Study On Thermoregulation Mechanism Of Electrically Heated Sole For Footwear By Developing A Two-dimensional Heat Transfer Model

Harsh winter climate threatens human safety and health.Feet are vulnerable to coldness since they are the end of the limbs and have limited heat exchange with the blood.In this case,the electrically heated footwear(EHF)with thermoregulation is effective to protect feet from coldness.However,there is no abundant evidence for the set of design parameters,leading to overheating or underheating during use.With the rapid development of computer numerical simulation technology,numerical simulation methods provide convenience for the thermoregulation design of the EHF.However,there are few numerical models of the EHG.These models mainly focus on onedimensional heat transfer simulation,which is not applied to the electric heater with non-uniform heating.Based on the above,a two-dimensional heat transfer model for the electrically heated sole of footwear(EHSF)under extremely cold environments is developed in this study.The electrothermal characteristics of electric heaters and their influencing factors are investigated to build the model.The thermoregulation and electrothermal performances of the EHSF are analyzed by the model.Thus,the main research contents and findings are summarized as follows:(1)Two-dimensional heat transfer of electric heater.In the experiments,a cold-contact protective performance tester was used to simulate cold environments.The surface temperature of an alloy heating pad and a carbon nanotube(CNT)heating pad were recorded.The results showed that the heating process is divided into three phases: the pending phase where the heating pad is energized but does not heat up,the initial heating/cooling phase where the temperature rises rapidly and drops rapidly after reaching a peak,and the fluctuating phase where the heating pad heats intermittently according to the set temperature.Since the heated and unheated zones formed by heaters present distinct temperature differences,the alloy heating pad has obvious two-dimensional heat transfer characteristics.While the temperature inhomogeneity of the CNT heating pad is smaller than that of the alloy heating pad,there is no obvious twodimensional heat transfer characteristics.It was also showed that the contact temperature and the contact material are important for the electrothermal characteristics of the heating pad,while the change of excessive power supply has no obvious effect on the electrothermal characteristics.(2)Two-dimensional heat transfer model for the EHSF.The two-dimensional heat transfer simulation is mainly divided into four parts: a heat transfer model of footwear materials based on the law of porous heat transfer;a thermoregulation model of the electric heater based on their two-dimensional temperature distribution and electrothermal characteristics;the heat transfer of the air layer formed by the foot arch based on the plantar shape and thermophysical properties of air;and the biological heat transfer of the skin by the biological heat transfer mechanism of the foot.To predict the temperature distribution of the EHSF,the finite volume method was used to discrete equations and calculate the coupling model.Then,the skin temperature and the heating pad temperature were verified with changing footwear materials,cold contact pressures and temperature control modes.The results showed that the maximum predicted deviation of heating pad temperature was 13.52% and 6.53% in the initial rising/cooling phase and fluctuating phase,respectively.Meanwhile,the maximum of the mean predicted deviation of skin temperature was 9.87%.Therefore,the two-dimensional heat transfer model for the EHSF can effectively simulate the temperature regulation and heat transfer process of the electric heater,and accurately predict the skin temperature changes under cold contact conditions.(3)Thermoregulation and electrothermal performances of the EHSF.The model parameters were studied based on the two-dimensional heat transfer model for the EHSF.Among the parameters of the electric heater,the increase of the set temperature under the mode of heating pad temperature control(HPTC)increases the skin stable temperature and the working time of the electric heater.The model prediction also showed that the set temperature is reasonable at 38～42℃ for the HPTC mode.Meanwhile,the increase of heating power also increases the skin temperature and the energy consumption of electric heater,and the influence on the energy consumption in the fluctuating phase is greater than that in the initial heating phase.In addition,the arrangement of heaters mainly changes the intensity of heat source through the resistance value of heaters,thus affecting the skin temperature and the energy consumption of electric heater.For example,the arrangement of larger spacing presents higher skin temperature and energy consumption.Besides,the series arrangement leads to lower skin temperature and energy consumption than parallel arrangement.The model prediction also suggested that the sole composition has an important impact on the thermoregulation of the EHSF.The air formed by the foot arch has a negative effect on the shin thermal comfort and energy-saving performance of the EHSF.When the air thickness increases from0 mm to 5.84 mm,the time it takes for skin temperature under the mode of skin temperature control(STC)to stabilize increases by 98.08%,and the working time of the electric heater increases by52.73%.Hence,using the insole to adapt to the arch is conducive to functioning the EHSF.For the sole materials,the inner layer of the insole is not conducive to the heat transfer from the EHSF to the skin,while the outer layer of the insole is on the contrary,which is related to the position relative to the heating layer.Meanwhile,the inner and outer layers of the insole present different extent of influence on the energy-saving performance of the EHSF,and the thickness and thermal conductivity of outer layer dominates.Under the influence of cold contact environments,the skin temperatures are stable in the thermal comfort range.Meanwhile,the working time of the electric heater increases with the decrease of the cold contact temperature and the increase of the cold contact pressure(1.50～3.00 k Pa).This subject enriches the theory of cold protection and two-dimensional heat transfer between footwear and the foot,and provides guidance for the evaluation of materials,structural configuration and electrothermal performance of the EHSF,which is of positive significance for the development of active heating equipment for the foot in extreme cold environments.