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Parameters of the modelTable 5The coefficient values of correlation between input variables for the heat exchanger.Pairs of variables Data files (start-up the exchanger)Ro2 Ro3 Ro5 Ro6wf–sf 0.78 0.92 0.96 0.21wf–st 0.43 0.56 0.63 0.27wf–sp 0.49 0.62 0.77 0.27sf–sp 0.096 0.83 0.66 0.87sf–st 0.12 0.78 0.52 0.82sp–st 0.9 0.93 0.89 0.95Table 3The transmittance parameters values in models P3ZU for sf.Data files KTw f Tp3 Tz FIT FPERo3 0.35047 2173.1 1.1649 138.62 245.92 81.02 1.465Ro5 1.3401 10816 0.3028 50.68 14261 72.26 7.516Table 4The transmittance parameters values in models for sp. and of fitting are given in the Table 6. The courses of the STEP char-acteristic are presented in Fig. 8c (for Ro3) and in Fig. 8d (for Ro5).All of the models have showed an oscillatory character of theheat exchanger STEP characteristic. It suggested that the oscillationhave been occurred in the transient states of the exchanger. It maybe the kind of an energy conversion – as it is in the pendulum or inthe spring in the mechanics. The sort of a potential energy is con-verting to the sort of a kinetic energy and vice versa. The parame-ters connected with the oscillation amplitude and the dumping aredepended upon the exchanger construction and character of theinput signal course.The oscillations are also observed during different heat exchan-ger investigations presented in [28–31], but there are notexplained.
4.3. The model of heat exchangerThe current intensity (for the resistance heating) and the tem-perature of the active element (for the investigation of the passiveelement heating) has been taken into consideration as the inputsignal u(t). The temperature of the investigated element has beenalways taken as the output signal y(t).4.3.1. The copper barThe copper elements observed during the experiments indi-cated some changes in the properties of the copper during the pro-cess of their oxidation (during annealing). The physical propertiesare changed (the surface of copper turned dark grey and it becomeplastic). But the dynamic properties have changed also (Fig. 9a andb).Fig. 9a presents the STEP characteristic for the new copper barand the Fig. 9b for the bar of an annealed copper. The best linearmodel for both of them is P3U with the form (6) of transferfunction.The transfer function parameters values and the model fittingparameters values are presented in the Table 7.4.3.2. The copper spiralThe oscillations which have appeared in the STEP characteristicin the Fig. 9a have been also observed not only for the ‘‘new’’ cop-per elements, but also for the ‘‘old’’ (annealed) copper – in the caseof copper spiral resistance heating (Fig. 9c). But the oscillation inthe STEP characteristic has not been observed in the same experi-ments for the copper spiral ‘‘induced’’ (Fig. 4b) situated in veryclose neighborhood of a heating spiral (as a secondary side of anexchanger) (Fig. 9d). The STEP has an inertial character.The transfer function has a form(6) for the heating spiral but forthe ‘‘induced’’ spiral the form is:GðsÞ¼ Kð1 þ T1 sÞð1 þ T2 sÞð1 þ T3 sÞð8ÞThe values of the parameters for both models being the bestapproximations of the experiments are presented in the Table 8.Table 6The transmittance parameters values in models for st.Data file K x f Tz FIT FPERo3 0.94776 302.07 0.92016 574.15 86.38 0.7496Ro5 0.94813 728.98 0.66551 1017.5 77.95 4.737 4.3.3. The kanthal bar and spiralThe experiments for the kanthal bar and spiral have also dem-onstrated an ambiguity in the investigated phenomenon. The bestfitted models for the resistance heating of the kanthal bar and theSTEP characteristics for the best models for the resistance heatingof the kanthal bar and spiral have been presented in the Fig. 10.Fig. 9. The STEP for copper bar (a and b) and spiral (c and d): (a) new, transfer function (6), (b) ‘‘old’’ (annealed), transfer function (6); coefficients in Table 7. (c) heating,transfer function (6), (d) ‘‘induced’’, transfer function (8); coefficients in Table 8.Table 7The transmittance parameters values in models P3U for copper bars.Bar of Cu KTw f Tp3 FIT FPE‘‘new’’ 0.95896 109.19 0.4057 223.45 98.27 3.71‘‘old’’ 0.83463 179.52 0.83848 36.328 97.62 4.86