Page 524 - Modelling in Transport Phenomena A Conceptual Approach

504 APPENDIX A. MATHEMATICAL PRELIMINARIES

Partial differentiation of EQ. (A.6-13) gives

aCxq+bCxi+cN=Cyi (A. 6- 17)
i i i
These equations may then be solved for the constants a, b, and c.
If the equation is of the form
y=axn+b (A.6-18)

then the parameters a, b, and n can be determined as follows:

1. Least squares values of a and b can be found for a series of chosen values of
n.

2. The sum of the squares of the deviations can then be calculated and plotted
versus n to find the minimum and, hence, the best value of n. The corre-
sponding values of a and b are readily found by plotting the calculated values
versus n and interpolating.

Alternatively, Eq. (A.6-18) might first be arranged as
log(y - b) = nlogx + loga (A.6-19)

and least squares values of n and loga are determined for a series of chosen values
of b, etc.

Example A.3l It is proposed to correlate the data for forced convection heat
transfer to a sphere in tern of the equation
Nu=2+aRen

The following values were obtained from McAdams (1954) for heat transfer from
air to spheres by forced convection:

Re Nu
10 2.8
100 6.3
1000 19.0

'This problem is taken from Churchill (1974).