Mathematical Modeling of the Thermal State of an Isothermal Element with Account of the Radiant Heat Transfer Between Parts of a Spacecraft

Abstract

A. V. Paleshkin, V. V. Terent′ev, UDC 629.78 and S. O. FirsyukA methodological approach to determination of the thermal state at a point on the surface of an isothermal element of a small spacecraft has been developed. A mathematical model of heat transfer between surfaces of intricate geometric confi guration has been described. In this model, account was taken of the external fi eld of radiant fl uxes and of the differentiated mutual infl uence of the surfaces. An algorithm for calculation of the distribution of the density of the radiation absorbed by surface elements of the object under study has been proposed. The temperature fi eld on the lateral surface of the spacecraft exposed to sunlight and on its shady side has been calculated. By determining the thermal state of magnetic controls of the orientation system as an example, the authors have assessed the contribution of the radiation coming from the solar-cell panels and from the spacecraft surface.The most diffi cult thing about mathematical modeling of heat transfer of a nonhermetic spacecraft (sp) is to determine the external and internal radiant heat transfer. In engineering practice, there is a great need for a universal and rather userfriendly model of external and internal radiant heat transfer of a spacecraft. Considering the exterior and interior surfaces of the spacecraft as an aggregate of a fi nite number of isothermal elements, we determine the density of the radiant fl ux incident on each of these elements under the following conditions:(1) the spacecraft can be in an assigned fi eld of radiant fl uxes coming from the sun and, if the craft is on a low circumplanetary orbit, from the planet; (2) the spacecraft surfaces in heat transfer can have an intricate geometric confi guration, as a result of which there is a possibility for mutual occultation of some surfaces from the radiation of external sources of radiant fl uxes and from the radiation of the surfaces of the spacecraft itself; (3) within each isothermal element (portion of the spacecraft surface), the radiation characteristics of the surface must be uniform.The problem of radiant heat transfer was solved under the following simplifying assumptions:(1) the surfaces taking part in the heat transfer are diffuse-type, i.e., the directed emissivity factor and directed absorptivity of these surfaces, do not depend on the direction; (2) the surfaces are gray in two characteristic spectral ranges: in the range of wavelengths from 0.2 to 2 μm, where practically all the energy of solar radiation is concentrated, and in the range from 5 to 50 μm, in which there is a release of most of the energy of self-radiation of bodies having a moderate temperature at the level of 200-500 K; (3) within each portion of subdivision of the spacecraft surface into isothermal elements, the density of the incident radiation fl ux is uniform on the portion′s surface.

Thermal state simulation of radioelectronic components as a part of space vehicle with regard to internal heat and external heat exchange

“…The original formulation of the problem comes from the need to performance adjusted check of magnetic executive body control unit, which can be installed on the non-hermetic spacecraft discussed in [1]. However, taking into account the concept of a model experiment described in [5], it is necessary to simplify the investigated element to the sample or model, which could be produced and tested on the available research bench.…”

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Numerical Study of Heat Transfer in Extended Surfaceswith Mutual Radiation Between Parallel Fins

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