A simple and accurate model for conduction shape factor of hollow cylinders

One of the common and practical ways to calculate steady conduction heat flow in an enclosure between two surfaces with constant temperatures is to use the concept of conduction shape factor (CSF). The major advantage of using this parameter is that it depends only on the geometrical characteristics of the domain. Indeed, CSF is defined as the ratio of a heat-transfer-area to a heat-transfer-length. Based on this definition, in the present study, a simple and accurate model is proposed to calculate the CSF of hollow prismatic cylinders whose inner and outer cross-sections can be either n-sided regular polygons or circles. For this purpose, an integral averaging technique is employed to compute the heat-transfer-length. Moreover, a weighted average method between logarithmic and geometric means is used to estimate the heat-transfer-area. In order to evaluate the accuracy and reliability of the proposed model, an in-house computational code based on the finite-volume approach has been developed to predict the CSF for the studied configurations. The provided code has been validated against the exact analytical expressions as well as the available experimental data. The comparison between the results of the current model, available data, and the present numerical results shows that the suggested model is greatly reliable and estimates the CSF of the considered hollow cylinders very accurately. The average of absolute relative differences between the results of the presented model and the numerical data is less than 7.1% for all cases. •A simple model is proposed to calculate conduction shape factor of hollow cylinders.•Two methods are suggested to find the heat-transfer-length and heat-transfer-area.•The model is verified against the results of an in-house computational code.•The maximum deviation is 13.6% and relates to a circular bar with a triangular hole.•The average of absolute relative differences is less than 7.1% for all cases.