A research study is presented that examines laminar natural convection heat transfer in the arbitrarily shaped region formed between an isothermal heated body and its surrounding enclosure. The goal of the study is to develop a modelling procedure to predict the average heat transfer rate in these types of enclosures.

Experimental tests are conducted for seventeen different enclosure configurations, including the concentric spheres and cubes, as well as different combinations inner body and outer enclosure shapes. Through the use of the transient test method in a reduced pressure environment, measurements are performed for a wide range of Rayleigh number, from laminar boundary layer convection to the diffusive limit.

A modelling procedure is developed that predicts the average heat transfer rate for the arbitrarily shaped enclosure formed between concentric inner and outer body shapes. The model is based on a linear superposition of conduction and convection solutions, where the convective component is determined based on a combination of two limiting cases, laminar boundary layer convection and transition flow in the vertical cavity. Data from the experimental test program is used to validate the model for a wide range of Rayleigh number:​ from 10 ≤ R_{Ai} ≤ 3 × 10⁵ for d_o/d_i = 5 concentric spheres to 1000 ≤ Ra_{Ai} ≤ 1 × 10⁷ for d_o/d_i = 1 .5 concentric spheres. The modelling procedure is also validated using data measured over similar ranges of Rayleigh numbers for other boundary shape combinations. The model accurately predicts the experimental data with an RMS difference of 2–7 % for all enclosure configurations and test conditions and is also in good agreement with the data available in the literature.