Advances in nano research

  • 제15권2호
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  • Pages.91-104
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  • 2023
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  • 2287-237X(pISSN)
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  • 2287-2388(eISSN)
테크노프레스 (Techno-Press)
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DOI QR코드

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Thin CNTs nanoliquid film development over a rough rotating disk

  • Swatilekha Nag (Department of Mathematics, Pandit Deendayal Upadhyaya Adarsha Mahavidyalaya) ;
  • Susanta Maity (Department of Basic and Applied Science, National Institute of Technology Arunachal Pradesh) ;
  • Sanjeev K. Metya (Department of Electronics and Communication Engineering, National Institute of Technology Arunachal Pradesh)
  • 투고 : 2020.01.14
  • 심사 : 2023.05.30
  • 발행 : 2023.08.25
⟨ 이전 논문 다음 논문 ⟩

초록

Development of thin carbon nanotubes (CNTs) nanoliquid film over the rough surface of a horizontal rotating disk is investigated by considering symmetric roughness either along the azimuthal or radial directions. The disk surface is either heated or cooled axisymmetrically from below. The effects of single-walled carbon nanotubes (SWCNTs), multi-walled carbon nanotubes (MWCNTs) are analyzed on the film thinning process with different types of base liquids. Closed form solutions for velocity and temperature field are obtained for small values of Reynolds number whereas the numerical solution is derived for moderate values of Reynolds number. It is found that fluid retention / depletion takes place when the roughness is symmetric along the azimuthal / radial directions. It is also seen that the film thinning rate enhances for MWCNTs compare to SWCNTs. Further it is found that two different heat transfer regions exits within the flow domain depending on the fact that heat is transferred from disk to liquid film and vice-versa.

키워드

과제정보

Authors express their sincere gratitude to the Council of Scientific and Industrial Research (CSIR), New Delhi, India for the financial support with file number 25(0267)/17/EMR-II.

참고문헌

  1. Akbar, N.S., Nadeem, S. and Khan, Z.H. (2014), "The combined effects of slip and convective boundary conditions on stagnation-point flow of CNT suspended nanofluid over a stretching sheet", J. Mol. Liq. 196, 21-25. https://doi.org/10.1016/j.molliq.2014.03.006
  2. Akbar, N.S. and Butt, A.W. (2015), "Carbon nanotubes analysis for the peristaltic flow in curved channel with heat transfer", Appl. Math. Comput., 259, 231-241. https://doi.org/10.1016/j.amc.2015.02.052
  3. Akbar, N.S., Raza, M. and Ellahi, R. (2015), "CNT suspended CuO + H2O nano fluid and energy analysis for the peristaltic flow in a permeable Channel", Alex. Eng. J., 54(3), 623-633. https://doi.org/10.1016/j.aej.2015.05.009
  4. Avramenko A.A. and Shevchuk Igor, V. (2022), Physical Foundations and Mathematical Models of Transport Processes in Nanofluids, in Modelling of Convective Heat and Mass Transfer in Nanofluids with and without Boiling and Condensation, Springer, Switzerland, 1-12.
  5. Buongiorno, J. (2006), "Convective transport in nanofluids", J. Heat Transfer, 128(3), 240-250. https://doi.org/10.1115/1.2150834
  6. Choi, S.U.S. (1995), "Enhancing thermal conductivity of fluids with nanoparticles", Proceedings of the 1995 ASME International Mechanical Engineering Congress and Exposition, San Francisco, USA, ASME, FED231/MD66, 99-105.
  7. Cregan, V. and O'Brien, S.B.G. (2013), "Extended asymptotic solutions to the spin-coating model with small evaporation", Appl. Math. Comput., 223, 76-87. https://doi.org/10.1016/j.amc.2013.07.071
  8. Dandapat, B.S. (2001), "Unsteady flow of thin liquid film on a disk under nonuniform rotation", Phys. Fluids, 13, 1860-1868. https://doi.org/10.1063/1.1377615
  9. Dandapat, B.S. and Maity, S. (2009), "Effects of air-flow and evaporation on the development of thin liquid film over a rotating annular disk", Int. J. Non-Linear Mech., 44(8), 877-882. https://doi.org/10.1016/j.ijnonlinmec.2009.06.002
  10. Dandapat, B.S., Maity, S. and Singh, S.K. (2017), "Two-layer film flow on a rough rotating disk in the presence of air shear", Acta Mechanica, 228, 4055-4065. https://doi.org/10.1007/s00707-017-1933-1
  11. Dandapat, B.S. and Roy, P.C. (1990), "Film cooling on a rotating disk", Int. J. Non-Linear Mech., 25(5), 569-582. https://doi.org/10.1016/0020-7462(90)90019-6
  12. Dandapat, B.S. and Roy, P.C. (1994), "The effect of themo-capillarity on the flow of a thin liquid film on a rotating disc", J. Phys. D: Appl. Phys., 27, 2041-2045. https://doi.org/10.1088/0022-3727/27/10/009
  13. Dandapat, B.S., Santra, B. and Kitamura, A. (2005), "Thermal effects on film development during spin coating", Phys. Fluids, 17, 062102(1-6). https://doi.org/10.1063/1.1927525
  14. Dandapat, B.S. and Singh, S.K. (2015), "Unsteady two-layer film flow on a non-uniform rotating disk in presence of uniform transverse magnetic field", Appl. Math. Comput., 258, 545-555. https://doi.org/10.1016/j.amc.2015.02.050
  15. Ellahi, R., Zeeshan, A., Hussain, F. and Abbas, T. (2018), "Study of shiny film coating on multi-fluid flows of a rotating disk suspended with nano-sized silver and gold particles: A comparative analysis", Coatings, 8(12), 422. https://doi.org/10.3390/coatings8120422
  16. Emslie, A.C., Bonner, F.D. and Peck, L.G. (1958), "Flow of a viscous liquid on a rotating disk", J. Appl. Phys., 29, 858-862. https://doi.org/10.1063/1.1723300
  17. Fletcher, C.A.J. (1988), Computational Technique for Fluid Dynamics, Springer, New York, U.S.A.
  18. Haq, R.U., Rashid, I. and Khan, Z.H. (2017), "Effects of aligned magnetic field and CNTs in two different base fluids over a moving slip surface", J. Mol. Liq., 243, 682-688. https://doi.org/10.1016/j.molliq.2017.08.084
  19. Higgins, B.G. (1986), "Film flow on a rotating disk", Phys. Fluids, 29, 3522-3529. https://doi.org/10.1063/1.865829
  20. Iijima, S. (1991), "Helical microtubules of graphitic carbon", Nature, 354, 56-58. https://doi.org/10.1038/354056a0
  21. Iijima, S. and Ichihashi, T. (1993), "Single-shell carbon nanotubes of 1-nm diameter", Nature, 363, 603-605. https://doi.org/10.1038/363603a0
  22. Jenekhe, S.A. and Schuldt, S.B. (1984), "Coating flow of non-Newtonian fluids on a flat rotating disk", Ind. Eng. Chem. Fund., 23(4), 432-436. https://doi.org/10.1021/i100016a009
  23. Karpitschka, S., Weber, C.M. and Riegler, H. (2015), "Spin casting of dilute solutions: Vertical composition profile during hydrodynamic-evaporative film thinning", Chem. Eng. Sci., 129, 243-248. https://doi.org/10.1016/j.ces.2015.01.028
  24. Khan, M.R., Pana, K., Khanb, A.U. and Ullah, N. (2020), "Comparative study on heat transfer in CNTs-water nanofluid over a curved surface", Int. Commun. Heat Mass Transf., 116, 104707. https://doi.org/10.1016/j.icheatmasstransfer.2020.104707
  25. Kitamura, A. (2001), "Thermal effects on liquid film flow during spin coating", Phys. Fluids, 13, 2788-2794. https://doi.org/10.1063/1.1398280
  26. Krishanan, R., Maity, S., Singh, S.K. and Dandapat, B.S. (2020), "Modelling of Thin CNTs Nano-liquid Film Flow Over a Bidirectional Stretching Surface", Int. J. Appl. Comput. Math., 6, 147. https://doi.org/10.1007/s40819-020-00900-8
  27. Kumar, M.S., Sandeep, N. and Kumar, R.B. (2017), "Unsteady MHD nonlinear radiative squeezing slip-flow of Casson fluid between parallel disks", J. Comput. Appl. Res. Mech. Eng., 7(1), 35-45. https://doi.org/10.22061/jcarme.2017.644
  28. Ma, F. and Hwang, J.H. (1990), "The effect of air shear on the flow of a thin liquid film over a rough rotating disk", J. Appl. Phys., 68, 1265-1271. https://doi.org/10.1063/1.346727
  29. Maity, S. (2017), "Thermocapillary flow of thin Cu-water nanoliquid film during spin coating process", Int. Nano Lett., 7, 9-23. https://doi.org/10.1007/s40089-016-0196-5
  30. Masuda, H., Ebata, A., Teramae, K. and Hishinuma, N. (1993), "Alterlation of thermal conductivity and viscosity of liquid by dispersing ultra-fine particles (Dispersion of g-Al2O3, SiO2, and TiO2ultra-fine particles)", Netsu Bussei, 7(4), 227-233. https://doi.org/10.2963/jjtp.7.227
  31. Matsumoto, Y., Ohara, T., Teruya, I. and Ohashi, H. (1989), "Liquid film formation on a rotating disk", JSME Int. J. Ser. II, 32(1), 52-56. https://doi.org/10.1299/jsmeb1988.32.1_52
  32. McIntyre, A. and Brush, L.N. (2010), "Spin-coating of vertically stratified thin liquid films", J. Fluid Mech., 647, 265-285. https://doi.org/10.1017/S002211200999259X
  33. Mouhamad, Y., Mokarian-Tabari, P., Clarke, N., Jones, R.A.L. and Geoghegan, M. (2014), "Dynamics of polymer film formation during spin coating", J. Appl. Phys., 116(12), 123513. https://doi.org/10.1063/1.4896674
  34. Miklavcic, M. and Wang, C.Y. (2004), "The flow due to a rough rotating disk", ZAMP, 55, 235. https://doi.org/10.1007/s00033-003-2096-6
  35. Myerhofer, D.J. (1978), "Characteristics of resist films produced by spinning", J. Appl. Phys., 49(7), 3993-3997. https://doi.org/10.1063/1.325357
  36. Niled, D.A. and Kuznetsov, A.V. (2009), "Thermal instability in a porous medium layer saturated by a nanofluid", Int. J. Heat Mass Transf., 52(25-26), 5796-5801. https://doi.org/10.1016/j.ijheatmasstransfer.2009.07.023
  37. Peurrung, L.M. and Graves, D.B. (1991), "Film thickness profiles over topography in spin coating", J. Electrochem. Soc., 138, 2115-2124. https://doi.org/10.1149/1.2085935
  38. Radushkevich, L. and Lukyanovich, V. (1952), "O strukture ugleroda obrazujucegosja pritermiceskomrazlozenii okisi ugleroda na zeleznom kontakte", Zurn Fisic Chim, 26, 88-95.
  39. Robert, G.O. (1971), Lecture Notes in Physics, Springer, New York, U.S.A.
  40. Sahoo, S., Arora, A. and Doshi, P. (2016), "Two-layer spin coating flow of Newtonian liquids: A computational study", Comput. Fluids, 131, 180-189. https://doi.org/10.1016/j.compfluid.2016.03.016
  41. Shevchuk, I.V. (2022), "An asymptotic expansion method vs a self-similar solution for convective heat transfer in rotating cone-disk systems", Phys. Fluids, 34, 103610. https://doi.org/10.1063/5.0120922
  42. Shevchuk, I.V. (2023), "Concerning the effect of radial thermal conductivity in a self-similar solution for rotating cone-disk systems", Int. J. Num. Methods Heat Fluid Flow, 33(1), 204-225. https://doi.org/10.1108/HFF-03-2022-0168
  43. Sidik, N.A.C., Muhammad Yazid, M.N.A.W. and Samion, S. (2017), "A review on the use of carbon nanotubes nanofluid for energy harvesting system", Int. J. Heat Mass Trans., 111, 782-794. https://doi.org/10.1016/j.ijheatmasstransfer.2017.04.047
  44. Tlili, I., Mustafa, M.T., Kumar, K.A. and Sandeep N. (2020), "Effect of asymmetrical heat rise/fall on the film flow of magnetohydrodynamic hybrid ferrofluid", Sci. Rep., 10, 6677. https://doi.org/10.1038/s41598-020-63708-y
  45. Tlili, I., Samrat, S.P., Sandeep, N. and Nabwey, H.A. (2021), "Effect of nanoparticle shape on unsteady liquid film flow of MHD Oldroyd-B ferrofluid", Ain Shams Eng. J., 12(1), 935-941. https://doi.org/10.1016/j.asej.2020.06.007
  46. Turkyilmazoglu, M. (2010), "The MHD boundary layer flow due to a rough rotating disk", Z. Angew. Math. Mech. (ZAMM), 90(1), 72-82. https://doi.org/10.1002/zamm.200900259
  47. Turkyilmazoglu, M. (2014), "Nanofluid flow and heat transfer due to a rotating disk", Comput. Fluids, 94, 139-146. https://doi.org/10.1016/j.compfluid.2014.02.009
  48. Usha, R. and Gotz, T. (2001), "Spinning of a liquid film from a rotating disc in the presence of amagnetic field: A numerical solution", Acta Mech. 147, 137-151. https://doi.org/10.1007/BF01182358
  49. Usha, R., Ravindran, R. and Uma, B. (2005), "Dynamics and stability of a thin liquid film on a heated rotating disk film with variable viscosity", Phys. Fluids, 17, 102103(1-10). https://doi.org/10.1063/1.2099007
  50. Von Karman, T. (1921), "Uber laminare und turbulente Reibung", Z. Angew. Math. Mech. (ZAMM),1(4), 233-252. https://doi.org/10.1002/zamm.19210010401
  51. Wang, J., Zhu, J., Zhang, X. and Chen, Y. (2014), "Heat transfer and pressure drop of nanofluids containing carbon nanotubes in laminar flows", Exp. Therm. Fluid Sci., 44, 716-721. https://doi.org/10.1016/j.expthermflusci.2012.09.013
  52. Washo, B.D. (1977), "Rheology and modeling of the spin coating process", IBM J. Res. Develop., 21(2), 190-198. https://doi.org/10.1147/rd.212.0190
  53. Wu, L. (2006), "Spin coating of thin liquid films on an axisymmetrically heated disk", Phys. Fluids, 18, 063602. https://doi.org/10.1063/1.2207007