Closed-Form Solutions for Locating Heat-Concentrated Sources Using Temperature Difference

Daoyuan Sun, Yifan Wu, Longjun Dong and Qiaomu Luo ()
Additional contact information
Daoyuan Sun: School of Resources and Safety Engineering, Central South University, Changsha 410083, China
Yifan Wu: College of Foreign Languages and Cultures, Xiamen University, Xiamen 361005, China
Longjun Dong: School of Resources and Safety Engineering, Central South University, Changsha 410083, China
Qiaomu Luo: School of Resources and Safety Engineering, Central South University, Changsha 410083, China

Mathematics, 2022, vol. 10, issue 16, 1-11

Abstract: The closed-form solution, one of the effective and sufficient optimization methods, is usually less computationally burdensome than iterative and nonlinear minimization in optimization problems of heat source localization. This work presents two-dimensional, closed-form solutions for locating heat-concentrated sources using temperature differences for known and unknown temperature gradient systems. The nonlinear location equations for heat-concentrated source location are simplified to linear equations, and they are solved directly to obtain the analytical solution. To validate the accuracy of the proposed analytical solutions, three numerical examples of heat source localization were conducted. Results show that the proposed analytical solutions have a higher accuracy than iterative results by Levenberg–Marquardt. The locating accuracy for the three sources using AS-KTG improved by 94.82%, 90.40%, and 92.77%, while the locating accuracy for the three sources using AS-UTG improved by 68.94%, 16.72%, and 46.86%, respectively. It is concluded that the proposed method can locate the heat sources using temperatures and coordinates of sensors without the need for a heat transfer coefficient, a heat transfer rate, and thermal conductivity. These proposed analytical solutions can provide a new approach to locating heat sources for more complicated conditions using temperature differences, such as the localization of geothermal sources and nuclear waste leak points.

Keywords: heat-concentrated source; optimization of heat source location; temperature gradient; closed-form solution; temperature difference (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
References: View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/10/16/2843/pdf (application/pdf)
https://www.mdpi.com/2227-7390/10/16/2843/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:10:y:2022:i:16:p:2843-:d:884521

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().