IDEAS home Printed from https://ideas.repec.org/a/wly/jnljam/v2013y2013i1n219486.html

New Analytical and Numerical Solutions for Mixed Convection Boundary‐Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium

Author

Listed:
  • Emad H. Aly
  • Abdelhalim Ebaid

Abstract

Two different analytical and numerical methods have been applied to solve the system describing the mixed convection boundary‐layer nanofluids flow along an inclined plate embedded in a porous medium, namely, homotopy perturbation method (HPM) and Chebyshev pseudospectral differentiation matrix (ChPDM), respectively. Further, ChPDM is used as a control method to check the accuracy of the results obtained by HPM. The analytical method is applied using a new way for the deformed equations, and the resulted solution was expressed in terms of a well‐known entire error function. In addition, using only two terms of the homotopy series, the approximate analytical solution is compared with the numerical solution obtained by the accurate ChPDM approach. The results reveal that good agreements have been achieved between the two approaches for various values of the investigated physical parameters.

Suggested Citation

  • Emad H. Aly & Abdelhalim Ebaid, 2013. "New Analytical and Numerical Solutions for Mixed Convection Boundary‐Layer Nanofluid Flow along an Inclined Plate Embedded in a Porous Medium," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    • Handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:219486
    DOI: 10.1155/2013/219486
    as

    Download full text from publisher

    File URL: https://doi.org/10.1155/2013/219486
    Download Restriction: no
    File URL: https://libkey.io/10.1155/2013/219486?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Emad H. Aly & Abdelhalim Ebaid, 2012. "On the Exact Analytical and Numerical Solutions of Nano Boundary-Layer Fluid Flows," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-22, September.
    2. Emad H. Aly & Abdelhalim Ebaid, 2012. "On the Exact Analytical and Numerical Solutions of Nano Boundary‐Layer Fluid Flows," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. He, Ji-Huan, 2005. "Application of homotopy perturbation method to nonlinear wave equations," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 695-700.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Emad H. Aly & Abdelhalim Ebaid, 2013. "Exact Analytical Solution for Suction and Injection Flow with Thermal Enhancement of Five Nanofluids over an Isothermal Stretching Sheet with Effect of the Slip Model: A Comparative Study," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. He, Ji-Huan, 2009. "Nonlinear science as a fluctuating research frontier," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2533-2537.
    3. Abbasbandy, S., 2007. "A numerical solution of Blasius equation by Adomian’s decomposition method and comparison with homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 31(1), pages 257-260.
    4. Çelik, Nisa & Seadawy, Aly R. & Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "A model of solitary waves in a nonlinear elastic circular rod: Abundant different type exact solutions and conservation laws," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    5. Alipanah, Amjad & Zafari, Mahnaz, 2023. "Collocation method using auto-correlation functions of compact supported wavelets for solving Volterra’s population model," Chaos, Solitons & Fractals, Elsevier, vol. 175(P1).
    6. Ya Qin & Adnan Khan & Izaz Ali & Maysaa Al Qurashi & Hassan Khan & Rasool Shah & Dumitru Baleanu, 2020. "An Efficient Analytical Approach for the Solution of Certain Fractional-Order Dynamical Systems," Energies, MDPI, vol. 13(11), pages 1-14, May.
    7. Yu, Guo-Fu & Tam, Hon-Wah, 2006. "Conservation laws for two (2+1)-dimensional differential–difference systems," Chaos, Solitons & Fractals, Elsevier, vol. 30(1), pages 189-196.
    8. Moghimi, Mahdi & Hejazi, Fatemeh S.A., 2007. "Variational iteration method for solving generalized Burger–Fisher and Burger equations," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1756-1761.
    9. Keramati, B., 2009. "An approach to the solution of linear system of equations by He’s homotopy perturbation method," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 152-156.
    10. Demiray, Hilmi, 2006. "Interaction of nonlinear waves governed by Boussinesq equation," Chaos, Solitons & Fractals, Elsevier, vol. 30(5), pages 1185-1189.
    11. Siddiqui, A.M. & Ahmed, M. & Ghori, Q.K., 2007. "Thin film flow of non-Newtonian fluids on a moving belt," Chaos, Solitons & Fractals, Elsevier, vol. 33(3), pages 1006-1016.
    12. Shidfar, A. & Molabahrami, A. & Babaei, A. & Yazdanian, A., 2009. "A study on the d-dimensional Schrödinger equation with a power-law nonlinearity," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2154-2158.
    13. Ramos, J.I., 2009. "Piecewise-adaptive decomposition methods," Chaos, Solitons & Fractals, Elsevier, vol. 40(4), pages 1623-1636.
    14. Hassan A. Zedan & W. Barakati & Nada Hamad, 2013. "The Application of the Homotopy Analysis Method and the Homotopy Perturbation Method to the Davey‐Stewartson Equations and Comparison between Them and Exact Solutions," Journal of Applied Mathematics, John Wiley & Sons, vol. 2013(1).
    15. Héctor Vázquez-Leal, 2012. "Rational Homotopy Perturbation Method," Journal of Applied Mathematics, John Wiley & Sons, vol. 2012(1).
    16. Mădălina Sofia Paşca & Olivia Bundău & Adina Juratoni & Bogdan Căruntu, 2022. "The Least Squares Homotopy Perturbation Method for Systems of Differential Equations with Application to a Blood Flow Model," Mathematics, MDPI, vol. 10(4), pages 1-14, February.
    17. Mingsheng Hu & Zhijuan Jia & Qiaoling Chen & Suiming Jia, 2014. "Exact Solutions for Nonlinear Wave Equations by the Exp‐Function Method," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    18. Al-Khaled, Kamel, 2007. "Theory and computation in singular boundary value problems," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 678-684.
    19. Golbabai, A. & Javidi, M., 2009. "A spectral domain decomposition approach for the generalized Burger’s–Fisher equation," Chaos, Solitons & Fractals, Elsevier, vol. 39(1), pages 385-392.
    20. Mei, Shu-Li & Du, Cheng-Jin & Zhang, Sen-Wen, 2008. "Asymptotic numerical method for multi-degree-of-freedom nonlinear dynamic systems," Chaos, Solitons & Fractals, Elsevier, vol. 35(3), pages 536-542.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wly:jnljam:v:2013:y:2013:i:1:n:219486. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Wiley Content Delivery (email available below). General contact details of provider: https://onlinelibrary.wiley.com/journal/4185 .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.