IDEAS home Printed from https://ideas.repec.org/a/plo/pone00/0191103.html
   My bibliography  Save this article

Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations

Author

Listed:
  • Azmat Ullah
  • Suheel Abdullah Malik
  • Khurram Saleem Alimgeer

Abstract

In this paper, a hybrid heuristic scheme based on two different basis functions i.e. Log Sigmoid and Bernstein Polynomial with unknown parameters is used for solving the nonlinear heat transfer equations efficiently. The proposed technique transforms the given nonlinear ordinary differential equation into an equivalent global error minimization problem. Trial solution for the given nonlinear differential equation is formulated using a fitness function with unknown parameters. The proposed hybrid scheme of Genetic Algorithm (GA) with Interior Point Algorithm (IPA) is opted to solve the minimization problem and to achieve the optimal values of unknown parameters. The effectiveness of the proposed scheme is validated by solving nonlinear heat transfer equations. The results obtained by the proposed scheme are compared and found in sharp agreement with both the exact solution and solution obtained by Haar Wavelet-Quasilinearization technique which witnesses the effectiveness and viability of the suggested scheme. Moreover, the statistical analysis is also conducted for investigating the stability and reliability of the presented scheme.

Suggested Citation

  • Azmat Ullah & Suheel Abdullah Malik & Khurram Saleem Alimgeer, 2018. "Evolutionary algorithm based heuristic scheme for nonlinear heat transfer equations," PLOS ONE, Public Library of Science, vol. 13(1), pages 1-18, January.
    • Handle: RePEc:plo:pone00:0191103
    DOI: 10.1371/journal.pone.0191103
    as

    Download full text from publisher

    File URL: https://journals.plos.org/plosone/article?id=10.1371/journal.pone.0191103
    Download Restriction: no
    File URL: https://journals.plos.org/plosone/article/file?id=10.1371/journal.pone.0191103&type=printable
    Download Restriction: no
    File URL: https://libkey.io/10.1371/journal.pone.0191103?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. Suheel Abdullah Malik & Ijaz Mansoor Qureshi & Muhammad Amir & Aqdas Naveed Malik & Ihsanul Haq, 2015. "Numerical Solution to Generalized Burgers'-Fisher Equation Using Exp-Function Method Hybridized with Heuristic Computation," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-15, March.
    2. Dehghan, Maziar & Rahmani, Yousef & Domiri Ganji, Davood & Saedodin, Seyfollah & Valipour, Mohammad Sadegh & Rashidi, Saman, 2015. "Convection–radiation heat transfer in solar heat exchangers filled with a porous medium: Homotopy perturbation method versus numerical analysis," Renewable Energy, Elsevier, vol. 74(C), pages 448-455.
    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. Srivastava, Raj Shekhar & Kumar, Anuruddh & Thakur, Harishchandra & Vaish, Rahul, 2022. "Solar assisted thermoelectric cooling/heating system for vehicle cabin during parking: A numerical study," Renewable Energy, Elsevier, vol. 181(C), pages 384-403.
    2. Huu-Quan, Do & Memarian, Amir & Izadi, Mohsen & Shehzad, Sabir Ali, 2020. "Thermal performance and effectiveness of a dual-porous domestic heat exchanger for building heating application," Renewable Energy, Elsevier, vol. 162(C), pages 1874-1889.
    3. Rashidi, Saman & Esfahani, Javad Abolfazli & Rashidi, Abbas, 2017. "A review on the applications of porous materials in solar energy systems," Renewable and Sustainable Energy Reviews, Elsevier, vol. 73(C), pages 1198-1210.
    4. Singh, Somveer & Devi, Vinita & Tohidi, Emran & Singh, Vineet Kumar, 2020. "An efficient matrix approach for two-dimensional diffusion and telegraph equations with Dirichlet boundary conditions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    5. Siavashi, Majid & Hosseini, Farzad & Talesh Bahrami, Hamid Reza, 2021. "A new design with preheating and layered porous ceramic for hydrogen production through methane steam reforming process," Energy, Elsevier, vol. 231(C).
    6. Rashidi, Saman & Kashefi, Mohammad Hossein & Kim, Kyung Chun & Samimi-Abianeh, Omid, 2019. "Potentials of porous materials for energy management in heat exchangers – A comprehensive review," Applied Energy, Elsevier, vol. 243(C), pages 206-232.
    7. Norouzi, Amir Mohammad & Siavashi, Majid & Ahmadi, Rouhollah & Tahmasbi, Milad, 2021. "Experimental study of a parabolic trough solar collector with rotating absorber tube," Renewable Energy, Elsevier, vol. 168(C), pages 734-749.
    8. Jamal-Abad, Milad Tajik & Saedodin, Seyfolah & Aminy, Mohammad, 2016. "Heat transfer in concentrated solar air-heaters filled with a porous medium with radiation effects: A perturbation solution," Renewable Energy, Elsevier, vol. 91(C), pages 147-154.
    9. Jouybari, H. Javaniyan & Saedodin, S. & Zamzamian, A. & Nimvari, M. Eshagh & Wongwises, S., 2017. "Effects of porous material and nanoparticles on the thermal performance of a flat plate solar collector: An experimental study," Renewable Energy, Elsevier, vol. 114(PB), pages 1407-1418.
    10. Zogheib, Bashar & Tohidi, Emran, 2016. "A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions," Applied Mathematics and Computation, Elsevier, vol. 291(C), pages 1-13.

    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:plo:pone00:0191103. 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: plosone (email available below). General contact details of provider: https://journals.plos.org/plosone/ .

    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.