temperature. The tube outer surface was taken to have an emissivity of 0. 9 (e. g. white paint). Three values, 0.1, 0.4 and 1.0, were used for the emissivity of the inner wall, and as expected, the higher the emissivity of the inner wall, the lower the maximum temperature This is due to the increased thermal communication between the hot bottom and the cool top afforded by the higher inner wall emissivity. Figure 3. 3-15 shows the temperature difference between the bottom and top of the tube for the three interior emissivities. These temperature differences induce bending stresses within the tubes. To sustain these induced stresses, the tube wall must have a minimum thickness. Based on Fig. 6 of Ref 22, Fig. 3. 3-16 was generated. It is apparent from this figure that stresses induced in aluminum are considerable and that the required tube wall thickness would have to be an order of magnitude greater than that required for a graphite/epoxy tube. Furthermore, the need to paint the inside of aluminum tubes black is obvious, otherwise the required tube wall thickness will lead to an excessively heavy beam. For example, a tube diameter of 0.1 meter requires a minimum tube wall thickness of 1 mm (0.039 inch) to sustain the induced bending stress associated with a temperature difference of 235° K. Painting the inside surface black will reduce the required thickness to 0.43 mm (0.017 inch), a greater than 50% reduction in weight. An alternate approach to painting the inside of the tubes black is to manufacture the tubes with holes in the walls. This may prove even more effective than the black paint in reducing the maximum temperature and temperature gradient. A review of Fig. 3. 3-14 shows that neither aluminum nor graphite/epoxy can be used in a tubular geometry in locations where the effective surface temperature is greater than 500° K because the maximum working temperature of these materials will be exceeded. Insulating the bottom half of the tube with layers of aluminized Kapton will lower the temperature sufficiently so that they can be used. Note, however, that the temperature gradient will not be significantly reduced. This is apparent from Fig. 3.3-15 which shows the temperature difference to be a weak function of effective antenna temperature. (Insulating the bottom half of the tube can be viewed as reducing the effective antenna temperature). Wrapping the entire tube with insulation will result in smaller temperature gradients but higher temperatures. In conclusion, a tube is considered a poor geometry for a structural member that is parallel to the antenna surface due to the high temperature and gradient that will exist within the tube.
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