A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity
A modified perturbation method (MPM) is applied to obtain the solution of the heat transfer equation for convective fins with temperature-dependent thermal conductivity. In this method, the nonlinear term is split into linear and nonlinear terms to obtain the perturbation solution. The solution of a...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
The Japan Society of Mechanical Engineers
2025-04-01
|
| Series: | Mechanical Engineering Journal |
| Subjects: | |
| Online Access: | https://www.jstage.jst.go.jp/article/mej/12/3/12_24-00354/_pdf/-char/en |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1839639796199194624 |
|---|---|
| author | Sumio KATO Shoichi MATSUDA |
| author_facet | Sumio KATO Shoichi MATSUDA |
| author_sort | Sumio KATO |
| collection | DOAJ |
| description | A modified perturbation method (MPM) is applied to obtain the solution of the heat transfer equation for convective fins with temperature-dependent thermal conductivity. In this method, the nonlinear term is split into linear and nonlinear terms to obtain the perturbation solution. The solution of a convective fin with linearly temperature-dependent thermal conductivity by the MPM is simple to use and very accurate. Calculated results show that the solution by the MPM agrees well with the FDM (Finite Difference Method) solution in a wide range of the small parameter ε (thermal conductivity parameter), whereas the solution by the conventional perturbation method (CPM) is accurate only in a small range of ε. For example, the RMS error δRMS of the MPM solution with respect to the FDM solution is less than 10-4 for N (fin parameter) = 1 and -0.505 ≤ ε ≤ 10, on the other hand the RMS error of the CPM solution is less than 10-4 for N = 1 and -0.141 ≤ ε ≤ 0.142. The fin efficiencies obtained by the CPM, MPM and FDM are examined. The modification of the perturbation method by splitting the nonlinear term helps reduce the contribution of the nonlinear term upon the solution, which drastically improves the convergence characteristics of the solution. |
| format | Article |
| id | doaj-art-c5d51a3dc54c41c7b0ac5852ab86e0ee |
| institution | Matheson Library |
| issn | 2187-9745 |
| language | English |
| publishDate | 2025-04-01 |
| publisher | The Japan Society of Mechanical Engineers |
| record_format | Article |
| series | Mechanical Engineering Journal |
| spelling | doaj-art-c5d51a3dc54c41c7b0ac5852ab86e0ee2025-07-04T05:20:33ZengThe Japan Society of Mechanical EngineersMechanical Engineering Journal2187-97452025-04-0112324-0035424-0035410.1299/mej.24-00354mejA modified perturbation method for convective straight fins with temperature-dependent thermal conductivitySumio KATO0Shoichi MATSUDA1Faculty of Engineering, University of the RyukyusFaculty of Engineering, University of the RyukyusA modified perturbation method (MPM) is applied to obtain the solution of the heat transfer equation for convective fins with temperature-dependent thermal conductivity. In this method, the nonlinear term is split into linear and nonlinear terms to obtain the perturbation solution. The solution of a convective fin with linearly temperature-dependent thermal conductivity by the MPM is simple to use and very accurate. Calculated results show that the solution by the MPM agrees well with the FDM (Finite Difference Method) solution in a wide range of the small parameter ε (thermal conductivity parameter), whereas the solution by the conventional perturbation method (CPM) is accurate only in a small range of ε. For example, the RMS error δRMS of the MPM solution with respect to the FDM solution is less than 10-4 for N (fin parameter) = 1 and -0.505 ≤ ε ≤ 10, on the other hand the RMS error of the CPM solution is less than 10-4 for N = 1 and -0.141 ≤ ε ≤ 0.142. The fin efficiencies obtained by the CPM, MPM and FDM are examined. The modification of the perturbation method by splitting the nonlinear term helps reduce the contribution of the nonlinear term upon the solution, which drastically improves the convergence characteristics of the solution.https://www.jstage.jst.go.jp/article/mej/12/3/12_24-00354/_pdf/-char/enmodified perturbation methodconventional perturbation methodheat transfer problemtemperature-dependent thermal conductivityconvective finfin efficiency |
| spellingShingle | Sumio KATO Shoichi MATSUDA A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity Mechanical Engineering Journal modified perturbation method conventional perturbation method heat transfer problem temperature-dependent thermal conductivity convective fin fin efficiency |
| title | A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity |
| title_full | A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity |
| title_fullStr | A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity |
| title_full_unstemmed | A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity |
| title_short | A modified perturbation method for convective straight fins with temperature-dependent thermal conductivity |
| title_sort | modified perturbation method for convective straight fins with temperature dependent thermal conductivity |
| topic | modified perturbation method conventional perturbation method heat transfer problem temperature-dependent thermal conductivity convective fin fin efficiency |
| url | https://www.jstage.jst.go.jp/article/mej/12/3/12_24-00354/_pdf/-char/en |
| work_keys_str_mv | AT sumiokato amodifiedperturbationmethodforconvectivestraightfinswithtemperaturedependentthermalconductivity AT shoichimatsuda amodifiedperturbationmethodforconvectivestraightfinswithtemperaturedependentthermalconductivity AT sumiokato modifiedperturbationmethodforconvectivestraightfinswithtemperaturedependentthermalconductivity AT shoichimatsuda modifiedperturbationmethodforconvectivestraightfinswithtemperaturedependentthermalconductivity |