Lucas Wavelet Analysis of the Squeeze Film Characteristics Between a Sphere and a Flat Plate of Couple Stress Fluid Model
DOI:
https://doi.org/10.26713/cma.v16i4.3267Keywords:
Lucas wavelet, Squeeze film, Couple stress fluid model, Microcontinuum theory, Sphere and plateAbstract
This study presents a numerical examination of the influence of couple stresses on the squeeze film behavior between a sphere and a flat plate, grounded in microcontinuum theory. The revised Reynolds equation that regulates the squeezing film pressure is formulated by employing the Stokes constitutive equations to incorporate the couple stress effects resulting from the lubricant mixed with distinct additives. Lucas wavelet based numerical scheme is developed for the numerical solution of the governing modified Reynolds equation. The numerical solution indicates that the presence of couple stresses results in an increase in the film pressure. Overall, the effects of couple stress, as defined by the couple stress parameter, lead to an enhancement in the load-carrying capacity when compared to the traditional Newtonian-lubricant scenario. The characteristics of the squeeze film in the system are enhanced.
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[1] T. Ariman, M. A. Turk and N. D. Sylvester, Microcontinuum fluid mechanics — A review, International Journal of Engineering Science 11(8) (1973), 905 – 930, DOI: 10.1016/0020-7225(73)90038-4.
[2] T. V. Biradar, Squeeze film lubrication between porous parallel stepped plates with couple stress fluids, Tribology Online 8(5) (2013), 278 – 284, DOI: 10.2474/trol.8.278.
[3] A. S. Burbidge and C. Servais, Squeeze flows of apparently lubricated thin films, Journal of Non-Newtonian Fluid Mechanics 124(1-3) (2004), 115 – 127, DOI: 10.1016/j.jnnfm.2004.07.011.
[4] P. Chang and P. Piau, Haar wavelet matrices designation in numerical solution of ordinary differential equations, IAENG International Journal of Mathematics 38(3) (2008), 5 pages, URL: https://www.iaeng.org/IJAM/issues_v38/issue_3/IJAM_38_3_11.pdf.
[5] A. H. Choudhury and R. K. Deka, Wavelet-Galerkin solutions of one dimensional elliptic problems, Applied Mathematical Modelling 34(7) (2010), 1939 – 1951, DOI: 10.1016/j.apm.2009.10.011.
[6] H. Dehestani, Y. Ordokhani and M. Razzaghi, Combination of Lucas wavelets with Legendre–Gauss quadrature for fractional Fredholm–Volterra integro-differential equations, Journal of Computational and Applied Mathematics 382 (2021), 113070, DOI: 10.1016/j.cam.2020.113070.
[7] L. Fox, Numerical Solution of Ordinary and Partial Differential Equations, Pergamon Press, Inc., 520 pages (1962).
[8] C. F. Gerald and P. O. Wheatley, Applied Numerical Analysis, Pearson Education India, Boston, 609 pages (1999).
[9] P. S. Gupta and A. S. Gupta, Squeezing flow between parallel plates, Wear 45(2) (1977), 177 – 185, DOI: 10.1016/0043-1648(77)90072-2.
[10] H. Hashimoto, Viscoelastic squeeze film characteristics with inertia effects between two parallel circular plates under sinusoidal motion, ASME Journal of Tribology 116(1) (1994), 161 – 166, DOI: 10.1115/1.2927034.
[11] J. D. Jackson, A study of squeezing flow, Applied Science Research, Section A 11 (1963), 148 – 152, DOI: 10.1007/BF03184719.
[12] A. Kumar, The operational matrix method based on modified Lucas wavelets for the approximation solution of initial and boundary value problems, International Journal of Applied and Computational Mathematics 9 (2023), article number 147, DOI: 10.1007/s40819-023-01620-5.
[13] S. Kumbinarasaiah, M. P. Preetham and N. A. Shah, Analysis of magnetohydrodynamic laminar boundary layer flow, heat, and mass transfer of nanofluids on a moving surface with thermal radiation via Bernoulli wavelets technique, Numerical Heat Transfer, Part B: Fundamentals 86(5) (2025), 1414 – 1437, DOI: 10.1080/10407790.2024.2312960.
[14] R.-F. Lu and J.-R. Lin, A theoretical study of combined effects of non-Newtonian rheology and viscosity-pressure dependence in the sphere-plate squeeze-film system, Tribology International 40(1) (2007), 125 – 131, DOI: 10.1016/j.triboint.2006.03.004.
[15] N. Mai-Duy and T. Tran-Cong, An integrated-RBF technique based on Galerkin formulation for elliptic differential equations, Engineering Analysis with Boundary Elements 33(2) (2009), 191 – 199, DOI: 10.1016/j.enganabound.2008.05.001.
[16] V. Mehandiratta, M. Mehra and G. Leugering, An approach based on Haar wavelet for the approximation of fractional calculus with application to initial and boundary value problems, Mathematical Methods in the Applied Sciences 44(4) (2021), 3195 – 3213, DOI: 10.1002/mma.6800.
[17] N. B. Naduvinamani, P. S. Hiremath and G. Gurubasavaraj, Static and dynamic behaviour of squeeze-film lubrication of narrow porous journal bearings with coupled stress fluid, Proceedings of the Institution of Mechanical Engineers, Part J: Journal of Engineering Tribology 215(1) (2001), 45 – 62, DOI: 10.1243/1350650011541738.
[18] O. Oruç, A new algorithm based on Lucas polynomials for approximate solution of 1D and 2D nonlinear generalized Benjamin–Bona–Mahony–Burgers equation, Computers & Mathematics with Applications 74(12) (2017), 3042 – 3057, DOI: 10.1016/j.camwa.2017.07.046.
[19] P. Rahimkhani, Y. Ordokhani and E. Babolian, Müntz-Legendre wavelet operational matrix of fractional-order integration and its applications for solving the fractional pantograph differential equations, Numerical Algorithms 77(4) (2018), 1283 – 1305, DOI: 10.1007/s11075-017-0363-4.
[20] J. N. Reddy, Introduction to Finite Element Method, McGraw-Hill Education, 784 pages (2006).
[21] S. C. Shiralashetti, A. M. Sangolli and P. R. Badiger, Daubechies wavelet multigrid method for accurate solution of typical differential equations arising in hydrodynamic lubrication theory, Indian Journal of Science and Technology 18(6) (2025), 430 – 442, DOI: 10.17485/IJST/v18i6.2416.
[22] S. C. Shiralashetti, V. R. Pala and S. I. Hanaji, Jacobi wavelet integration operational matrix method for the numerical solution of laminar nanofluid flow problem, International Journal of Ambient Energy 46(1) (2025), Article: 2458178, DOI: 10.1080/01430750.2025.2458178.
[23] V. K. Stokes, Couple stresses in fluids, Physics of Fluids 9(9) (1966), 1709 – 1715, DOI: 10.1063/1.1761925.
[24] C. Torrence and G. P. Compo, A practical guide to wavelet analysis, Bulletin of the American Meteorological Society 79(1) (1998), 61 – 78, DOI: 10.1175/1520-0477(1998)079<0061:APGTWA>2.0.CO;2.
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