A dynamic thermal identification method applied to condutor ... - IEM

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522 V. L. Borges et al.Table 1. Statistical data of the average value of (initial value of ¼ 1.0 10 6 m 2 s 1 ). (m 2 s 1 ) Initial S p Final S p (m 2 s 1 )3.762 10 6 20 1.16 10 3 4.0 10 8Table 2. Statistical data of the average value of l (initial value of l ¼ 10 W m K 1 ).l (W m K 1 ) Initial S p Final S p (m 2 s 1 )14.64 14700 18.3 3.1 10 1Table 3.Summary of and l for AISI304 sample.Thermal properties This work References [13,14] Error (%) 10 6 (m 2 s 1 ) 3.762 3.82 1.54l (W m K 1 ) 14.64 14.90 1.771210Temperature (°C)8642θ t1θ t2θ e1θ e200 50 100 150 200 250 300Time (s)Figure 13. Output of a typical run.These results show the potential of the method proposed here. The comparison betweenthe experimental and estimated temperatures for ¼ 3.76 10 6 m 2 s 1 andl ¼ 14.64 W m K 1 is shown in figure 13. In this figure a good agreement between thedata can be observed; the residuals are situated in the range of uncertainty measurementof thermocouples, that in this work is 0.3 K.
A dynamic thermal identification method 523Figure 14. Experimental apparatus used for determining and l.Table 4. Statistical data of the average value of (initial value of ¼ 1.0 10 8 m 2 s 1 ). (m 2 s 1 ) 10 7 Initial S p 10 2 Final S p 10 7 (m 2 s 1 ) 10 101.24 6.0 3.6 7.064.2. Nonconductor material applicationThe thermal identification technique can also be applied to nonconductor solidmaterials. In this case, a one-dimensional model can be used. This section presents someresults of and l estimation for two different polymers: polythene and polyvinylchloride (PVC). More details about the 1D model and its respective sensitivity analysiscan be found in [10].Two polymers samples were used, polythene and PVC, both with thickness of 50 mmand lateral dimensions of 305 305 mm. Figure 14 shows the experimental apparatuswhere at time t ¼ 0, the sample is in thermal equilibrium at T 0 . At this instant, thesample is submitted to a unidirectional and uniform heat flux on its upper surface.The heat is supplied by a 22 electrical resistance heater, covered with silicone rubber,with lateral dimensions of 305 305 mm and thickness 1.4 mm. The heat flux andtemperature are acquired using sensor and instruments with the same specification ofthat described here in the conductor material application.Fifty independent runs for PVC and twenty independent runs for polythene wererealized. For both samples 1024 points were taken. The time intervals, t, were 7.034 sfor PVC and 6.243 s for polythene. The time duration of heating, t h , was approximately150 s for PVC and 90 s for polythene with a heat pulse generated at 40 V (DC) forboth samples.Tables 4 and 5 present respectively the value estimated of and l for the fifty runsof PVC, with 99.87% confidence interval. In table 6 a summary of the simultaneousestimation of and l of the PVC sample is presented. In this table, the comparison withthe values obtained for by using the Flash method [14] and l by using the guardedhot plate method [15] presented errors of 3.22 and 3.30% for and l, respectively.In figure 15a a comparison between experimental and estimated phase factor ispresented. A very good agreement can be observed between them. Figure 15b shows theresiduals.
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A dynamic thermal identification method applied to condutor ... - IEM

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