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On the performance of a mitt heating multilayer: a numerical study Sandra Couto and Joao B.L.M. Campos Departamento de Engenharia Quı´mica, Transport Phenomena Research Centre, Faculdade de Engenharia da Universidade do Porto, Porto, Portugal, and
A mitt heating multilayer
373 Received 2 February 2011 Revised 12 April 2011 Accepted 12 April 2011
Tiago S. Mayor Centre for Nanotechnology and Smart Materials, Vila Nova de Famalica˜o, Portugal Abstract Purpose – The purpose of this paper is to investigate the heat transfer on an alpine-climbing mitt featuring an electrical heating multilayer, in order to provide information for the optimization of its thermal performance. Design/methodology/approach – A numerical model was developed to simulate the heat transfer across an electrical-heated alpine mitt. The model was used to study the heat losses as a function of the environmental conditions, to optimise the positioning of the heating elements, to determine the optimal power input to the heating system, to estimate the battery capacity requirements and to assess the effect of low-emissivity surfaces. Findings – The results show that: the heating elements assure approximately constant temperatures across the skin provided they are not more than 6-7 mm apart; the use of low-emissivity surfaces facing the skin can reduce the total heat loss by 8-36 per cent (for air layer thicknesses in the range 102 3 to 102 2 m) and to increase the skin temperature during the transient operation of the heating multilayer; the heat losses from the mitt are practically independent of the chosen heating power; and a battery capacity of 4 A h assures active temperature regulation for more than 18-23 h. Practical implications – By enhancing the thermal performance of an electrical heating mitt, the use of low-emissivity surfaces (facing the skin) can favour the thermal comfort perception of its user. Originality/value – The influence of several parameters on the thermal performance of an electrical-heated mitt is analysed and discussed. The findings are relevant for improving the performance of existing electrical heating garments. Keywords Heat transfer, Electrical heating layer, Low-emissivity, Metallization, Alpine mitt, Radiation, Convection Paper type Research paper
Nomenclature
G ¼ solar irradiance (1,373 W m2 2) x, y, z ¼ coordinates (m) P ¼ heating power (W m2 2) Q ¼ source term (W m2 3) T ¼ temperature (8C) t ¼ time (s) Subscripts avg ¼ average
min max Greek a 1 s
D
¼ minimum ¼ maximum symbols ¼ surface absorptivity ¼ surface emissivity ¼ Stefan-Boltzmann constant (5.67 £ 102 8 W m2 2 K4) ¼ difference
International Journal of Clothing Science and Technology Vol. 23 No. 5, 2011 pp. 373-387 q Emerald Group Publishing Limited 0955-6222 DOI 10.1108/09556221111166301
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1. Introduction The use of electrically heating elements in clothing/footwear products has been increasing in the last years as improvements in battery performances allow for longer effects (Holmer, 2005). Given that battery life is often strongly correlated with battery weight, this can be of paramount importance for activities involving strenuous efforts, such as in alpine climbing. In such activities, all unnecessary weight is severely questioned and, therefore, it is important in terms of products acceptance that any heating solution does not imply a marked increased in the weight to be carried. In that sense, it is crucial that the power requirements of such systems be thoroughly studied in order to allow for minimum battery weights. Low-emissivity surfaces are known to decrease the heat transfer by radiation (Cengel, 2002). They are used in very different applications such as building/construction, machinery, space technology, clothing apparel, etc. (Cengel, 2002; Holmer, 2005; Ma¨kinen, 2005). When used on clothing outer surfaces, they help to reduce the heat loss to surrounding colder mediums (e.g. a worker inside a cold chamber or an unlit astronaut outside the spacecraft) or diminish the thermal loads on the human body by reflecting partially the incident infrared radiation (e.g. a fire fighter near a ground fire or an astronaut exposed to solar radiation). When used facing the skin, they can contribute to the reduction of the radiant heat loss from the body (e.g. emergency care thermal blankets). However, the impact of low-emissivity surfaces in the reduction of the heat loss and gain from the human body depends on the relevancy of the radiant resistance when compared to the conductive (clothing) and convective resistances. For thinner clothes, for which the conductive resistance is small, the radiant resistances are more important. In these scenarios, changes in the emissivity of the surfaces may have a strong impact on the total heat exchange. The relevancy of this impact diminishes for clothes with increasing thickness (i.e. with higher conductive resistance) and for windier environmental conditions (where convective heat losses predominate over radiant ones (Holmer, 2005)). Thus, for every particular scenario, i.e. clothing ensemble and environmental conditions, it is necessary to evaluate the relative importance of the aforementioned resistances to assess the effect changes in clothing surface emissivity may have over the overall heat exchange to and from a human body. In order to address these questions, a thorough analysis was conducted focussing on the heat transfer across an alpine-climbing mitt featuring an electrical heating multilayer. The relevancy of conduction, convection and radiation heat transfer mechanisms was studied for different environmental conditions and heating powers, in order to allow the optimization of the heating system performance and weight. The impact of surface metallization over the total heat exchange across the mitt and over the heating and cooling performance of the multilayer heating system was analysed. This provided valuable information for the development and optimization of the heating system. 2. Materials and methods 2.1 Physical situation under consideration This study aimed at the optimization of the thermal performance of a heating multilayer, developed for use with an alpine-climbing mitt, during extreme climbing activities (i.e. expeditions up to altitudes above 8,000 m). The heating multilayer (Figure 1) consists of a heating wire grid, knitted onto a fleece layer and covered by a thin lining. The whole heating multilayer
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Figure 1. Heating wire grid (infrared image)
(fleece þ heating wire grid þ lining) is intended for use in the interior of the glove, in contact with the skin. For the purpose of this study, four different environmental scenarios were considered (Table I), covering from harsh to mild conditions at the Everest Mountain. The air temperatures at this location are reported to vary between 2 368C in winter and 2 198C in summer whereas the wind is mentioned to reach 160 km h2 1 (Hambrey et al., 2008). However, according to alpinists (personal communication), it is not advisable to initiate expeditions when the wind is stronger than 60 km h2 1 (16.7 m s2 1), thus it was assumed that this is the maximum air velocity to which a climber may be exposed to. Table I summarises the air temperatures and velocities together with the corresponding heat transfer convective coefficients used in this study. The heat transfer coefficients were computed based on empirical correlations relating Nusselt, Reynolds and Prandtl numbers (Lienhard IV and Lienhard V, 2003). The scenarios shown in the table were chosen to address the conditions a climber might encounter during an expedition and to allow straightforward assessment of the relevancy of conduction, convection and radiation contributions in the total heat losses. 2.2 Heating multilayer The heating elements, electrically conductive yarns, are taken as perfect cylinders. The physical properties of the heating elements are assumed homogeneous (and equal to those of stainless steel, the main component: domain D in Table II). The heat production by Joule effect is taken constant throughout the yarn volume Scenarios I II III IV
Air temperature (8C)
Air velocity (m s2 1)
Heat transfer coefficienta ( J kg2 1 K2 1)
236 236 219 219
16.7 1 16.7 1
26.8 5.2 26.3 5.2
Notes: aCalculated for a pressure of 0.33 atm (summit of Everest mountain, altitude of 8,850 m; West (1996) and Mason and Barry (2007))
Table I. Environmental scenarios
Height z (m) 3.5 £ 102 2 2.5 £ 102 3 1.7 £ 102 4 1 £ 102 3
Width x (m)
3 £ 102 3 3 £ 102 3 3 £ 102 3 5 £ 102 4
A B C D
Table II. Dimensions and physical properties of the different model domains (Figure 2(c))
Domains 1 £ 102 3 1 £ 102 3 1 £ 102 3 1 £ 102 3
Thickness y (m) 0.046 0.045 0.043 44.5
Thermal conductivity k (W m2 1 K2 1)
116 68 358 7,850
Density r (kg m2 3)
350 210 370 475
Heat capacity Cp ( J kg2 1 K2 1)
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(consequence of constant electrical resistivity) and a function of the power supply and circuit association (serial/parallel). The operation mode (ON/OFF) of the heating multilayer depends on the temperature of the heating elements and on the evolution of their temperature over time. The system is ON and OFF when its temperature is lower than Tmin and higher than Tmax, respectively. When its temperature is in the range Tmin to Tmax the system provides heating as long as the temperature is increasing over time. The lower temperature limit (Tmin) was set to 238C since the onset of cold-induced pain has been reported to occur between 148C and 238C during contact with cold surfaces (Havenith et al., 1992; cit. by: Brajkovic et al., 2001; Geng et al., 2006). The higher limit (Tmax) was set to 288C as this is mentioned as the threshold temperature for assuming comfort at the hands (Brajkovic et al., 2001).
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3. Simulation model The simulations were performed following a FEM approach, using a Core I7 2.80 GHz PC, with 20 Gb of RAM. The following sections provide details on the simulation model used in this study. 3.1 Geometry of simulation domain and material properties Figure 2(a) shows the glove plus the heating multilayer (fleece þ heating wire þ lining) placed in its interior whereas Figure 2(b) shows a section cut perpendicular to the arm axis (along plane xz, in Figure 2(a)). Owing to the existence of several planes of symmetry (along and perpendicular to the wire axis and along the midpoint between wires), only a small portion of the entire heating multilayer has to be considered in the simulation (Figure 2(c)). The dimensions and physical properties of the simulation domains are shown in Table II. 3.2 Boundary conditions 3.2.1 At the external surface. Four different environmental scenarios were considered for defining the heat flux boundary conditions at the glove external surface. The imposed heat fluxes, different for each of the four scenario considered, were computed based on the corresponding air temperatures and heat transfer coefficients (as given in Table I). Radiant heat losses to the environment were considered at the glove external surface, based on a surface emissivity of 0.92 (measured with a calibrated infrared camera). In the calculation of the radiant heat loss at the glove external surface, no radiant sources other than the glove itself were considered. Thus, the effect of the heat
a
b A
c a
Hand
y
b
z c
z (a)
(b)
Dy
B
x
Heating Band
x
C (c)
x z
Figure 2. (a) Glove þ heating multilayer (positioned in the glove’s interior); (b) section cut (along plane xz) of the glove þ heating multilayer; (c) geometry of the simulation domain; A – insulation layer, B – fleece layer, C – lining layer, D – heating wire
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gains from the solar and atmospheric radiation was discarded in these analyses (see the Appendix for details on the extension of this effect). 3.2.2 At the internal surface. Different boundary conditions were used depending on the type of simulation (steady-state versus transient). Although the operation of the described heating band is intrinsically transient, meaning that its temperature varies over time in a transient way, it is obvious that this variation occurs within a given temperature range, dependent on the operation limits of the heating multilayer (in this case, 238C and 288C). Therefore, the steady-state analyses were based on a temperature boundary condition at the skin of 25.58C, i.e. midway between the mentioned limits (the consideration of average skin temperature in the steady-state analyses does not constitute a significant deviation from reality, particularly for increasing thickness of the internal air layer; see Section 4.3.2. for further information). In these analyses (Sections 4.2.2 and 4.2.3), no heat generation was considered at the heating wires. The exception was the analysis on the effect of the distance between heating wires (Section 4.2.1), for which preference was given to a heat flux boundary condition at the skin (similar to that used for transient simulations), in order to study the temperature profiles along the skin due to the local heat generation of the heating wires. A skin emissivity of 0.98 (Kurazumi et al., 2008) was used when considering radiant heat exchange between the skin and the lining. For the transient simulations, preference was given to a heat flux boundary condition at the skin in order to allow the evolution of its temperature over time as the natural outcome of the heating multilayer operation. In order to estimate the heat fluxes at the skin (hand), one could use complex thermal/comfort models (Fiala et al., 1999; Huizenga et al., 2001; Salloum et al., 2007) and perform whole-body simulations, in which the local and core temperatures should be obtained taking into account the heat transfer between different body segments as well as heat losses at the skin level (dry versus evaporation heat losses). However, such approach would require estimates of a considerable amount of parameters (thermal properties of the main body tissues, heat transfer coefficients, blood perfusion rates, etc.), describing the thermal contributions of each body segment/portion. Such a holistic description of the thermal balance of the human body would be outside the scope of this work, thus, an alternative approach was followed for estimating the heat flux at the skin (hand). This parameter was based on the local basal metabolic rate of the hand, despite the associated clear under-prediction. This simpler approach was considered reasonable since it implies an over-prediction of the average heating requirements of the heating system which, ultimately, assures the resulting system is able to provide all the heating an alpinist may ever need. Different figures were found in the literature for the basal metabolic rate at the hands, namely 0.14, 0.188 and 0.25 W (Raman and Vanhuyse, 1975; Tanabe et al., 2002; Salloum et al., 2007, respectively). Using the medium value (0.188 W) and the hand surface area, one obtained the estimate of the heat flux at the skin (4.1 W m2 2) that was used as boundary condition in the transient simulations. 3.2.3 At the heating wires. The effect of the heating wires was introduced in the transient simulations through the use of a source term (Q in W m2 3, where m3 refers to the volume of heating wire) in the heat balance equation, whose value depends on the operation of the heating system (Q is 0 when the heating system if OFF and equal to the heating power, when the system is ON). The source term was computed based on the heating power of the multilayer (in W m2 2, where m2 refers to the surface area of the portion of skin considered in the simulation domain), the cross-sectional area of
its heating elements taken as perfect cylinders and the length and number of the heating elements existing in the simulation domain. 3.3 Simulation approach Steady-state and transient analyses were developed in this study. Steady-state analyses were performed in order to highlight the relevancy of each transfer mechanism in the total heat loss as well as to allow a straightforward analysis of the influence of infrared reflective surfaces on the overall performance of the system under consideration (e.g. at the glove outer surface or at the skin-facing lining surface). Transient analyses were performed to study the effect over time of the heating multilayer power, to establish the energy requirements of the corresponding battery and to allow a thorough analysis of the effect of internal infrared reflective surfaces during the heating and cooling cycles.
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4. Results and discussion The following sections describe the main results obtained for the steady-state and transient analyses performed. 4.1 Convergence, grid testing and computational requirements For all simulations geometries, grid tests were performed in order to define the grid characteristics which guarantee grid-independent results. Depending on the geometry in question, grids with 4.3 £ 104 to 3.8 £ 105 elements were used, which resulted in a maximum error of 0.2 per cent in the average normalized temperature of each simulation domain (Table III; grid 3). Similar approaches were developed to determine the time-step adequate for running the transient simulations. A compromise was found between accuracy and computational power requirements with a time-step of 0.1 s (resulting in a negligible error (8 £ 102 2 per cent) in the duration of an entire heating-cooling cycle). Depending on the type and characteristics of the simulations (transient/steady-state, geometry of the simulation domain, with or without radiant heat exchange), up to 16GB of RAM were needed during the simulations. 4.2 Steady-state results 4.2.1 Distance between heating wires. In order to determine the ideal distance between the heating wires, several simulations were conducted with varying number of wires for the same total power (70 W m2 2, where the m2 refers to surface area of the portion of skin considered in the simulation domain, in this case 0.02 m £ 0.001 m; the total
Domains Grids
Nodes
A
B
C
D
1 2 3 4
892 24,538 43,021 68,765
0.9993 1.0000 1.0000 1.0000
1.0189 1.0004 1.0002 1.0000
1.0000 1.0000 1.0000 1.0000
0.8329 0.9967 0.9983 1.0000
Note: Data normalized by the temperatures obtained with the denser grid
Table III. Average normalized temperature of each simulation domain (Figure 2(c)), for grids with increasing density
45
30 25 20 15 0
0.005
0.01
0.015
0.025
∆T
20 DT (°C)
T (°C)
35
0.020
∆x
15
0.015
10
0.010
5
0.005
0.000 0 1 Wire 2 Wires 3 Wires 4 Wires
0.02
x (m) (a)
(b)
120
10 Conductive Flux Convective Flux Radiative Flux Glove outer Temperature
100 80
0 –10
60 –20
40
–30
20
–40
0 I
II
III (a)
IV
T (°C)
Figure 4. (a) Heat fluxes through the glove þ heating multilayer and temperature of the glove outer surface; (b) thermal resistances (conductive resistance and convection þ radiation equivalent resistance), for the four environmental scenarios studied (Table I) and constant skin temperature (25.58C)
25
1 Wire 2 Wires 3 Wires 4 Wires
40
Heat Flux (W m–2)
Figure 3. (a) Temperature profile along x coordinate for different number of wires (for the same total power; 70 W m2 2); (b) maximum temperature difference at the lining (DT) and distance between wires (Dx), for different number of wires
Dx (m)
380
heating power from the wires (70 W m2 2) was chosen so that, together with the heat flux boundary condition at the skin (4.1 W m2 2), one obtains at the skin an average temperature of 25.58C). The environmental conditions of scenario I were considered for this purpose (air temperature of 2 368C, air velocity of 16.7 m s2 1). As can be seen in Figure 3, the temperature profile flattens (i.e. the heating becomes more homogeneous) as the number of wires increases. For the conditions considered here (total power: 70 W m2 2), it was found that the heating wires should dist approximately 6-7 mm to assure that the temperature along the lining does not vary more than 38C. Although smaller distances would assure flatter temperature profiles, that was considered unpractical from the manufacture point of view. The width of the simulation domain mentioned in Table II (3 mm) was defined based on these results (i.e. separation between wires of 6-7 mm). 4.2.2 Heat losses for several climatic conditions. The heat fluxes through the glove þ heating multilayer, for each of the environmental scenarios of Table I, are shown in Figure 4(a), whereas the corresponding thermal resistances are shown in Figure 4(b). These analyses were done considering a constant skin temperature of 25.58C and no heat generation at the heating wires (see Section 3.2.2 for details). Owing to the steady-state nature of the simulations, the conductive flow through the glove equals the convective plus the radiant flows at the glove outer
Thermal Resistance (°C m–2 W–1)
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1.2
Equivalent (Conv. + radiat.)
1 0.8
96%
87%
96%
87%
0.6 0.4 0.2
4%
13%
4%
13%
0 I
II
III (b)
IV
surface (the convective and radiant resistances are parallel but in series with the conductive resistance). Moreover, depending on the environmental scenario, the conductive resistance accounts for 87-96 per cent of the total existing resistance (0.81-0.90 K m2 W2 1). This is why a 17-fold decrease in the air velocity (e.g. scenarios I and II or III and IV) results in less than 10 per cent decrease in the total heat loss from the glove. Owing to lower convective losses, the temperature of the gloves external surface is higher for the less windy scenarios (II and IV), which accounts for the higher radiant heat losses observed (when compared to the similar but more windy scenarios, i.e. I and III, respectively). Nevertheless, the convective heat losses are 1.5-9.5-fold higher than the radiant heat losses observed. 4.2.3 Influence of surface emissivity. Metallisation surface treatments are known to offer materials infrared reflection capacity and low radiant heat losses. In order to evaluate the relevancy of such treatments in the system under study, a series of parametric simulations were performed, in which the emissivity of the surfaces in question (either the glove outer surface or the skin-facing lining) was changed gradually from 0.95 to 0.05 (approaching the emissivity of aluminium foil). These simulations where conducted considering a constant skin temperature of 25.58C and no radiant sources other than the glove itself (so the effect of the heat gains from the sun was discarded in these analyses). Figure 5(a) and (b) show the results of the mentioned simulations for environmental scenarios I and IV, regarding changes in the emissivity of the glove outer surface. There is a decrease in the radiant heat loss and (accordingly) an increase in the temperature of the glove external surface as the emissivity decreases. The escalation of the glove external temperature is accompanied by the corresponding increase of the convective heat loss, although to a lesser extent than the change in the radiant component. This produces an overall decrease in the total heat loss from the glove, reaching, however, no more than 7 per cent. These results indicate that, in the absence of any other radiant sources than the alpinist himself (i.e. in the absence of solar and atmospheric radiation), it is advantageous to use a low-emissivity cover over the gloves (or other body region) as this will reduce slightly the total heat loss. Such an advantage can be particularly relevant during the night when the effective sky temperature decreases sharply (increasing the relevancy of the effect of the radiant heat loss (Cengel, 2002)). However, during a daylight mountain activity, there is enough solar and atmospheric radiation to clearly overcome
20 0 0.05
Total Flux Convective Flux Radiative Flux Mitt Temperature
0.35
–33.5
0.65
–33.6 0.95
60
–12
40 –14
20 0 0.05
0.35
0.65
e
e
(a)
(b)
–16 0.95
T (°C)
40
–33.4
Heat Flux (W m–2)
60
–10
80
–33.3
T (°C)
Heat Flux (W m–2)
80
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Figure 5. Heat fluxes and temperature of the glove outer surface versus emissivity of the glove outer surface for (a) scenario I (2368C, 16.7 m s2 1) and (b) scenario IV (2198C, 1 m s2 1); all simulations based on a constant skin temperature of 25.58C
80 60
25.0
Total Flux Conductive Flux Radiative Flux Lining Temperature
24.7 24.4
40
24.1
20
23.8
0 0.05
0.35
0.65
23.5 0.95
100
25
80
20
60
15
40
10
20
5
0 0.05
0.35
0.65
e
e
(a)
(b)
0 0.95
T (°C)
100
Heat Flux (W m–2)
Figure 6. Heat fluxes (across the air layer between skin and lining) and lining temperature versus emissivity of the skin-facing lining surface for scenario IV (2 198C, 1 m s2 1), considering air layer thickness of (a) 102 3 m and (b) 102 2 m; all simulations based on a constant skin temperature of 25.58C
T (°C)
382
the aforementioned effect, which, ultimately, advises against the use of low-emissivity coverings in such conditions (see the Appendix for details). The effect of metallisation of the skin-facing lining was also studied as there is an increasing trend towards the use of such solutions in apparel industry. This was done for the environmental conditions of scenario IV (for which the radiant flux is more important in relative terms) and considering conductive and radiant heat exchange between the skin (1 ¼ 0.98) and the lining, for air layers thicknesses of 102 3 and 102 2 m. For these simulations, radiant heat loss was also considered at the glove outer surface based on an emissivity of 0.92. In these analyses, the emissivity of the lining was gradually changed from 0.95 to 0.05, while registering the corresponding heat fluxes for every particular emissivity. The obtained results are shown in Figure 6. When the emissivity of the lining decreases (thus increasing its reflectivity), there is a decrease in both the net radiant heat flux and the lining temperature. There is however an increase in the conductive flux across the air layer. This is obviously related to the decrease in the lining temperature (which augments the temperature gradient between the skin and the lining). The opposing variation of the radiant and conductive fluxes, for decreasing lining emissivity, results in an overall slight decrease in the total flux across the glove. The extent of this effect escalates with increasing air layer thickness since it is obviously related to the augmentation of the temperature difference between the opposing surfaces (e.g. when the lining emissivity decreased from 0.95 to 0.05, the total heat flux across the glove decreased by 8 per cent for an air layer thickness of 102 3 m and by 36 per cent for an air layer thickness of 102 2 m, respectively). These results highlight the clear benefit associated to the inclusion of low-emissivity (infrared reflective) internal surfaces in the clothing apparel. However, it should be stressed that this effect is only relevant if air layers/gaps between skin and the reflective surfaces do exist. Furthermore, the results highlight the shift between conduction and radiation heat transfer occurring when the emissivity of the surfaces exchanging heat is altered. For that reason, further studies were developed in transient mode in order to fully understand the influence of changes in surface emissivity over the performance of the heating multilayer, during the cooling and heating phases. These analyses are described in Section 4.3.2.
Heat Flux (W m–2)
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4.3 Transient results 4.3.1 Temperature curves and battery duration. Several transient simulations were performed in order to determine the optimal power of the heating multilayer. The mostand least-demanding environmental conditions were considered (i.e. scenarios I and IV). Convective and radiant (1 ¼ 0.92) heat losses were considered at the glove outer surface. Constant heat flux (4.1 W m2 2) was imposed at the lining (perfect contact between skin and lining was assumed). Figure 7 shows the variation of the heating wire temperature over time for power supplies of 75, 250 and 500 W m2 2 (where the m2 refers to surface area of the portion of skin considered in the simulation domain, in this case 0.003 m £ 0.001 m). Not surprisingly, the temperature curves are strongly dependent on the external environmental conditions and on the power of the heating multilayer. The harsher the environmental conditions, the steeper the temperature variations during the cooling phase (Figure 7(a) and (c)). Moreover, the higher the power, the more pronounced its temperature oscillation, during both the heating and the cooling phases (Figure 7(b)). The latter derives from the steeper temperature profiles existing across the multilayer, for increasing heating power. This indicates that this parameter should be as low as possible (in order to favour homogeneous heating across the multilayer rather than more or less evident hot spots around the heating wires). Although a heating power of 75 W m2 2 appears sufficient for the milder scenario (Figure 7(c)), it results in an almost asymptotic temperature escalation for the harsher conditions (Figure 7(a)). This advises the use of higher heating powers (to produce less unsymmetrical heating/cooling curves and, therefore, average skin temperature more stable over time). For both scenarios, the remaining heating powers (250 and 500 W m2 2) produce heating periods shorter than the cooling ones (about 61-90 per cent). Considering that the heat flux imposed at the lining is under-predicted (as it is based on the metabolic rate of the hands), the real heating and cooling periods will be even shorter and longer, respectively. For that reason, it is advisable to use heating powers lower than those mentioned before, arguably in the range 125-250 W m2 2. In order to determine the adequate battery capacity, the average heating powered (Pavg) was calculated. This parameter was obtained by Pavg ¼ P · tON/(tON þ tOFF), where P is the heating power delivered to the multilayer and tON and tOFF are the duration of the heating and cooling phases, respectively. It is interesting to notice that, for a given environmental condition, similar average heating powers are obtained regardless of the chosen heating power (75, 250 and 500 W m2 2; for high heating power, the multilayer is in ON mode for short periods of time, leading to full compensation). This indicates that the heat loss from the mitt and, thus, the temperature of its outer surface, are practically independent of the chosen heating power. This is obviously a consequence of the high conductive insulation provided by the glove and the fixed limits (temperature wise) of operation of its heating multilayer. The fact that the average power consumption of the heating system does not depend on the chosen heating power is very convenient as it enables its design independently of energy-related restrictions. For the two scenarios analysed here (I and IV), the average heating power is 44.6 and 70.7 W m2 2 (the average heating powers for the scenarios II and III are within these values). The battery capacity required for powering the heating multilayer depends obviously on the required effect duration. Mountain climbers mention the summit
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T (°C)
27
384
26 25 24 23 0
100
200
300
400 t (s)
75 W m–2
500
600
700
250 W m–2
800
500 W m–2
(a) 28
T (°C)
27 75 W m–2 250 W m–2 500 W m–2
26 25 24 23 0
40
28 27 T (°C)
Figure 7. Heating wire temperature over time, for heating powers of 75, 250 and 500 W m2 2, for (a) scenario I (2 368C, 16.7 m s2 1), time span of 800 s; (b) scenario I (2368C, 16.7 m s2 1), time span of 50 s; (c) scenario IV (2198C, 1 m s2 1); all simulations based on a constant skin heat flux of 4.1Wm2 2
20 t (s) (b)
26 25 24 23 0
100
200
300
400
500
t (s) 75 W m–2
250 W m–2
500 W m–2
(c)
attack can last up to 12-24 h (personal communication). With this figure in mind, one concludes that, for the conditions studied here, a 4 A h battery can assure up to 18-23 h of operation of the described heating multilayer: charge duration ¼ pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi : P avg =Resistance As already mentioned, due to the under-prediction in the hand heat flux, the real effect duration should be even longer than the mentioned 18-23 h which, ultimately, indicates
wire, ε(lining) = 0.05
skin, ε(lining) = 0.05
wire, ε(lining) = 0.95
skin, ε(lining) = 0.95
28
28
27
27
26
26
T (°C)
T (°C)
that the system described here should comply with the duration requirements mentioned by climbers. 4.3.2 Influence of the internal surface emissivity. Transient simulations were conducted in order to study the influence of changes in the emissivity of the skin-facing lining surface, over the performance of the heating multilayer, during the cooling and heating phases. The simulations focussed on the environmental conditions of scenario IV (for which the radiant flux is more important in relative terms) for a heating power of 250 W m2 2. Convective and radiant heat (1 ¼ 0.92) losses were considered at the glove outer surface. Both conductive and radiant heat exchange were considered between the skin (1 ¼ 0.98) and the lining (1 ¼ 0.05 and 1 ¼ 0.95), for two distinct air layers thicknesses (1 £ 102 3 m and 5 £ 102 3 m). At the skin, a constant heat flux was imposed as boundary condition (4.1 W m2 2). Figure 8 shows the variation of the skin and heating wire temperatures over time, for lining emissivities of 0.05 and 0.95, for air layer thicknesses of 1 £ 102 3 m and 5 £ 102 3 m (Figure 8(a) and (b)), respectively. As expected, the thermal resistance and inertia of the air layers dampens and delays the temperature oscillations of the heating wires. This effect escalates obviously with increasing air layer thickness (distance between skin and lining). For the thinner air layer (1 £ 102 3 m; Figure 8(a)), the skin temperature is practically independent of the lining emissivity. Indeed, the temperature and the amplitude of its oscillation over time, obtained with the lining emissivity of 0.05 and 0.95, are almost identical. This indicates that, for such a thin air layer (1 £ 102 3 m in thickness), the lining emissivity does not have a significant effect over the thermal performance of the heating multilayer. However, if the air layer is allowed to be thicker, e.g. 5 £ 102 3 m, the skin temperatures obtained with the different lining emissivities, do differ (Figure 8(b)). The results show that, for the tested conditions, the skin temperature obtained with the lower emissivity (0.05) is between 0.38C and 0.58C higher than that obtained with the higher emissivity (0.95). Moreover, they show that the oscillation (over time) of the skin temperature is less pronounced with the lining featuring the lower emissivity
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Figure 8. Skin and heating wire temperatures over time for lining emissivity of 0.05 and 0.95, for air layer thicknesses of (a) 1 £ 102 3 m and (b) 5 £ 102 3 m; heating power of 250 W m2 2 and environmental conditions of scenario IV (2198C, 1 m s2 1); constant skin heat flux of 4.1 W m2 2
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(0.48C versus 0.68C). These results indicate that the use of low-emissivity surfaces facing the skin is beneficial for the performance of the heating system, provided relatively thick air layer/gaps are allowed to exist between the skin and the heating multilayer. Furthermore, given that the use of such surfaces reduces the total heat loss from the body when no electrical heating system is considered/present (as discussed in Section 4.2.3), such solution seems to have interesting potential for clothing apparel applications (heated or not). However, due attention must be given to its effects over other parameters relevant for comfort perceptions (e.g. water vapour resistance, moisture management, tactile sensation, etc.). 5. Conclusion A series of steady-state and transient simulations were implemented using a FEM approach in order to study and optimise the thermal performance of a heating multilayer, for use inside an alpine-climbing mitt. Several issues were addressed, namely, the heat losses as a function of environmental conditions, the positioning of the heating wires, the power input to the heating system, the battery capacity requirements and the effect of the use of low-emissivity surfaces. These are shown to reduce the total heat loss through the mitt and increase the skin temperature during the transient operation of the heating multilayer. References Brajkovic, D., Ducharme, M.B. and Frim, J. (2001), “Relationship between body heat content and finger temperature during cold exposure”, Journal of Applied Physiology, Vol. 90 No. 6, pp. 2445-52. Cengel, Y.A. (2002), Heat Transfer: A Practical Approach, McGraw-Hill, London. Fiala, D., Lomas, K.J. and Stohrer, M. (1999), “A computer model of human thermoregulation for a wide range of environmental conditions: the passive system”, Journal of Applied Physiology, Vol. 87 No. 5, pp. 1957-72. Geng, Q., Holmer, I., Hartog, D.E.A., Havenith, G., Jay, O., Malchaire, J., Piette, A., Rintamaki, H. and Rissanen, S. (2006), “Temperature limit values for touching cold surfaces with the fingertip”, Ann. Occup. Hyg., Vol. 50 No. 8, pp. 851-62. Hambrey, M.J., Quincey, D.J., Glasser, N.F., Reynolds, J.M., Richardson, S.J. and Clemmens, S. (2008), “Sedimentological, geomorphological and dynamic context of debris-mantled glaciers, Mount Everest (Sagarmatha) region, Nepal”, Quaternary Science Reviews, Vol. 27 Nos 25/26, pp. 2361-89. Havenith, G., van de Linde, E.J. and Heus, R. (1992), “Pain, thermal sensation and cooling rates of hands while touching cold materials”, European Journal of Applied Physiology and Occupational Physiology, Vol. 65, pp. 43-51. Holmer, I. (2005), “Textiles for protection against cold?”, in Scott, R.A. (Ed.), Textiles for Protection, Woodhead, Cambridge. Huizenga, C., Hui, Z. and Arens, E. (2001), “A model of human physiology and comfort for assessing complex thermal environments”, Building and Environment, Vol. 36 No. 6, pp. 691-9. Kurazumi, Y., Tsuchikawa, T., Ishii, J., Fukagawa, K., Yamato, Y. and Matsubara, N. (2008), “Radiative and convective heat transfer coefficients of the human body in natural convection”, Building and Environment, Vol. 43 No. 12, pp. 2142-53.
Lienhard IV, J.H. and Lienhard V, J.H. (2003), A Heat Transfer Textbook, Phlogiston Press, Cambridge, MA. ¨ Makinen, H. (2005), “Fire fighters protective clothing?”, in Scott, R.A. (Ed.), Textiles for Protection, Woodhead, Cambridge. Mason, N.P. and Barry, P.W. (2007), “Altitude-related cough”, Pulmonary Pharmacology & Therapeutics, Vol. 20 No. 4, pp. 388-95. Raman, E.R. and Vanhuyse, V.J. (1975), “Temperature dependence of the circulation pattern in the upper extremities”, Journal of Physiololgy, Vol. 249, pp. 197-210. Salloum, M., Ghaddar, N. and Ghali, K. (2007), “A new transient bioheat model of the human body and its integration to clothing models”, International Journal of Thermal Sciences, Vol. 46 No. 4, pp. 371-84. Tanabe, S.-I., Kobayashi, K., Nakano, J., Ozeki, Y. and Konishi, M. (2002), “Evaluation of thermal comfort using combined multi-node thermoregulation (65MN) and radiation models and computational fluid dynamics (CFD)”, Energy and Buildings, Vol. 34 No. 6, pp. 637-46. West, J.B. (1996), “Prediction of barometric pressures at high altitudes with the use of model atmospheres”, Journal of Applied Physiology, Vol. 81 No. 4, pp. 1850-4. Appendix The net radiant heat flux (qnet) to a surface exposed to solar and atmospheric radiation can be computed by the following energy balance (Cengel, 2002): q_ net ¼ asolar Gsolar þ 1s T 4sky 2 T 4 where asolar is the solar absorptivity, Gsolar is the total solar irradiance (1,373 W m2 2), 1 is the emissivity of the surface at room temperature, a is the Stefan-Boltzmann constant (5.67 £ 102 8 W m2 2 K4), Tsky is the effective sky temperature (230-285 K (Cengel, 2002)) and T is the temperature of the surface exchanging radiant heat (in K). For a mitt with a low-emissivity outer surface (1 ¼ 0.05 and asolar ¼ 0.15, taken equal to those of aluminium foil (Cengel, 2002)), the net radiant heat flux can be as high as 200-215 W m2 2 (depending on the temperature of the glove outer surface and the effective sky temperature). This value can be even higher, if considering a mitt with no low-emissivity outer surface.
Corresponding author Tiago S. Mayor can be contacted at:
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