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