On the Theoretical Approximation of Radiant Grey Body Transfer in Concentric Cylindrical Clock Geometries

摘要

In precise time systems, thermal effects are generally agreed to be a non-negligible contributor to frequency instabilities. Moreover, in atomic standards wherein a mechanical resonant cavity is employed in the acquisition of the atomic transition signal, thermal expansion of the mechanical cavity is known to lead to frequency drift. Hence, mitigation of thermal effects is crucial in ensuring frequency stability in timing systems. Typically, the impact of thermal effects is suppressed in frequency standards through the implementation of active thermal control systems. Many frequency standards include vacuum sealed physics packages which incorporate features to mitigate both convective and conductive heat transfer. However, this mitigation of convective and conductive heat transfer inadvertently results in the elevation of radiant heat transfer as an important thermal transfer mode. Furthermore, due to the popularity of cylindrical mechanical structures in atomic standards and OCXOs, this radiant heat exchange typically takes place between geometric surfaces which can be described as concentric cylinders. To date, no full theoretical treatment of cylindrical, grey body radiant heat transfer exists in the literature. However, a full theoretical model of spherical, diffuse grey body radiant transfer is available. This paper evaluates the suitability of this theoretical model for the task of describing radiant heat transfer between the cylindrical geometries found in atomic clocks. This generalized cylindrical radiant transfer approximation is evaluated via a parametric study utilizing Finite Element Analysis (FEA) simulation software. This study evaluates the influence of four variables of interest: total surface area, view factor, emissivity, and aspect ratio.