Shape Factor: Square-in-Square

M.M. Yovanovich

SHPSQSQ2.MWS

Shape factor for a square cylinder of sides inside a larger square cylinder of sides .

The length of the cylinders is which is much larger than .

> restart:

Two-Rule Relation.

> S:= 4*Pi*L/ln(1 + Pi/4*((beta/alpha)^2 - 1));

Two Correlation Equations Based on Analog Experiments.

For .

> S1:= 2*Pi*L/(0.93*ln(beta/alpha) - 0.0502);

For .

> S2:= 2*Pi*L/(0.785*ln(beta/alpha));

Comparison of Correlation Equations at .

> Sval:= evalf(subs(L = 1, beta = 1.4*alpha, S), 5);

> S1val:= evalf(subs(L = 1, beta = 1.4*alpha, S1), 5);

> S2val:= evalf(subs(L = 1, beta = 1.4*alpha, S2), 5);

The two expressions obtained from analog experiments give values which differ by approximately . The anlog values are approximately greater than the two-rule value which is within of a theoretical value.