Modeling Transient Conduction in Enclosed Regions Between Isothermal Boundaries of Arbitrary Shape

Analytical models are developed to predict dimensionless heat flow rate for transient conduction in the doubly connected region formed between an arbitrarily shaped, isothermal inner body and its surrounding isothermal enclosure. This modeling procedure is based on limiting cases and trends identified in the exact solution for the concentric spheres. Asymptotic solutions for the limiting cases of small and large relative domain size, as well as for short and long times, are combined to provide comprehensive models applicable to the full range of the independent parameters. Validation of the models by the spherical enclosure solution and numerical data for the concentric cubes has shown excellent agreement between the model and the data, within less than a 3% rms difference for most cases.