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This paper presents the derivation of the equations for circumferential, longitudinal and radial heat transfer conductance for a thin shell toroid or a segment of the toroid. A thin shell toroid is one in which the radius to thickness ratio is greater than 10. The equations for the surface area of a toroid or of a toroidal segment will also be derived along with the equation to determine the location of the centroid. The surface area is needed to determine the radial conductance in the toroid or toroidal segment and the centroid is needed to determine the heat transfer center of the toroid or toroidal segment for circumferential and longitudinal conductance. These equations can be used to obtain more accurate results for conductive heat transfer in toroid which is a curved spacecraft components. A comparison will be made (1) using the equations derived in this paper which takes into account the curvature of the toroid (true geometry) and (2) using flat plates to simulate the toroid.

Candidate Aeroshell Test models composed of a quasi-isotropic Carbon/Carbon(C/C) front face sheet (F/S), eggcrate core, C/C back F/S, Carbon Aerogel insulation, C/C radiation shield and the C/C close-out were constructed based on the analytical temperature predictions presented in Part One of this work[1]. The analytical results obtained for a simulated Mars entry of a 2.9 meter diameter cone shaped Carbon-Carbon Aeroshell demonstrated the feasibility of the design. These results showed that the maximum temperature the front F/S reached during the decent was 1752 °C with the resulting rear temperature reaching 326 °C in the thermal model. Part Two of this work documents the thermal modeling and correlation for the Mars Aeroshell test sample and fixture. A finite difference, SINDA/G, thermal math model of the test fixture and sample was generated and correlated to data from an arc jet test conducted at the NASA Ames Research Center's interactive heating facility.

The deployment and curing of multi-layer film structures for inflatable and large Gossamer-type space structures requires accurate modeling of the temperature distributions within and among the different layers of the structure. The Sinda Temperature Translator (STT) was developed to specifically provide the application of accurate thermal load profiles on each component of thin film multi-layer space inflatable structures during the performance of multidiscipline analyses. STT provides a methodology to accurately map the temperatures obtained during transient thermal orbital analyses (finite difference methods) to structural finite element analyses (FEA) models. The derivation of the equations are for the translation of temperatures from the thermal models such as SINDA/G, which places the temperatures at the centroid of the elements, to traditional structural models, such as Cosmos/M and NASTRAN that places the temperatures at the corners of the element.

This paper presents the derivation of the equations for circumferential, longitudinal and radial heat transfer conductance for a right circular thin shell parabola or a segment of the parabola. A thin shell parabola is one in which the radius to thickness ratio is greater than 10. The equations for the surface area of a parabola or of a parabolic segment will also be derived along with the equation to determine the location of the Centroid. The surface area is needed to determine the radial conductance in the parabola or parabolic segment and the Centroid is needed to determine the heat transfer center of the parabola or parabolic segment for circumferential and longitudinal conductance. These equations can be used to obtain more accurate results for conductive heat transfer in parabola which is a curved spacecraft components.