IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v177y2023ics0960077923011384.html
   My bibliography  Save this article

Nonlinear dynamics of porous fin temperature profile: The extended simplest equation approach

Author

Listed:
  • Samina, Samina
  • Jhangeer, Adil
  • Chen, Zili

Abstract

This paper discusses the extended simplest equation method for analyzing the behavior of a porous fin while taking into account the porous and convection parameters. This method helps in obtaining exact solutions and understanding the temperature distribution and heat transfer characteristics of the fin. Furthermore, the equation is transformed into a planar dynamical system using the Galilean transformation. Under dynamic and quasiperiodic conditions, the behavior of the equation is extensively discussed. The bifurcation of the planar system of dynamics described by the transformed equation is studied using bifurcation theory and phase portrait analysis. Additionally, a perturbed force is introduced to the dynamical system, and the RK4 method is employed to identify periodic or quasiperiodic patterns in the system. Sensitivity and multistability analysis are applied to the porous fin equation, considering different initial conditions to investigate its quasiperiodic and periodic behavior. The chaotic structure of the perturbed dynamical system using Lyapunov exponent analysis has also been discussed. Through a comparison between numerical solutions and graphical representations, the validity and applicability of the exact technique are demonstrated. The reported findings contribute novel insights into understanding the behavior of nonlinear equations encountered in mathematical physics.

Suggested Citation

  • Samina, Samina & Jhangeer, Adil & Chen, Zili, 2023. "Nonlinear dynamics of porous fin temperature profile: The extended simplest equation approach," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
  • Handle: RePEc:eee:chsofr:v:177:y:2023:i:c:s0960077923011384
    DOI: 10.1016/j.chaos.2023.114236
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923011384
    Download Restriction: Full text for ScienceDirect subscribers only

    File URL: https://libkey.io/10.1016/j.chaos.2023.114236?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
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Natiq, Hayder & Banerjee, Santo & Misra, A.P. & Said, M.R.M., 2019. "Degenerating the butterfly attractor in a plasma perturbation model using nonlinear controllers," Chaos, Solitons & Fractals, Elsevier, vol. 122(C), pages 58-68.
    2. Seadawy, Aly R., 2016. "Stability analysis solutions for nonlinear three-dimensional modified Korteweg–de Vries–Zakharov–Kuznetsov equation in a magnetized electron–positron plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 455(C), pages 44-51.
    3. Cheng Chen & Zuolei Wang, 2021. "New Exact Solutions, Dynamical and Chaotic Behaviors for the Fourth-Order Nonlinear Generalized Boussinesq Water Wave Equation," Advances in Mathematical Physics, Hindawi, vol. 2021, pages 1-13, September.
    4. Yun-Mei Zhao & Ying-Hui He & Yao Long, 2013. "The Simplest Equation Method and Its Application for Solving the Nonlinear NLSE, KGZ, GDS, DS, and GZ Equations," Journal of Applied Mathematics, Hindawi, vol. 2013, pages 1-7, December.
    5. Rizvi, Syed T.R. & Seadawy, Aly R. & Ahmed, Sarfaraz & Younis, Muhammad & Ali, Kashif, 2021. "Study of multiple lump and rogue waves to the generalized unstable space time fractional nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 151(C).
    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. Li, Hongtao & Gedikli, Ersegun Deniz & Lubbad, Raed, 2020. "Exploring time-delay-based numerical differentiation using principal component analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).
    2. Seadawy, Aly R. & Iqbal, Mujahid & Lu, Dianchen, 2020. "Propagation of kink and anti-kink wave solitons for the nonlinear damped modified Korteweg–de Vries equation arising in ion-acoustic wave in an unmagnetized collisional dusty plasma," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 544(C).
    3. El-Sheikh, Mohamed M.A. & Seadawy, Aly R. & Ahmed, Hamdy M. & Arnous, Ahmed H. & Rabie, Wafaa B., 2020. "Dispersive and propagation of shallow water waves as a higher order nonlinear Boussinesq-like dynamical wave equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 537(C).
    4. Hu, Xiang & Yin, Zhixiang, 2022. "A study of the pulse propagation with a generalized Kudryashov equation," Chaos, Solitons & Fractals, Elsevier, vol. 161(C).
    5. Rizvi, Syed T.R. & Seadawy, Aly R. & Farah, N. & Ahmad, S., 2022. "Application of Hirota operators for controlling soliton interactions for Bose-Einstien condensate and quintic derivative nonlinear Schrödinger equation," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    6. Nguyen, Thu Ha & Nguyen, Van Chung & Bui, Dang Quang & Dao, Phuong Nam, 2024. "An efficient Min/Max Robust Model Predictive Control for nonlinear discrete-time systems with dynamic disturbance," Chaos, Solitons & Fractals, Elsevier, vol. 180(C).
    7. Çelik, Nisa & Tetik, Duygu, 2024. "New dynamical analysis of the exact traveling wave solutions to a (3+1)-dimensional Gardner-KP equation by three efficient architecture," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    8. Tian, Yang & Tian, Hui & Cui, Qimei & Zhu, Xuzhen, 2024. "Phase transition phenomena in social propagation with dynamic fashion tendency and individual contact," Chaos, Solitons & Fractals, Elsevier, vol. 178(C).
    9. Zhang, Xin & Shi, Ran, 2022. "Novel fast fixed-time sliding mode trajectory tracking control for manipulator," Chaos, Solitons & Fractals, Elsevier, vol. 162(C).
    10. Sağlam Özkan, Yeşim & Yaşar, Emrullah, 2021. "Breather-type and multi-wave solutions for (2+1)-dimensional nonlocal Gardner equation," Applied Mathematics and Computation, Elsevier, vol. 390(C).
    11. Seadawy, Aly R. & Nasreen, Naila & Lu, Dianchen & Arshad, Muhammad, 2020. "Arising wave propagation in nonlinear media for the (2+1)-dimensional Heisenberg ferromagnetic spin chain dynamical model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    12. Aly R. Seadawy & Syed T. R. Rizvi & Hanadi Zahed, 2023. "Stability Analysis of the Rational Solutions, Periodic Cross-Rational Solutions, Rational Kink Cross-Solutions, and Homoclinic Breather Solutions to the KdV Dynamical Equation with Constant Coefficien," Mathematics, MDPI, vol. 11(5), pages 1-16, February.
    13. Xu, Zhihao & Lv, Zhiqiang & Chu, Benjia & Li, Jianbo, 2024. "A Fast Spatial-temporal Information Compression algorithm for online real-time forecasting of traffic flow with complex nonlinear patterns," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).

    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:eee:chsofr:v:177:y:2023:i:c:s0960077923011384. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.