Abstract
In this paper, the 3D flow in a rotating channel with the lower permeable stretching wall is investigated. The unsteady squeezing flow in the presence of transverse magnetic flux is mathematically modeled by utilizing Navier-Stokes equations. A new optimal wavelet method based on coupling the Legendre wavelets and the hat functions with some auxiliary convergence-control parameters is proposed to solve the obtained fourth-order system of nonlinear differential equations. In the proposed method, the residual function and its error of norm two are employed for converting the main problem into an optimization one to optimally choose the auxiliary convergence-control parameters. The main idea behind this approach is to reduce solving such problems to those of solving optimization ones which greatly simplifies the problem and also leads to obtaining a good approximate solution for the problem under consideration.
Similar content being viewed by others
References
Munawar S, Mehmood A, Ali A (2012) Three-dimensional squeezing flow in a rotating channel of lower stretching porous wall. Comput Math Appl 64:1575–1586
Ali A, Mehmood A (2008) Homotopy analysis of unsteady boundary layer flow adjacent to permeable stretching surface in a porous medium. Commun Nonlinear Sci Numer Simul 13:340–349
Mehmood A, Ali A (2006) Analytic solution of generalized three-dimensional flow and heat transfer over a stretching plane wall. Int Commun Heat Mass Transf 33:1243–1252
Ariel PD (2001) Axisymmetric flow of a second grade fluid past a stretching sheet. Int J Eng Sci 39:529–553
Zaturska MB, Banks WHH (2003) New solutions for flow in a channel with porous walls and/or non-rigid walls. Fluid Dyn Res 33:57–71
Shadloo-Jahromi A, Kharati-Koopaee M, Bavi O (2020) Friction factor calculation in nanochannels comprising different wall hydrophobicities and superhydrophobic structures: Molecular dynamic simulations. Int Commun Heat Mass Transf 117:104763
Elbashbeshy EMA, Bazid MAA (2004) Heat transfer over an unsteady stretching surface. Heat Mass Transf 41(1):1–4
Fang T, Zhang J (2008) Flow between two stretchable disks-an exact solution of the Navier-Stokes equations. Int Commun Heat Mass Transf 35:892–895
Robert A, Gorder V, Sweet E, Vajravelu K (2010) Analytical solutions of a coupled nonlinear system arising in a flow between stretching disks. Appl Math Comput 216:1513–1523
Tamayol A, Hooman K, Bahrami M (2010) Thermal analysis of flow in a porous medium over a permeable stretching wall. Transp Porous Media 85(3):661–676
Munawar S, Mehmood A, Ali A (2011) Effects of slip on flow between two stretchable disks using optimal homotopy analysis method. Can J Appl Sci 1(2):50–68
Borkakoti AK, Bharali A (1983) Hydromagnetic flow and heat transfer between two horizontal plates, the lower plate being a stretching sheet. Q Appl Math 41:461–467
Hayat T, Saleem N, Elamboud YA, Asghar S (2011) Effect of induced magnetic field on peristaltic flow of a second order fluid in a symmetric channel. Int J Numer Methods Fluids 67:537–558
Vajravelu K, Kumar BVR (2004) Analytical and numerical solutions of a coupled non-linear system arising in a three-dimensional rotating flow. Int J Non Linear Mech 39:13–24
Mehmood A, Ali A (2007) Analytic homotopy solution of generalized three-dimensional channel flow due to uniform stretching plate. Acta Mech Sin 23:503–510
Mehmood A, Ali A (2011) Across mass transfer phenomenon in a channel of lower stretching wall. Chem Eng Commun 198:678–691
Ullah A, Shah Z, Kumam P, Ayaz M, Islam S, Jameel M (2019) Viscoelastic MHD nanofluid thin film flow over an unsteady vertical stretching sheet with entropy generation. Processes 7(5):262
Shadloo-Jahromi A, Kharati-Koopaee M, Bavi O (2021) Molecular dynamics simulation of fluid flow through nanochannels consisting of different superhydrophobic patterns. Int Commun Heat Mass Transf 124:105278
Crane LJ (1970) Flow past a stretching plate. Z Angew Math Phys 21:645
Sobamowo MG, Kamiyo OM, Yinusa AA, Akinshilo TA (2020) Magneto-squeezing flow and heat transfer analyses of third grade fluid between two disks embedded in a porous medium using Chebyshev spectral collocation method. Eng Appl Sci Lett 4:305–322
Yinusa AA, Sobamowo MG, Usman MA, Abubakar EH (2021) Exploration of three dimensional squeezed flow and heat transfer through a rotating channel with coupled dufour and soret influences. Therm Sci Eng Prog 21:100788
Hamza EA, Macdonald DA (1981) A fluid film squeezed between two parallel plane surfaces. J Fluid Mech 109:147–160
Hamza EA (1991) The magnetohydrodynamic effects on a fluid film squeezed between two rotating surfaces. J Phys D Appl Phys 24:547–554
Rashidi MM, Shahmohamadi H, Dinarvand S (2008) Unsteanalytic approximate solutions for unsteady two-dimensional and axisymmetric squeezing flows between parallel plates. Math Probl Eng 2008:12 (Article ID 935095)
Kurosaka M (1973) The oscillatory boundary layer growth over the top and bottom plates of a rotating channel. J Fluids Eng 95:68–71
Pop I, Soundelgekar VM (1975) On unsteady boundary layers in rotating flow. J Inst Math Appl 15:343–349
Takhar HS, Chamkha AJ, Nath G (2002) Mhd flow over a moving plate in a rotating fluid with magnetic field, hall currents, and free stream velocity. Int J Eng Sci 40(13):1511–1527
Heydari MH, Avazzadeh Z, Atangana A (2021) Orthonormal shifted discrete Legendre polynomials for solving a coupled system of nonlinear variable-order time fractional reaction-advection-diffusion equations. Appl Numer Math 161:425–436
Heydari MH, Avazzadeh Z (2021) Jacobi-Gauss-Lobatto collocation approach for non-singular variable-order time fractional generalized Kuramoto-Sivashinsky equation. Eng Comput. https://doi.org/10.1007/s00366-021-01283-0
Elkot NA, Zaky MA, Doha EH, Ameen IG (2021) On the rate of convergence of the Legendre spectral collocation method for multi-dimensional nonlinear Volterra-Fredholm integral equations. Commun Theor Phys 73:025002
Ezz-Eldien SS, Wang Y, Abdelkawy MA, Zaky MA, Machado JT, Aldraiweesh AA (2020) Chebyshev spectral methods for multi-order fractional neutral pantograph equations. Nonlinear Dyn 100:3785–3797
Kim H, Kim KH, Jang B (2020) Shifted Jacobi spectral-Galerkin method for solving fractional order initial value problems. J Comput Appl Math 380:112988
Heydari MH, Hooshmandasl MR, Ghaini FM, Fereidouni F (2013) Two-dimensional Legendre wavelets for solving fractional Poisson equation with Dirichlet boundary conditions. Eng Anal Bound Elem 37:1331–1338
Heydari MH, Hooshmandasl MR, Ghaini FM, Cattani C (2015) Wavelets method for the time fractional diffusion-wave equation. Phys Lett A 379:71–76
Heydari MH, Hosseininia M, Avazzadeh Z (2020) An efficient wavelet-based approximation method for the coupled nonlinear fractal—fractional 2D Schrödinger equations. Eng Comput. https://doi.org/10.1007/s00366-020-00934-y
Hosseininia M, Heydari MH, Ghaini FM, Avazzadeh Z (2019) A wavelet method to solve nonlinear variable-order time fractional 2D Klein-Gordon equation. Comput Math Appl 78:3713–3730
Heydari MH (2019) Chebyshev cardinal wavelets for nonlinear variable-order fractional quadratic integral equations. Appl Numer Math 144:190–203
Dehestania H, Ordokhani Y, Razzaghi M (2020) Fractional-order Bessel wavelet functions for solving variable order fractional optimal control problems with estimation error. Int J Syst Sci 51(6):1032–1052
Heydari MH, Hooshmandasl MR, Ghaini FM, Cattani C (2014) A computational method for solving stochastic Itô-Volterra integral equations based on stochastic operational matrix for generalized hat basis functions. J Comput Phys 270:402–415
Tripathi MP, Baranwal VK, Pandey RK, Singh OP (2013) A new numerical algorithm to solve fractional differential equations based on operational matrix of generalized hat functions. Commun Nonlinear Sci Numer Simul 18:1327–1340
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Heydari, M.H., Bavi, O. An optimization method based on the Legendre wavelets for 3D rotating, squeezing and stretching magnetohydrodymanic flow in a channel with porous wall. Engineering with Computers 38 (Suppl 3), 2583–2592 (2022). https://doi.org/10.1007/s00366-021-01421-8
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00366-021-01421-8