A, Marzban A, Ahmadi GR. The effect of velocity and dimension of solid nanoparticles on heat transfer in non-Newtonian nanofluid. Phys E. 2017;86:68–75.CrossRefGoogle Scholar
  41. 41.
    Yari Ghale Z, Haghshenasfard M, Nasr Esfahany M. Investigation of nanofluids heat transfer in a ribbed microchannel heat sink using single-phase and multiphase CFD models. Int Commun Heat Mass Transf. 2015;68:122–9.CrossRefGoogle Scholar
  42. 42.
    Sarlak R, Yousefzadeh Sh, Akbari OA, Toghraie D, Sarlak S, Assadi F. The investigation of simultaneous heat transfer of water/Al2O3 nanofluid in a close enclosure by applying homogeneous magnetic field. Int J Mech Sci. 2017;133:674–88.CrossRefGoogle Scholar
  43. 43.
    Parsaiemehr M, Pourfattah F, Akbari OA, Toghraie D, Sheikhzadeh Gh. Turbulent flow and heat transfer of water/Al2O3 nanofluid inside a rectangular ribbed channel. Phys E. 2018;96:73–84.CrossRefGoogle Scholar
  44. 44.
    Li YF, Xia GD, Ma DD, Jia YT, Wang J. Characteristics of laminar flow and heat transfer in microchannel heat sink with triangular cavities and rectangular ribs. Int J Heat Mass Transf. 2016;98:17–28.CrossRefGoogle Scholar
  45. 45.
    Andreozzi A, Manca O, Nardini S, Ricci D. Forced convection enhancement in channels with transversal ribs and nanofluids. Appl Therm Eng. 2016;98:1044–53.CrossRefGoogle Scholar
  46. 46.
    Mashayekhi R, Khodabandeh E, Bahiraei M, Bahrami L, Toghraie D, Akbari OA. Application of a novel conical strip insert to improve the efficacy of water–Ag nano-fluid for utilization in thermal systems: a two-phase simulation. Energ Conv Manag. 2017;151:573–86.CrossRefGoogle Scholar
  47. 47.
    Toghraie D, Davood Abdollah MM, Pourfattah F, Akbari OA, Ruhani B. Numerical investigation of flow and heat transfer characteristics in smooth, sinusoidal and zigzag-shaped microchannel with and without nano-fluid. J Therm Anal Calorim. 2017.  https://doi.org/10.1007/s10973-017-6624-6.CrossRefGoogle Scholar
  48. 48.
    Pourfattah F, Motamedian M, Sheikhzadeh Gh, Toghraie D, Akbari OA. The numerical investigation of angle of attack of inclined rectangular rib on the turbulent heat transfer of water–Al2O3 nano-fluid in a tube. Int J Mech Sci. 2017;131–132:1106–16.CrossRefGoogle Scholar
  49. 49.
    Mehdi Derakhshan M, Akhavan-Behabadi MA. Mixed convection of MWCNTeheat transfer Oil nanofluid inside inclined plain and microfin tubes under laminar assisted flow. Int J Therm Sci. 2016;99:1–8.CrossRefGoogle Scholar
  50. 50.
    Raisia A, Aminossadati SM, Ghasemi B. An innovative nanofluid-based cooling using separated natural and forced convection in low Reynolds flows. J Taiwan Ins Chem Eng. 2016;62:259–66.CrossRefGoogle Scholar
  51. 51.
    Aminossadati SM, Raisi A, Ghasemi B. Effects of magnetic field on nanofluid forced convection in a partially heated microchannel. Int J Non-Lin Mech. 2011;46:1373–82.CrossRefGoogle Scholar
  52. 52.
    Raisi A, Ghasemi B, Aminossadati SM. A numerical study on the forced convection of laminar nanofluid in a microchannel with both slip and No slip condition. Numer Heat Transf A Appl. 2011;59:114–29.CrossRefGoogle Scholar
  53. 53.
    Alipour H, Karimipour A, Safaei MR, Semiromi DT, Akbari OA. Influence of T-semi attached rib on turbulent flow and heat transfer parameters of a silver–water nanofluid with different volume fractions in a three-dimensional trapezoidal microchannel. Phys E. 2016;88:60–76.CrossRefGoogle Scholar
  54. 54.
    Akbari OA, Goodarzi M, Safaei MR, Zarringhalam M, Shabani GAS, Dahari M. A modified two-phase mixture model of nanofluid flow and heat transfer in 3-d curved microtube. Adv Powder Tech. 2016;27:2175–85.CrossRefGoogle Scholar
  55. 55.
    Chon CH, Kihm KD, Lee SP, Choi SUS. Empirical correlation finding the role of temperature and particle size for nanofluid (Al2O3) thermal conductivity enhancement. Appl Phys Lett. 2005;87:153107–153107-3.CrossRefGoogle Scholar
  56. 56.
    Brinkman H. The viscosity of concentrated suspensions and solutions. J Chem Phys. 1952;20:571.  https://doi.org/10.1063/1.1700493.CrossRefGoogle Scholar
  57. 57.
    Akbari OA, Afrouzi HH, Marzban A, Toghraie D, Malekzade H, Arabpour A. Investigation of volume fraction of nanoparticles effect and aspect ratio of the twisted tape in the tube. J Therm Anal Calorim. 2017.  https://doi.org/10.1007/s10973-017-6372-7.CrossRefGoogle Scholar
  58. 58.
    Heydari M, Toghraie M, Akbari OA. The effect of semi-attached and offset mid-truncated ribs and water/TiO2 nanofluid on flow and heat transfer properties in a triangular microchannel. Therm Sci Eng Prog. 2017;2:140–50.CrossRefGoogle Scholar
  59. 59.
    Sheikholeslami M, Gorji-Bandpy M, Ganji DD. Effect of discontinuous helical turbulators on heat transfer characteristics of double pipe water to air heat exchanger. Energy Convers Manag. 2016;118:75–87.CrossRefGoogle Scholar
  60. 60.
    M Safaei MR. Gooarzi M. Akbari OA. Safdari Shadloo M. Dahari M. Performance evaluation of nanofluids in an inclined ribbed microchannel for electronic cooling applications, “electronics cooling” In: Sohel Murshed SM editor. InTech, 2016.  https://doi.org/10.5772/62898. Available from: http://www.intechopen.com/books/electronics-cooling/performance-evaluation-of-nanofluids-in-an-inclined-ribbed-microchannel-for-electronic-cooling-appli.Google Scholar
  61. 61.
    Chai L, Xia G, Zhou M, Li J, Qi J. Optimum thermal design of interrupted microchannel heat sink with rectangular ribs in the transverse microchambers. Appl Therm Eng. 2013;51:880–9.CrossRefGoogle Scholar
  62. 62.
    Shamsi MR, Akbari OA, Marzban A, Toghraie D, Mashayekhi R. Increasing heat transfer of non-Newtonian nanofluid in rectangular microchannel with triangular ribs. Phys E. 2017;93:167–78.CrossRefGoogle Scholar
  63. 63.
    Vanaki SM, Mohammed HA. Numerical study of nanofluid forced convection flow in channels using different shaped transverse ribs. Int Commun Heat Mass Transf. 2015.  https://doi.org/10.1016/j.icheatmasstransfer.2015.07.004.CrossRefGoogle Scholar
  64. 64.
    Safaei MR, Saleh SR, Goodarzi M. Numerical studies of laminar natural convection in a square cavity with orthogonal grid mesh by finite volume. Int J Adv Des Manuf Technol (Majl J Mech Eng). 2008;1(2):13.Google Scholar
  65. 65.
    Moghiman M, Rahmanian B, Safaei MR, Goodarzi M. Numerical investigation of heat transfer in circular perforated plates exposed to parallel flow and suction. Int J Adv Des Manuf Technol (Majl J Mech Eng). 2008;1(3):43.Google Scholar
  66. 66.
    Seifia AR, Akbari OA, Alrashed AAAA, Afshary F, Ahmadi Sheikh Shabani Gh, Seifi R, Goodarzi M, Pourfattah F. Effects of external wind breakers of Heller dry cooling system in power plants. Appl Therm Eng. 2018.  https://doi.org/10.1016/j.applthermaleng.2017.10.118.CrossRefGoogle Scholar
  67. 67.
    Maghmoumi Y, Alavi MA, Safaei MR, Nourollahi I. Numerical analyses of steady non-Newtonian flow over flat plate on intermediate reynolds numbers by finite volume method. Int J Adv Des Manuf Technol (Majl J Mech Eng). 2008;1(4):21.Google Scholar
  68. 68.
    Nourollahi I, Zafarmand B, Safaei MR, Maghmoumi Y. An investigation of lid driven cavity flow by using large eddy simulation. Int J Adv Des Manuf Technol (Majl J Mech Eng). 2008;2(1):25.Google Scholar
  69. 69.
    Safaei MR, Goshayshi HR. Numerical Simulation of Laminar and Turbulent Mixed Convection in Rectangular Enclosure with Hot upper Moving Wall. Int J Adv Des Manuf Technol (Majl J Mech Eng). 2010;3(2):49.Google Scholar
  70. 70.
    Safaei MR, Goodarzi M, Mohammadi M. Numerical modeling of turbulence mixed convection heat transfer in air filled enclosures by finite volume method. Int J Multiphys. 2011;5(4):307–24.CrossRefGoogle Scholar
  71. 71.
    Karimipour A, Afrand M, Akbari M, Safaei MR. Simulation of fluid flow and heat transfer in the inclined enclosure. Int J Mech Aerosp Eng. 2012;2012(6):86–91.Google Scholar
  72. 72.
    Safaei MR, Goshayshi HR, Saeedi Razavi B, Goodarzi M. Numerical investigation of laminar and turbulent mixed convection in a shallow water-filled enclosure by various turbulence methods. Sci Res Essay. 2011;6(22):4826–38.Google Scholar
  73. 73.
    Safaei MR, Rahmanian B, Goodarzi M. Numerical study of laminar mixed convection heat transfer of power-law non-Newtonian fluids in square enclosures by finite volume method. Int J Phys Sci. 2011;6(33):7456–70.Google Scholar
  74. 74.
    Khodabandeh E, Rahbari A, Rosen MA, Ashrafi ZN, Akbari OA, Anvari AM. Experimental and numerical investigations on heat transfer of water-cooled lance for blowing oxidizing gas in electrical arc furnace. Energ Conv Manag. 2017;148:43–56.CrossRefGoogle Scholar
  75. 75.
    Khodabandeh E, Abbasi A. Performance optimization of water–Al2O3 nanofluid flow and heat transfer in trapezoidal cooling microchannel using constructal theory and two phase Eulerian–Lagrangian approach. Powder Technol. 2018;323:103–14.CrossRefGoogle Scholar
  76. 76.
    Arani AAA, Akbari OA, Safaei MR, Marzban A, Alrashed AAAA, Ahmadi GR, Nguyen TK. Heat transfer improvement of water/single-wall carbon nanotubes (SWCNT) nanofluid in a novel design of a truncated double layered microchannel heat sink. Int J Heat Mass Transf. 2017;113:780–95.CrossRefGoogle Scholar
  77. 77.
    Khodabandeh E, Pourramezan M, Pakravan MH. Effects of excess air and preheating on the flow pattern and efficiency of the radiative section of a fired heater. Appl Therm Eng. 2016;105:537–48.CrossRefGoogle Scholar
  78. 78.
    Rezaei O, Akbari OA, Marzban A, Toghraie D, Pourfattah F, Mashayekhi R. The numerical investigation of heat transfer and pressure drop of turbulent flow in a triangular microchannel. Phys E. 2017;93:179–89.CrossRefGoogle Scholar
  79. 79.
    Rezaei M, Azimian AR, Toghraie D. Molecular dynamics study of an electro-kinetic fluid transport in a charged nanochannel based on the role of the stern layer. Phys A Stat Mech Appl. 2015;426:25–34.CrossRefGoogle Scholar
  80. 80.
    Rezaei M, Azimian AR, Toghraie D. The surface charge density effect on the electro-osmotic flow in a nanochannel: a molecular dynamics study. Heat Mass Transf. 2015;51(5):661–70.CrossRefGoogle Scholar

Copyright information

© Akadémiai Kiadó, Budapest, Hungary 2017

Authors and Affiliations

  1. 1.Department of Mechanical Engineering, Aligoudarz BranchIslamic Azad UniversityAligoudarzIran
  2. 2.Young Researchers and Elite Club, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran
  3. 3.Department of Mechanical Engineering, Khomeinishahr BranchIslamic Azad UniversityKhomeinishahrIran
  4. 4.Young Researchers and Elite Club, South Tehran BranchIslamic Azad UniversityTehranIran

Personalised recommendations