Conduction Shape Factor Models for Three-Dimensional Enclosures

Analytical models are presented for conduction shape factors for three-dimensional regions formed between an isothermal, arbitrarily shaped body and its concentric, arbitrarily shaped surrounding enclosure. The model is based on the exact solution for the concentric spheres, and two methods are developed to predict the effective gap spacing. The models are validated using existing numerical data from the literature and data from simulations performed using a commercial computational fluid dynamics software package. The models are shown to be in excellent agreement with the data for all enclosures with geometrically similar boundary shape, within 3% rms. For enclosures formed between different boundary shapes, the models are shown to be accurate within 5% rms when the minimum aspect ratio, that is, the smallest outer boundary dimension over the largest inner dimension, is greater than 1.5.