c005ffa1-4c53-4e23-accf-dc869bfffff0 2 4 5 false false 0 decimal

&[DATE] &[TIME] - &[FILENAME]

Fitting function to data -many independent variables, -linear in parameters

//Independent

//Dependent

Re 49000686008480034200229001321931518346 122.9 54 84.6 12491021465 54.8 161 mat :

Pr 2.3 2.28 2.27 2.32 2.36 246247251273151815901521 107.4 1864141302161 mat :

Nu 277348421223177 114.8 95.9 68.3 49.1 56 39.9 47 94.2 99.9 83.1 35.9 161 mat :

//The expression we are interested in //Pr,Re-independent variables, b-vector of unknown parameters

Nu ln b 1 el b 2 el Re ln * + b 3 el Pr ln * + ≡

//Transforming original dependent variable

i 1 Nu length range y i el Nu i el ln : for

//Matrix of independent variables

xx Re Pr augment :

//from the function above we construct a vector function //with vector argument

x φ 1 x 1 el ln x 2 el ln 31 mat :

n Nu length :

k x φ length :

n 16

k 3

//X-matrix, matrix of experiment

j 1 k range i 1 n range X i j el xx i 1 el xx i 2 el 21 mat φ j el : for for

Φ X transpose X * :

d X transpose y * :

b Φ 1 -^eval d * :

b 0.412 - 0.5395 0.2454 31 mat

//Unknown parameters //found in the least-square sense

//Calculated Nu-values

x Nucalc e b x φ *^eval :

i 1 Nu length range Nuc i el xx i 1 el xx i 2 el 21 mat Nucalc : for

Calculated

Given

Plotting

Nuc 275.6408 329.8029 369.3706 227.513 184.0116 123.4589 102.3223 74.8695 61.4754 53.5773 34.7711 43.8216 97.7416 100.3158 79.861 33.3711 161 mat

Nu 277348421223177 114.8 95.9 68.3 49.1 56 39.9 47 94.2 99.9 83.1 35.9 161 mat

NuNu Nu Nu augment :

NuNu NuNu 1 csort eval :

NuNuc Nu Nuc augment :

NuNuc NuNuc 1 csort eval :

NuNu NuNuc 2 1 sys

Data

Fitted

Fitting function to data -many independent variables, -nonlinear on parameters

Nu e b 1 el b 2 el Re ln * + b 3 el Pr ln * +^≡

UNSOLVED !