A new analytical model for the conduction shape factor of annulus sectors

Abstract

Heat transfer devices, such as heat pipes, vapor chambers, thermosiphons, microchannel heat sinks, and Peltier cooling plates, rely on two-dimensional steady heat conduction to thermally manage telecommunications, aerospace, and microelectronics heat-generating components. The conduction shape factor can evaluate these devices’ two-dimensional steady heat conduction. The geometry of the device’s annulus and its mechanical attachment to the heat-generating component can vary. Given the prominence of single-sided heating and cooling, the two-dimensional heat conduction is commonly through an annulus sector. For the first time, an analytical model is developed to predict the conduction shape factor of annulus sectors. The present model is an extension of the previously developed equivalent concentric circular annulus model and applies the equivalent concentric circular annulus sector. The model is validated with results from finite element modeling for parametric boundary geometries, capturing most of the data across a variety of sectors within a relative difference of 10%. The present model provides a simple, closed-form analytical solution for the shape factor of an annulus sector formed between concentric arbitrarily shaped isothermal boundaries. More importantly, it provides a unified platform for designing and optimizing novel heat transfer devices.