电加热鞋帮二维瞬态传热模型及其实验验证

doi:10.13475/j.fzxb.20220808201

纺织学报 ›› 2023, Vol. 44 ›› Issue (10): 127-133.doi: 10.13475/j.fzxb.20220808201

电加热鞋帮二维瞬态传热模型及其实验验证

刘广菊¹, 苏云¹^,²(), 田苗¹^,², 李俊¹^,²

1.东华大学服装与艺术设计学院, 上海 200051
2.东华大学现代服装设计与技术教育部重点实验室, 上海 200051

收稿日期:2022-08-17 修回日期:2023-01-09 出版日期:2023-10-15 发布日期:2023-12-07
通讯作者: 苏云(1990—),男,副教授,博士。主要研究方向为功能防护服及纺织材料热湿传递模型。E-mail:suyun150@dhu.edu.cn。
作者简介:刘广菊(1998—),女,硕士生。主要研究方向为服装舒适性与功能服装。
基金资助:
国家自然科学基金项目(52004066);教育部人文社会科学研究青年基金项目(20YJC760087);中央高校基本科研业务费专项基金项目(2232022G-08);上海市教育发展基金会和上海市教育委员会“晨光计划”项目(20CG78)

Two-dimensional transient heat transfer model for electrically heated shoe upper and experimental validation

LIU Guangju¹, SU Yun¹^,²(), TIAN Miao¹^,², LI Jun¹^,²

1. College of Fashion and Design, Donghua University, Shanghai 200051, China
2. Key Laboratory of Clothing Design and Technology, Ministry of Education, Donghua University, Shanghai 200051, China

Received:2022-08-17 Revised:2023-01-09 Published:2023-10-15 Online:2023-12-07

摘要/Abstract

摘要：

为研究电加热元件的调温机制及其对足部热舒适的影响,基于有限体积法建立了电加热鞋帮二维传热模型,考虑了多孔介质织物传热以及加热区与非加热区的二维传热特性。通过冷暴露环境下电加热鞋帮织物的调温性能测试,验证了电加热鞋帮二维传热模型,并与一维模型进行了对比分析。结果表明:二维模型对于皮肤温度的预测偏差控制在2.59%~13.74%之间,随着鞋帮织物保暖性的改善,能够更准确地预测皮肤温度的变化;相比一维模型,二维模型能够更加科学地模拟电加热元件的调温规律,加热片温度在初始升温阶段的预测偏差减小了2.99%~25.09%。电加热鞋帮二维传热模型可更加准确地表征其调温机制,对丰富电加热元件二维传热理论、指导电加热元件的参数化设计具有重要意义。

关键词: 鞋帮, 二维热传递, 热舒适, 加热片, 有限体积法

Abstract:

Objective Local heating is an efficient way to improve thermal sensation and thermal comfort of foot. Currently, electrically heated products of footwear are available in the market. However, there are problems in terms of temperature control and parameters design such as heating temperature and power. Laboratory studies on personal electrically heated devices for foot are limited. The simulation of heated zones with distribution of heating elements in the numerical model is insufficient. The purpose of this study was to investigate the mechanism of temperature regulation by an electric heater and its influence on thermal comfort of foot.

Method Based on finite volume method, a two-dimensional model for electrically heated upper of foot-wear (EHUF) was developed. Characteristics of heat transfer in porous fabrics and two-dimensional heat transfer between heated and unheated zones were considered. The space-step of X and Y were defined as 5×10^-4 m and 5×10^-5 m respectively, and the time-step is 3 s. The maximum residual error was set at 0.001 ℃. The model was validated by testing the thermal regulative performance of the electrically heated footwear with cold exposure, and further compared with a one-dimensional model proposed.

Results The stable skin temperatures of two-dimensional model ranged from 34.57 ℃ to 36.19 ℃ (Fig. 3), and the deviations of skin temperature between two-dimensional model and the experiment were controlled to be in the band of 2.59% and 13.74% (Tab. 3). Under the premise of the same main parameter, both the one-dimension and two-dimensional models effectively predicted the skin temperature. It was found that the better the cold protective performance of fabrics, the smaller the difference between the one-dimension and two-dimensional model predictions. Specifically, when cold protective performance of fabrics matched the set temperature of the heating pad, the two-dimensional model under the mode of heating pad temperature control (HPTC) was better than the one-dimensional model. This was mainly represented by the difference of average predicted deviation between the one-dimensional and two-dimensional, -2.55% under the condition of double-layer fabrics and HPTC mode at 45 ℃ (HPTC45), and 0.53% under the condition of double-layer fabrics and HPTC mode at 35 ℃ (HPTC35). The skin temperature prediction ability of the two-dimensional model was improved compared to the one-dimensional model. Under the mode of skin temperature control (STC), the maximum prediction deviation of skin temperature in the two-dimensional model decreased by 1.49% to 3.93%. Compared with one-dimensional model, the two-dimensional model simulated the temperature regulation of heating pad more reliably. In the initial heating phase, the predicted deviations of heating pad temperature between two-dimensional model and experiment reduced by 2.99%-25.09% (Tab. 4). It is also shown that the prediction accuracy of STC model improved the most. In the temperature fluctuation phase, the predicted deviation of double-layer fabric under HPTC35 and HPTC45 mode decreased by 3.36% and 5.95% respectively, and the other conditions increased. Nevertheless, most of the increases were 1.57%-2.45%, which was attributed to the change of heating simulation in the two-dimensional model.

Conclusion This research numerically shows the mechanisms of heat transfer and thermal regulation of electrically heating pad in footwear. It is concluded that the two-dimensional heat transfer model for the EHUF characterizes the mechanism of temperature regulation more accurately than the one-dimensional model. The developed model helps to enrich the two-dimensional heat transfer theory of electric heater and is of great significance to study the parameters of the EHUF and other cold weather clothing system. It can be used to efficiently evaluate the thermal regulation of electrically heating pad in footwear, and provide references for the optimal design of thermal regulation and energy efficiency of the electrically heated footwear. By further investigating the heat source of the electric heater, the two-dimensional model can more accurately predict the temperature regulation performance of active heating garments. This is likely to lead to a contribution in foot thermal comfort for staffs performing in a severely cold environment.

Key words: upper of footwear, two-dimensional heat transfer, thermal comfort, heating pad, finite volume method

中图分类号:

TS941.73

刘广菊, 苏云, 田苗, 李俊. 电加热鞋帮二维瞬态传热模型及其实验验证[J]. 纺织学报, 2023, 44(10): 127-133.

LIU Guangju, SU Yun, TIAN Miao, LI Jun. Two-dimensional transient heat transfer model for electrically heated shoe upper and experimental validation[J]. Journal of Textile Research, 2023, 44(10): 127-133.

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参考文献 19

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织物层	材料	面密度/ (g·m^-2)	厚度/ mm	密度/ (kg·m^-3)
外层	天然皮革	654.8	1.712 6	382.342 6
	92%涤纶+ 8%聚氨酯	147.0	0.204 1	720.235 2
保暖层	聚氨酯	87.0	1.690 0	51.479 3
内层	涤纶	95.0	0.400 0	237.500 0
袜子	棉	288.0	1.233 6	233.463 0

成分	密度/ (kg·m^-3)	导热系数/ (W·m^-1·℃^-1)	比热/ (J·kg^-1·℃^-1)
聚酯纤维	1 380	0.084	1 340
天然皮革^[6]	998	0.180	2 010
聚氨酯纤维	1 250	0.250	1 120
棉纤维	1 540	0.071	1 210
空气	1.205	0.027	1 010
聚酰亚胺材料	1 380	0.100	1 090

模型	织物	HPTC35		HPTC45		STC35
模型	织物	平均	最大	平均	最大	平均	最大
一维	双层	5.31	8.98	11.19	19.16	3.56	8.95
	四层	5.19	6.81	6.08	11.08	2.98	8.13
二维	双层	4.78	7.55	13.74	22.56	3.33	5.02
	四层	7.46	9.69	5.89	10.33	2.59	6.64

模型	织物	HPTC35		HPTC45		STC35
模型	织物	RP	FP	RP	FP	RP	FP
一维	双层	16.11	3.84	27.18	17.66	37.21	5.49
	四层	20.21	7.11	27.72	11.85	27.32	1.41
二维	双层	11.28	5.56	24.19	23.55	12.12	7.06
	四层	15.35	3.75	22.24	5.90	19.36	3.86

电加热鞋帮二维瞬态传热模型及其实验验证

Two-dimensional transient heat transfer model for electrically heated shoe upper and experimental validation

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