Conduction Shape Factor Models for Hollow Cylinders with Non-Uniform Gap Spacing

Ananalytical conduction shape factormodel is developed for the two-dimensional annular region formed between concentric isothermal cylinders in which the inner and outer boundaries have similar or different shapes. Themodel is based on the equivalent circular annulus with amodified independent parameter to account for local variations in the gap thickness. Validation of the model is performed using existing numerical data and analytical expressions from the literature for various geometries, includingpolygonal and rectangular cylinderswith a circular hole and the circular cylinder with a polygonal hole. The root-mean-square difference between the data and themodel is less than 5 % in all cases. Nomenclature A = cross-sectional area, m2 A? = dimensionless gap thickness, Ap =Pi A0 = modified dimensionless gap thickness d = diameter, m L = general characteristic length, m N = number of polygon sides n = combination parameter P = perimeter, m r = radius, m s = side length, m S = conduction shape factor (per unit length) S?L = dimensionless shape factor, SL=Pi = apothem, minimum radial dimension of a polygon, m = gap spacing, m Subscripts e = effective i = inner body o = outer bod