Prediction of batch heat transfer coefficients for pseudoplastic fluids ...
Prediction of batch heat transfer coefficients for pseudoplastic fluids ... Prediction of batch heat transfer coefficients for pseudoplastic fluids ...
266 APPENDIX C CORRELATION OF DATA Regression Analysis Various portions of the calculations required the fitting of a straight line to a group of data points. A statistical method based on minimizing the s~un of the squares of the deviations of one of the variables from the straight line (least squares method) is described by Volk (198) and is a reliable and objective method for finding a linear relationship bett\l'een tHO or more variables. Complete descriptions of the methods may be fotmd in Levenspiel et ale (105) and Volk (198). One depende:nt and one independent variable.. r1any physical situations can be described by y=a+·bx (C-l Hhere y is a dependent variable and x is an independent variable. If several sets of data of Yi versus the corresponding xi are taken and plotted, the 1l1east squares lt line through the data can be expressed (C-2 v-Jhere the 1\ over the y differentiates betl..reen the predicted A y, y, and the measured Y, Yi- It has been established that the parameters ,_ a and b,
of a least squares line can be calculated from a=y-bi b = ~ (Xi -X) (Yi - fj) ~ (Xi - X)2 (0-3 (0-4 l"fhere x and y are the averages of the xi and Yi data values .. A relationship such as (c-5 can be rewritten as log 'I = log K + n log if (C-6 so that it is expressed in the form of equation 0-1, Hhere y :: log I x = log 1) a = log I{ b = n Thus it can be seen that the use of the above regression analysis can be used for many simple relationships, provided they can be l.vri tten in the form of equation C -1. A computer progra~ for solving equation 0-3 and C-L~ described by Eisen (59), Has used as the basic prograrn. for calculating the parameters of the pOHer law equation and the temperature dependent forms of the p01.ver lay.J as described in Appendix A. The computer progrom is given in Appendix A.
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266<br />
APPENDIX C<br />
CORRELATION OF DATA<br />
Regression Analysis<br />
Various portions <strong>of</strong> the calculations required the<br />
fitting <strong>of</strong> a straight line to a group <strong>of</strong> data points.<br />
A<br />
statistical method based on minimizing the s~un<br />
<strong>of</strong> the<br />
squares <strong>of</strong> the deviations <strong>of</strong> one <strong>of</strong> the variables from<br />
the straight line (least squares method) is described<br />
by Volk (198) and is a reliable and objective method <strong>for</strong><br />
finding a linear relationship bett\l'een tHO or more variables.<br />
Complete descriptions <strong>of</strong> the methods may be fotmd in Levenspiel<br />
et ale (105) and Volk (198).<br />
One depende:nt and one independent variable..<br />
r1any<br />
physical situations can be described by<br />
y=a+·bx<br />
(C-l<br />
Hhere y is a dependent variable and x is an independent<br />
variable.<br />
If several sets <strong>of</strong> data <strong>of</strong> Yi versus the corresponding<br />
xi are taken and plotted, the 1l1east squares lt line<br />
through the data can be expressed<br />
(C-2<br />
v-Jhere the 1\ over the y differentiates betl..reen the predicted<br />
A<br />
y, y, and the measured Y, Yi-<br />
It has been established that the parameters ,_ a and b,
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