IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v389y2010i17p3368-3374.html
   My bibliography  Save this article

The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems

Author

Listed:
  • Jiang, Xiaoyun
  • Xu, Mingyu

Abstract

In this paper a time fractional Fourier law is obtained from fractional calculus. According to the fractional Fourier law, a fractional heat conduction equation with a time fractional derivative in the general orthogonal curvilinear coordinate system is built. The fractional heat conduction equations in other orthogonal coordinate systems are readily obtainable as special cases. In addition, we obtain the solution of the fractional heat conduction equation in the cylindrical coordinate system in terms of the generalized H-function using integral transformation methods. The fractional heat conduction equation in the case 0<α≤1 interpolates the standard heat conduction equation (α=1) and the Localized heat conduction equation (α→0). Finally, numerical results are presented graphically for various values of order of fractional derivative.

Suggested Citation

  • Jiang, Xiaoyun & Xu, Mingyu, 2010. "The time fractional heat conduction equation in the general orthogonal curvilinear coordinate and the cylindrical coordinate systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(17), pages 3368-3374.
    • Handle: RePEc:eee:phsmap:v:389:y:2010:i:17:p:3368-3374
    DOI: 10.1016/j.physa.2010.04.023
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437110003626
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2010.04.023?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.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Lenzi, E.K. & Evangelista, L.R. & Zola, R.S. & Scarfone, A.M., 2022. "Fractional Schrödinger equation for heterogeneous media and Lévy like distributions," Chaos, Solitons & Fractals, Elsevier, vol. 163(C).
    2. Slawomir Blasiak, 2021. "Heat Transfer Analysis for Non-Contacting Mechanical Face Seals Using the Variable-Order Derivative Approach," Energies, MDPI, vol. 14(17), pages 1-13, September.
    3. Richard L. Magin & Ervin K. Lenzi, 2021. "Slices of the Anomalous Phase Cube Depict Regions of Sub- and Super-Diffusion in the Fractional Diffusion Equation," Mathematics, MDPI, vol. 9(13), pages 1-29, June.

    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:phsmap:v:389:y:2010:i:17:p:3368-3374. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.