Near-Field Radiative Energy Exchange Analysis of Nanospheres and Nanorods: Space Waste Heat Recovery Device Design

Abstract

In the present study, a theoretical method for sphere-to-sphere radiative heat exchange is implemented for silica, lithium fluoride, and arsenic triselenide nanospheres of equal and unequal radii. The method is extended to approximate a sphere-to-plane geometric configuration via an asymptotic method. The asymptotic method calls for an iterative process by which the radiative exchange is continuously calculated up to convergence as the radii of one microsphere is increased. These results are compared to previously published theoretical approximations and experimental data. A theoretical method for cylinder-to-cylinder radiative heat exchange is formulated. The method utilizes a modified version of the numerical method for near-field sphere-to-sphere radiative exchange. Modifications were made to the numerical procedure to make it applicable to cylindrical geometry of nanorods. Nanorods investigated had length to diameter ratios of 3: I and 7:1. The heat exchange of nanorods is plotted vs. gap to assess the impact of near-field radiative transfer as gap decreases. Graphical results of energy vs. nanorod radii are also presented. A nanorod-to-plane configuration is estimated utilizing a nanorod asymptotic ii method. The nanorod-to-nanorod method approximates a nanorod-to-plane geometric configuration when one nanorod radii is held constant, and the second nanorod radii is iteratively increased until the corresponding radiative exchange converges. A theoretical method for cylinder-to-cylinder radiative heat exchange is formulated by utilizing a sphere approximation method. The sphere approximation method calls for dividing the cylinders into smaller connected spheres and applying a previously published numerical method for near-field sphere-to-sphere radiative exchange. The overall radiative power exchange is obtained by an additive ray tracing assumption. These results are compared to results produced by a rigorous cylinder-to-cylinder radiative heat exchange method. The heat exchange of nanorods is plotted vs. gap to assess the impact of near-field radiative transfer as gap decreases. The unit sphere method is applied to nanorod configurations having length to diameter ratios of 3: 1, 5: 1, 7: 1. Graphical results of energy vs. nanorod radii are presented. A nanoradii/gap dimensionless relationship caused by geometric effects is found and related to power for nanorods of different aspect ratios and temperatures. A V -shaped configuration is considered with the results plotted for heat exchange vs. angle. An assessment of the number of spheres required to produce an accurate approximation of the V -shaped configuration of nanorods is presented. An error analysis of this method based on a ray blocking assumption from neighboring spheres is discussed. An analysis is presented of a new device that utilizes near-field radiative heat transfer incorporated with pyroelectric materials to convert spacecraft waste heat to electrical energy. A background of pyroelectric material devices is presented to show the background as applied to this application. Near-field plane-to-plane radiative heat exchange is implemented for calculation of the near-field radiative heat exchange within the device. The numerical method is iii based upon an asymptotic approximation shown in previous work for sphere-to-sphere. One sphere is iteratively increased with the radiative heat exchange continuously calculated until convergence, whereby, the geometric configuration approaches plane-to-sphere. By superimposing this method on multiple spheres, the plane-to-plane approximation is achieved. This procedure is applied for silica and lithium fluoride coated planes. Near-field radiative heat transfer results expected in the spacecraft device are presented.