Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters
Textile heaters are made from knitted conductive yarns integrated into their fabric, making them stretchable, washable, breathable and suitable for close-to-skin wear. However, the non-zero resistance in the lead wires causes non-uniform power distribution, which presents a design challenge. To addr...
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MDPI AG
2024-09-01
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| Series: | Thermo |
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| author | Kaspar M. B. Jansen |
| author_facet | Kaspar M. B. Jansen |
| author_sort | Kaspar M. B. Jansen |
| collection | DOAJ |
| description | Textile heaters are made from knitted conductive yarns integrated into their fabric, making them stretchable, washable, breathable and suitable for close-to-skin wear. However, the non-zero resistance in the lead wires causes non-uniform power distribution, which presents a design challenge. To address this, the electrical performance of the heaters is modeled as an n-ladder resistor network. By using the finite difference method, simple, closed-form expressions are derived for networks with their power source connected to input terminals <i>A</i><sub>1</sub><i>B</i><sub>1</sub> and <i>A</i><sub>1</sub><i>B<sub>n</sub></i>, respectively. The exact results are then used to derive approximations and design criteria. The solutions for the ladder networks presented in this paper apply to a wider class of physical problems, such as irrigation systems, transformer windings, and cooling fins. |
| format | Article |
| id | doaj-art-c1d8db06c6214178b5fb2ab6d3acca3c |
| institution | OA Journals |
| issn | 2673-7264 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | MDPI AG |
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| series | Thermo |
| spelling | doaj-art-c1d8db06c6214178b5fb2ab6d3acca3c2025-08-20T02:01:14ZengMDPI AGThermo2673-72642024-09-014443344410.3390/thermo4040023Closed-Form Solutions for Current Distribution in Ladder-Type Textile HeatersKaspar M. B. Jansen0Department of Sustainable Design Engineering, Delft University of Technology, 2628 CE Delft, The NetherlandsTextile heaters are made from knitted conductive yarns integrated into their fabric, making them stretchable, washable, breathable and suitable for close-to-skin wear. However, the non-zero resistance in the lead wires causes non-uniform power distribution, which presents a design challenge. To address this, the electrical performance of the heaters is modeled as an n-ladder resistor network. By using the finite difference method, simple, closed-form expressions are derived for networks with their power source connected to input terminals <i>A</i><sub>1</sub><i>B</i><sub>1</sub> and <i>A</i><sub>1</sub><i>B<sub>n</sub></i>, respectively. The exact results are then used to derive approximations and design criteria. The solutions for the ladder networks presented in this paper apply to a wider class of physical problems, such as irrigation systems, transformer windings, and cooling fins.https://www.mdpi.com/2673-7264/4/4/23knitted heaterelectrothermal performanceladder networkequivalent resistance |
| spellingShingle | Kaspar M. B. Jansen Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters Thermo knitted heater electrothermal performance ladder network equivalent resistance |
| title | Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters |
| title_full | Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters |
| title_fullStr | Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters |
| title_full_unstemmed | Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters |
| title_short | Closed-Form Solutions for Current Distribution in Ladder-Type Textile Heaters |
| title_sort | closed form solutions for current distribution in ladder type textile heaters |
| topic | knitted heater electrothermal performance ladder network equivalent resistance |
| url | https://www.mdpi.com/2673-7264/4/4/23 |
| work_keys_str_mv | AT kasparmbjansen closedformsolutionsforcurrentdistributioninladdertypetextileheaters |