IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v12y2024i10p1584-d1397505.html
   My bibliography  Save this article

An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques

Author

Listed:
  • Cheng-Hung Huang

    (Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan 701, Taiwan)

  • Kuan-Chieh Fang

    (Department of Systems and Naval Mechatronic Engineering, National Cheng Kung University, Tainan 701, Taiwan)

Abstract

In this study, an inverse conjugate heat transfer problem is examined to estimate temporally and spatially the dependent unknown surface heat flux using thermography techniques with a thermal camera in a three-dimensional domain. Thermography techniques encompass a broad set of methods and procedures used for capturing and analyzing thermal data, while thermal cameras are specific tools used within those techniques to capture thermal images. In the present study, the interface conditions of the plate and air domains are obtained using perfect thermal contact conditions, and therefore we define the problem studied as an inverse conjugate heat transfer problem. Achieving the simultaneous solution of the continuity, Navier–Stokes, and energy equations within the air domain, alongside the heat conduction equation in the plate domain, presents a more intricate challenge compared to conventional inverse heat conduction problems. The validity of our inverse solutions was verified through numerical simulations, considering various inlet air velocities and plate thicknesses. Notably, it was found that due to the singularity of the gradient of the cost function at the final time point, the estimated results near the final time must be discarded, and exact measurements consistently produce accurate boundary heat fluxes under thin-plate conditions, with air velocity exhibiting no significant impact on the estimates. Additionally, an analysis of measurement errors and their influence on the inverse solutions was conducted. The numerical results conclusively demonstrated that the maximum error when estimating heat flux consistently remained below 3% and higher measurement noise resulted in the accuracy of the heat flux estimation decreasing. This underscores the inherent challenges associated with inverse problems and highlights the importance of obtaining accurate measurement data in the problem domain.

Suggested Citation

  • Cheng-Hung Huang & Kuan-Chieh Fang, 2024. "An Inverse Problem for Estimating Spatially and Temporally Dependent Surface Heat Flux with Thermography Techniques," Mathematics, MDPI, vol. 12(10), pages 1-28, May.
  • Handle: RePEc:gam:jmathe:v:12:y:2024:i:10:p:1584-:d:1397505
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/12/10/1584/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/12/10/1584/
    Download Restriction: no
    ---><---

    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:gam:jmathe:v:12:y:2024:i:10:p:1584-:d:1397505. 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: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    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.