Shape Factor: Polygon-In-Polygon

M.M. Yovanovich

SHPPOLYPOLY.MWS

Shape factor for two-dimensional region bounded by isothermal regular polygons of sides.

The inscribed circles to the inner and outer polygons are denoted as and .

As the number of sides goes to infinity, the shape factor expression goes to the well-known expression for a region bounded by two isothermal circles, i.e. .

> restart:

General Expression for Sides.

> S:= 4*Pi*L/ln(1 + ((D/d)^2 - 1)/(N/Pi*tan(Pi/N)));

Shape Factor for Triangle-In-Triangle.

> S3:= subs(N=3, S);

Shape Factor for Square-In-Square.

> S4:= subs(N=4,S);

Calculation of Shape Factor for Square-In-Square for .

> Ssqsq_vals:= evalf([seq(subs(L=1, D=j*d, S4), j=2..10)], 4);