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VARIATIONAL PRINCIPLE FOR A GENERALIZED RABINOWITSCH LUBRICATION

ABSTRACT
This paper adopts Rotem and Shinnar’s modification of the Rabinowitsch fluid model for the one-dimensional non-Newtonian lubrication problem, a variational principle is established by the semi-inverse method, and a generalized Reynolds-type equation is obtained. This article opens a new avenue for the establishment of Reynolds-type equation of complex lubrication problems.
KEYWORDS
PAPER SUBMITTED: 2021-12-01
PAPER REVISED: 2022-03-31
PAPER ACCEPTED: 2022-04-04
PUBLISHED ONLINE: 2022-05-22
DOI REFERENCE: https://doi.org/10.2298/TSCI211201071M
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE Issue 3, PAGES [2001 - 2007]
REFERENCES
  1. He, J.H., et al. The Maximal Wrinkle Angle During the Bubble Collapse and Its Application to the Bubble Electrospinning, Frontiers in Materials, 8(2022), Feb., 800567
  2. Qian, M.Y. and He, J.H. Collection of polymer bubble as a nanoscale membrane, Surfaces and Interface, 28(2022), Feb., 101665
  3. He, J.H., et al. Insights into Partial Slips and Temperature Jumps of a Nanofluid Flow over a Stretched or Shrinking Surface, Energies, 14(2021), No.20, 6691
  4. Eldabe, N.T., et al. Effect of induced magnetic field on non-Newtonian nanofluid Al2O3 motion through boundary-layer with gyrotactic microorganisms, Thermal Science, 26(2022), No.1, pp.411-422
  5. He, J.H., et al. Nonlinear EHD Instability of Two-Superposed Walters' B Fluids Moving through Porous Media, Axioms, 10(2021), No.4, 258
  6. He, J.H., et al. Nonlinear instability of two streaming-superposed magnetic Reiner-Rivlin Fluids by He-Laplace method, Journal of Electroanalytical Chemistry, 895(2021), Aug., 115388
  7. Talebzadegan, M., et al. Melting process modelling of Carreau non-Newtonian phase change material in dual porous vertical concentric cylinders, Thermal Science, 26(2021), No. 6, pp.4283-4293
  8. He, J.H., et al. Insight into the Significance of Hall Current and Joule Heating on the Dynamics of Darcy-Forchheimer Peristaltic Flow of Rabinowitsch Fluid, Journal of Mathematics, 2021, Oct., 3638807
  9. Zuo YT. Effect of SiC particles on viscosity of 3-D print paste: A fractal rheological model and experimental verification, Thermal Science 25(3B)(2021):2405-2409
  10. Liang, Y.H. and Wang, K.J. A new fractal viscoelastic element: Promise and Applications to Maxwell-Rheological Model, Thermal Science, 25(2021), No.2, pp.1221-1227
  11. Rahul, A.K. and Rao, P.S. Rabinowitsch fluid flow with viscosity variation: Application of porous rough circular stepped plates. Tribology International, 154(2021), 106635.
  12. Boubendir, S., et al. Hydrodynamic self-lubricating journal bearings analysis using Rabinowitsch fluid lubricant. Tribology International, 140(2019), 105856.
  13. Lin, J.R., et al. Derivation of two-dimensional non-Newtonian Reynolds equation and application to power-law film slider bearings: Rabinowitsch fluid model. Applied Mathematical Modelling, 40(2016), pp. 8832-8841.
  14. Lin, J.R. Now-Newtonian effects on the dynamic characteristics of one-dimensional slider bearings: Rabinowitsch fluid model. Tribology Letters, 10(2001), No.4, pp. 237-243.
  15. Singh, U.P. Mathematical analysis of effects of surface roughness on steady performance of hydrostatic thrust bearings lubricated with Rabinowitsch Type Fluids. Journal of Applied Fluid Mechanics, 13(2020), No.4, pp. 1339-1347.
  16. Boldyrev, Y.Y. Variational rayleigh problem of gas lubrication theory: low compressibility numbers. Fluid Dynamics, 53(2018), pp. 471-478.
  17. Walicka, A., et al. Curvilinear squeeze film bearing with rough surfaces lubricated by a Rabinowitsch-Rotem-Shinnar fluid. Applied Mathematical Modelling, 40(2016), pp. 7916-7927.
  18. He, J.H. Variational principle for non-Newtonian lubrication: Rabinowitsch fluid model. Applied Mathematics and Computation, 157(2004), No.1 ,pp. 281-286.
  19. Rabinowitsc, B. Über die viskosität und elastizität von solen. Zeitschrift Fur Physikalische Chemie, 145(1929), pp. 1-26.
  20. Rotem, Z., et al. Non-Newtonian flow between parallel boundaries in linear movements. Chemical Engineering Science, 15(1961), pp. 130-143.
  21. Yao, S.W. Variational principle for non-linear fractional wave equation in a fractal space. Thermal Science, 25(2021), No.2, pp. 1243-1247.
  22. Ling, W.W., et al. Variational theory for a kind of non-linear model for water waves. Thermal Science, 25(2021), No.2, pp.1249-1254.
  23. Cao, X.Q., et al. Variational theory for 2+1 dimensional fractional dispersive long wave equations. Thermal Science, 25 (2021), No.2, pp.1277-1285.
  24. Cao, X.Q., et al. Variational principle for 2+1 dimensional Broer-Kaup equations with fractal derivatives. Fractals, 28(2020), No.7, 2050107.
  25. Wang, K. J. and Wang, G. D., Study on the nonlinear vibration of embedded carbon nanotube via the Hamiltonian-based method, Journal of Low Frequency Noise, Vibration & Active Control, 41 (2022), No.1, pp.112-117.
  26. Wang,K.J. and Zhu, H.W., Periodic wave solution of the Kundu-Mukherjee-Naskar equation in birefringent fibers via the Hamiltonian-based algorithm, EPL, 2021, doi.org/10.1209/0295-5075/ac3d6b.
  27. Wang K J, Generalized variational principle and periodic wave solution to the modified equal width-Burgers equation in nonlinear dispersion media, Physics Letters A, 2021, 419 (17):127723. doi.org/10.1016/j.physleta.2021.127723.
  28. Wang, K.J., and Wang, J.F., Generalized variational principles of the Benney-Lin equation arising in fluid dynamics, EPL, 2021, doi.org/10.1209/0295-5075/ac3cce.
  29. Wang, K.L., Exact solitary wave solution for fractal shallow water wave model by He's variational method, Modern Physics Letters B, (2022)2150602,doi: doi.org/10.1142/S0217984921506028.
  30. Wang, K.L., Solitary wave solution of nonlinear Bogoyavlenskii system by variational analysis method, International Journal of Modern Physics B, (2022)2250015
  31. Wang, K.L., New variational theory for coupled nonlinear fractal Schrodinger system, International Journal of Numerical Methods for Heat & Fluid Flow, 32(2)(2022)589-597.
  32. He, J.H. Generalized variational principles for buckling analysis of circular cylinders. Acta Mechanica, 231(2020), No.3, 899-906.
  33. He, J.H., et al., Variational approach to fractal solitary waves, Fractals, 29(2021), No.7, 2150199
  34. He, J.H., et al., Evans model for dynamic economics revised, AIMS mathematics, 6(2021), No.9, pp.9194-9206

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