Global Journal of Researches in Engineering, J: General Engineering, Volume 22 Issue 1

lobal Journal of Researches in Engineering ( ) Volume XxXII Issue I Version I J G 18 Year 2022 © 2022 Global Journals Figure 17 shows the results of the influence of palm kernel shell powder on the phase change temperatures, namely: glass transition temperature (Tg), melting temperature (Tf), crystallization temperature (Tcf), combustion temperature (Tc) and the ash temperature (Tce) of the elaborated PVCs. We observe that: The glass transition temperature of PVC F0 is Tg =108.71, that of F12.54 is Tg = 96.58, that of F32.01 is Tg = 96 and F 51.02 is Tg =76.56. The temperatures decrease as the loading rate of the palm kernel shell powder increases. The regression of the results shows that Tg has a polynomial trend. The arrangements of the results on the right hand side show that the mathematical equation governing the glass transition results is y = -0.0011x3 + 0.0774x2 - 1.768x + 108.71 with the regression coefficient R² = 1. This correlation shows the reliability of the results as obtained in some works in the literature [18, 19, 22]. In the same way asfor the F0 formulation (unloaded PVC tubes), from the F0 formulation to the F51.02 formulation, the results of the Tg, Tc and Tce measurements progressively decrease while those of Tf and Tcf, rather increase. The straight lines connecting the results of the measurements of each temperature have trends whose equations are polynomials of the type y=ax3+bx2+cx+d (where y represents the Thermal Properties and x the loading rate of the palm kernel shell powder in the tube). The arrangements of the results with respect to the lines show that they pass through all the points representing the measured temperature results. The calculated correlations are exactly 1, showing that the errors in formulation, elaboration and analysis are negligible, allowing us to write the mathematical models for the calculation of the thermo differential properties of the PVCs loaded with palm kernel shell powder in Table 1 Table 1: Mathematical models for the calculation of thermo differential properties of PVC. Properties Mathematical models Types Correlations Glass transition temperature (Tg) y = -0,0011x + 0,0774x 2 - 1,768x + 108,71 Polynomial R² = 1 Crystallization temperature (Tcf) y = 0,0013x 3 - 0,0547x 2 + 0,7164x + 274,71 Polynomial R² = 1 Melting temperature (Tf) y = 0,0012x 3 - 0,0537x 2 + 0,553x + 288,71 Polynomial R² = 1 Combustion temperature (Tc) y = -0,0005x 3 + 0,0116x 2 - 0,7907x + 494,71 Polynomial R² = 1 Ash temperature (Tce) y = 0,0022x 3 - 0,1685x 2 + 0,4783x + 675,71 Polynomial R² = 1 Table 1 above shows that the mathematical models for calculating the characteristic parameters in the phase transition temperatures are mathematical models of the polynomial type. The degree of the polynomials is 3 (two). The R2 correlation obtained for each equation in the phase transitions is exactly 1. So, since we obtained a mathematical equation whose degree is 3, it shows that there were small errors somewhere during the practices. The degree of the polynomial should have been 1. So:  Maybe we can say that the errors come from the elaborated tubes ;  Can we say that the errors come from the additives?  Can we say that the errors come from the assumptions of the characterization ; But the regression coefficient brings us answers in the sense that the errors observed are negligible given that the degree of the polynomials has remained at 3 for all the equations. So we can use these mathematical models to calculate the dosage of shell powder or to calculate the thermal parameters of the tubes during its elaboration according to the parameters or technical assumptions that we have available. 3 Mathematical Models for the Calculation of the Thermal Properties of PVCs as a Function of Dosage with the Load of Palm Kernel Shell Powder from the Results of Experimental Practice